Formula

📁 Source: Mathlib/AlgebraicGeometry/EllipticCurve/Jacobian/Formula.lean

Statistics

Metric	Count
Definitions addU, addX, addXYZ, addY, addZ, dblU, dblX, dblXYZ, dblY, dblZ, negAddY, negDblY, negY	13
Theorems Y_eq_iff', Y_eq_negY_of_Y_eq, Y_eq_of_Y_ne, Y_eq_of_Y_ne', Y_ne_negY_of_Y_ne, Y_ne_negY_of_Y_ne', Y_sub_Y_add_Y_sub_negY, Y_sub_Y_mul_Y_sub_negY, addU_ne_zero_of_Y_ne, addU_of_Z_eq_zero_left, addU_of_Z_eq_zero_right, addU_smul, addXYZ_X, addXYZ_Y, addXYZ_Z, addXYZ_of_X_eq, addXYZ_of_Z_eq_zero_left, addXYZ_of_Z_eq_zero_right, addXYZ_of_Z_ne_zero, addXYZ_self, addXYZ_smul, addX_eq, addX_eq', addX_of_X_eq, addX_of_X_eq', addX_of_Z_eq_zero_left, addX_of_Z_eq_zero_right, addX_of_Z_ne_zero, addX_self, addX_smul, addY_of_X_eq, addY_of_X_eq', addY_of_Z_eq_zero_left, addY_of_Z_eq_zero_right, addY_of_Z_ne_zero, addY_self, addY_smul, addZ_ne_zero_of_X_ne, addZ_of_X_eq, addZ_of_Z_eq_zero_left, addZ_of_Z_eq_zero_right, addZ_self, addZ_smul, baseChange_addX, baseChange_addXYZ, baseChange_addY, baseChange_dblU, baseChange_dblX, baseChange_dblXYZ, baseChange_dblY, baseChange_dblZ, baseChange_negAddY, baseChange_negDblY, baseChange_negY, dblU_eq, dblU_ne_zero_of_Y_eq, dblU_of_Z_eq_zero, dblU_smul, dblXYZ_X, dblXYZ_Y, dblXYZ_Z, dblXYZ_of_Y_eq, dblXYZ_of_Y_eq', dblXYZ_of_Z_eq_zero, dblXYZ_of_Z_ne_zero, dblXYZ_smul, dblX_of_Y_eq, dblX_of_Z_eq_zero, dblX_of_Z_ne_zero, dblX_smul, dblY_of_Y_eq, dblY_of_Z_eq_zero, dblY_of_Z_ne_zero, dblY_smul, dblZ_ne_zero_of_Y_ne, dblZ_ne_zero_of_Y_ne', dblZ_of_Y_eq, dblZ_of_Z_eq_zero, dblZ_smul, isUnit_addU_of_Y_ne, isUnit_addZ_of_X_ne, isUnit_dblU_of_Y_eq, isUnit_dblZ_of_Y_ne, isUnit_dblZ_of_Y_ne', map_addU, map_addX, map_addXYZ, map_addY, map_addZ, map_dblU, map_dblX, map_dblXYZ, map_dblY, map_dblZ, map_negAddY, map_negDblY, map_negY, negAddY_eq, negAddY_eq', negAddY_of_X_eq, negAddY_of_X_eq', negAddY_of_Z_eq_zero_left, negAddY_of_Z_eq_zero_right, negAddY_of_Z_ne_zero, negAddY_self, negAddY_smul, negDblY_of_Y_eq, negDblY_of_Z_eq_zero, negDblY_of_Z_ne_zero, negDblY_smul, negY_eq, negY_of_Z_eq_zero, negY_of_Z_ne_zero, negY_smul, nonsingular_iff_of_Y_eq_negY	115
Total	128

WeierstrassCurve.Jacobian

Definitions

Name	Category	Theorems
addU 📖	CompOp	10 math math: addXYZ_of_X_eq, negAddY_of_X_eq, addU_of_Z_eq_zero_right, addX_of_X_eq, addU_of_Z_eq_zero_left, addY_of_X_eq, addU_smul, map_addU, add_of_Y_ne, isUnit_addU_of_Y_ne
addX 📖	CompOp	15 math math: map_addX, addXYZ_X, negAddY_eq, baseChange_addX, addX_of_Z_ne_zero, addX_eq', addX_of_X_eq, addX_eq, addX_smul, addX_self, negAddY_eq', addX_of_X_eq', addX_neg, addX_of_Z_eq_zero_right, addX_of_Z_eq_zero_left
addXYZ 📖	CompOp	13 math math: addXYZ_of_Z_ne_zero, addXYZ_self, addXYZ_X, addXYZ_Z, addXYZ_of_X_eq, baseChange_addXYZ, addXYZ_smul, addXYZ_of_Z_eq_zero_right, addXYZ_neg, add_of_not_equiv, addXYZ_Y, addXYZ_of_Z_eq_zero_left, map_addXYZ
addY 📖	CompOp	11 math math: addY_neg, addY_smul, addY_of_Z_ne_zero, map_addY, addY_of_Z_eq_zero_right, addY_of_X_eq', addY_of_X_eq, addY_of_Z_eq_zero_left, addXYZ_Y, baseChange_addY, addY_self
addZ 📖	CompOp	18 math math: addXYZ_of_Z_ne_zero, addXYZ_Z, negAddY_eq, addZ_of_Z_eq_zero_right, addZ_smul, addZ_neg, addX_of_Z_ne_zero, addX_eq', map_addZ, addY_of_Z_ne_zero, addZ_of_Z_eq_zero_left, addZ_of_X_eq, add_of_X_ne, addX_eq, negAddY_of_Z_ne_zero, addZ_self, negAddY_eq', isUnit_addZ_of_X_ne
dblU 📖	CompOp	12 math math: dblX_of_Y_eq, add_of_Y_eq, baseChange_dblU, dblU_eq, dblXYZ_of_Y_eq', negDblY_of_Y_eq, dblY_of_Y_eq, dblU_smul, map_dblU, dblU_of_Z_eq_zero, dblXYZ_of_Y_eq, isUnit_dblU_of_Y_eq
dblX 📖	CompOp	7 math math: dblX_of_Y_eq, dblX_of_Z_ne_zero, map_dblX, dblXYZ_X, baseChange_dblX, dblX_smul, dblX_of_Z_eq_zero
dblXYZ 📖	CompOp	13 math math: dblXYZ_Z, dblXYZ_X, dblXYZ_of_Z_ne_zero, map_dblXYZ, add_of_eq, add_self, dblXYZ_of_Y_eq', add_of_equiv, baseChange_dblXYZ, dblXYZ_Y, dblXYZ_of_Z_eq_zero, dblXYZ_smul, dblXYZ_of_Y_eq
dblY 📖	CompOp	7 math math: dblY_of_Z_eq_zero, baseChange_dblY, dblY_of_Z_ne_zero, dblY_smul, dblY_of_Y_eq, dblXYZ_Y, map_dblY
dblZ 📖	CompOp	17 math math: dblXYZ_Z, add_of_Y_ne', dblX_of_Z_ne_zero, addY_neg, negAddY_neg, map_dblZ, dblZ_smul, dblXYZ_of_Z_ne_zero, dblY_of_Z_ne_zero, addXYZ_neg, dblZ_of_Z_eq_zero, isUnit_dblZ_of_Y_ne', baseChange_dblZ, dblZ_of_Y_eq, negDblY_of_Z_ne_zero, isUnit_dblZ_of_Y_ne, addX_neg
negAddY 📖	CompOp	12 math math: negAddY_of_Z_eq_zero_left, negAddY_eq, negAddY_of_Z_eq_zero_right, negAddY_of_X_eq, negAddY_neg, negAddY_of_X_eq', negAddY_smul, negAddY_of_Z_ne_zero, map_negAddY, negAddY_self, negAddY_eq', baseChange_negAddY
negDblY 📖	CompOp	6 math math: map_negDblY, baseChange_negDblY, negDblY_of_Z_eq_zero, negDblY_smul, negDblY_of_Y_eq, negDblY_of_Z_ne_zero
negY 📖	CompOp	13 math math: negAddY_of_Z_eq_zero_left, negY_eq, negY_of_Z_ne_zero, negAddY_of_Z_eq_zero_right, map_negY, Y_eq_of_Y_ne, Y_sub_Y_add_Y_sub_negY, Y_eq_iff', Y_sub_Y_mul_Y_sub_negY, neg_Y, negY_smul, baseChange_negY, negY_of_Z_eq_zero

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
Y_eq_iff' 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing EuclideanDomain.toCommRing Field.toEuclideanDomain Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield negY DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing WeierstrassCurve.Affine.negY toAffine	—	div_eq_div_iff pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain negY_of_Z_ne_zero
Y_eq_negY_of_Y_eq 📖	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	—	—	mul_left_injective₀ IsCancelMulZero.toIsRightCancelMulZero NoZeroDivisors.to_isCancelMulZero pow_ne_zero isReduced_of_noZeroDivisors Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Y_sub_Y_add_Y_sub_negY Mathlib.Tactic.LinearCombination.eq_rearrange Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
Y_eq_of_Y_ne 📖	mathematical	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	negY	—	sub_eq_zero mul_eq_zero Y_sub_Y_mul_Y_sub_negY sub_ne_zero
Y_eq_of_Y_ne' 📖	—	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—	sub_eq_zero mul_eq_zero Y_sub_Y_mul_Y_sub_negY sub_ne_zero
Y_ne_negY_of_Y_ne 📖	—	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—	mul_eq_zero Y_sub_Y_mul_Y_sub_negY sub_ne_zero_of_ne Mathlib.Tactic.Contrapose.contrapose₄ Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Y_sub_Y_add_Y_sub_negY Mathlib.Tactic.LinearCombination.mul_const_eq Mathlib.Tactic.LinearCombination.eq_rearrange Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
Y_ne_negY_of_Y_ne' 📖	—	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—	mul_eq_zero Y_sub_Y_mul_Y_sub_negY sub_ne_zero_of_ne Mathlib.Tactic.Contrapose.contrapose₄ Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Y_sub_Y_add_Y_sub_negY Mathlib.Tactic.LinearCombination.mul_const_eq Mathlib.Tactic.LinearCombination.eq_rearrange Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_add_gt
Y_sub_Y_add_Y_sub_negY 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Distrib.toAdd SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing negY	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq Mathlib.Tactic.LinearCombination.eq_rearrange negY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
Y_sub_Y_mul_Y_sub_negY 📖	mathematical	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing negY MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Mathlib.Tactic.LinearCombination.mul_const_eq equation_iff Mathlib.Tactic.LinearCombination.eq_rearrange negY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
addU_ne_zero_of_Y_ne 📖	—	—	—	—	neg_ne_zero div_ne_zero sub_ne_zero mul_ne_zero IsDomain.to_noZeroDivisors instIsDomain
addU_of_Z_eq_zero_left 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing EuclideanDomain.toCommRing Field.toEuclideanDomain	addU	—	addU.eq_1 MulZeroClass.zero_mul div_zero neg_zero
addU_of_Z_eq_zero_right 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing EuclideanDomain.toCommRing Field.toEuclideanDomain	addU	—	addU.eq_1 MulZeroClass.mul_zero div_zero neg_zero
addU_smul 📖	mathematical	—	addU instSMulForallFinOfNatNat EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	—	mul_neg Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq IsCancelMulZero.toIsLeftCancelMulZero instIsCancelMulZero Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul Mathlib.Tactic.FieldSimp.NF.div_eq_eval Mathlib.Tactic.FieldSimp.subst_sub Mathlib.Tactic.FieldSimp.NF.mul_eq_eval Mathlib.Tactic.FieldSimp.NF.pow_eq_eval Mathlib.Tactic.FieldSimp.NF.atom_eq_eval Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃ mul_one Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval one_mul Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div div_one Mathlib.Tactic.FieldSimp.NF.eval_cons Mathlib.Tactic.FieldSimp.zpow'_one Mathlib.Tactic.FieldSimp.zpow'_ofNat Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₁ Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁ Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃ Mathlib.Tactic.FieldSimp.NF.div_eq_eval₂ Mathlib.Tactic.FieldSimp.NF.one_div_eq_eval Mathlib.Tactic.FieldSimp.NF.cons_ne_zero one_ne_zero NeZero.one GroupWithZero.toNontrivial
addXYZ_X 📖	mathematical	—	addXYZ addX	—	—
addXYZ_Y 📖	mathematical	—	addXYZ addY	—	—
addXYZ_Z 📖	mathematical	—	addXYZ addZ	—	—
addXYZ_of_X_eq 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	addXYZ instSMulForallFinOfNatNat addU Matrix.vecCons AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Matrix.vecEmpty	—	addX_of_X_eq addY_of_X_eq addZ_of_X_eq mul_one MulZeroClass.mul_zero
addXYZ_of_Z_eq_zero_left 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addXYZ instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	addXYZ.eq_1 addX_of_Z_eq_zero_left addY_of_Z_eq_zero_left addZ_of_Z_eq_zero_left smul_fin3
addXYZ_of_Z_eq_zero_right 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addXYZ instSMulForallFinOfNatNat NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	addXYZ.eq_1 addX_of_Z_eq_zero_right addY_of_Z_eq_zero_right addZ_of_Z_eq_zero_right smul_fin3
addXYZ_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain	addXYZ instSMulForallFinOfNatNat addZ Matrix.vecCons WeierstrassCurve.Affine.addX toAffine DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield WeierstrassCurve.Affine.slope WeierstrassCurve.Affine.addY AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Matrix.vecEmpty	—	IsUnit.pow isUnit_addZ_of_X_ne addXYZ.eq_1 smul_fin3 addX_of_Z_ne_zero IsUnit.mul_div_cancel addY_of_Z_ne_zero mul_one
addXYZ_self 📖	mathematical	Equation	addXYZ Matrix.vecCons MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Matrix.vecEmpty	—	addXYZ.eq_1 addX_self addY_self addZ_self
addXYZ_smul 📖	mathematical	—	addXYZ instSMulForallFinOfNatNat Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	—	addXYZ.eq_1 addX_smul addY_smul addZ_smul smul_fin3 addXYZ_X addXYZ_Y addXYZ_Z
addX_eq 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain	addX DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield Distrib.toMul WeierstrassCurve.a₁ addZ WeierstrassCurve.a₂	—	addX_eq' mul_div_cancel_right₀ EuclideanDomain.toMulDivCancelClass pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain mul_ne_zero
addX_eq' 📖	mathematical	Equation	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing addX Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing Distrib.toAdd WeierstrassCurve.a₁ addZ WeierstrassCurve.a₂	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Mathlib.Tactic.LinearCombination.mul_const_eq equation_iff Mathlib.Tactic.LinearCombination.eq_rearrange addX.eq_1 addZ.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one
addX_of_X_eq 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	addX addU	—	addU.eq_1 neg_sq div_pow addX_of_X_eq' mul_div_cancel_right₀ EuclideanDomain.toMulDivCancelClass pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain mul_ne_zero
addX_of_X_eq' 📖	mathematical	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	addX SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing	—	addX_eq' addZ_of_X_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos
addX_of_Z_eq_zero_left 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addX Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	addX.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_zero
addX_of_Z_eq_zero_right 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addX Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing	—	addX.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit0 Mathlib.Meta.NormNum.one_natPow
addX_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing addX Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addZ WeierstrassCurve.Affine.addX toAffine WeierstrassCurve.Affine.slope	—	addX_eq addZ_ne_zero_of_X_ne
addX_self 📖	mathematical	Equation	addX MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	—	Mathlib.Tactic.LinearCombination.eq_of_eq Nat.instAtLeastTwoHAddOfNat AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq equation_iff Mathlib.Tactic.LinearCombination.eq_rearrange addX.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.mul_pf_right Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero
addX_smul 📖	mathematical	—	addX instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_gt
addY_of_X_eq 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	addY addU	—	addU.eq_1 neg_div div_pow addY_of_X_eq' mul_div_cancel_right₀ EuclideanDomain.toMulDivCancelClass pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain mul_ne_zero
addY_of_X_eq' 📖	mathematical	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	addY NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd negAddY_of_X_eq' Mathlib.Tactic.LinearCombination.eq_rearrange addY.eq_1 negY_eq addZ_of_X_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.cast_zero Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit1 Mathlib.Tactic.Ring.pow_one Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf
addY_of_Z_eq_zero_left 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addY Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	addY.eq_1 negY_eq negAddY_of_Z_eq_zero_left negY.eq_1 addX_of_Z_eq_zero_left addZ_of_Z_eq_zero_left Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.isInt_add Mathlib.Meta.NormNum.isNat_mul
addY_of_Z_eq_zero_right 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addY Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing	—	addY.eq_1 negY_eq negAddY_of_Z_eq_zero_right negY.eq_1 addX_of_Z_eq_zero_right addZ_of_Z_eq_zero_right Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit1 Mathlib.Meta.NormNum.one_natPow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.intPow_negOfNat_bit0 Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.isInt_add Mathlib.Meta.NormNum.isNat_mul
addY_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing addY Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addZ WeierstrassCurve.Affine.addY toAffine WeierstrassCurve.Affine.slope	—	addY.eq_1 negY_of_Z_ne_zero addZ_ne_zero_of_X_ne addX_of_Z_ne_zero negAddY_of_Z_ne_zero WeierstrassCurve.Affine.addY.eq_1
addY_self 📖	mathematical	Equation	addY MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	—	addY.eq_1 negY_eq addX_self negAddY_self addZ_self Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_zero Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_zero Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.pow_zero
addY_smul 📖	mathematical	—	addY instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	addX_smul negAddY_smul addZ_smul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add
addZ_ne_zero_of_X_ne 📖	—	—	—	—	sub_ne_zero
addZ_of_X_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	addZ MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass	—	addZ.eq_1 sub_self
addZ_of_Z_eq_zero_left 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addZ Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	addZ.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.IsNat.of_raw
addZ_of_Z_eq_zero_right 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	addZ Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing	—	addZ.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_zero Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_zero Mathlib.Tactic.Ring.cast_pos Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.mul_one
addZ_self 📖	mathematical	—	addZ MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	—	sub_self
addZ_smul 📖	mathematical	—	addZ instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add
baseChange_addX 📖	mathematical	—	addX WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_addX WeierstrassCurve.map_baseChange
baseChange_addXYZ 📖	mathematical	—	addXYZ WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_addXYZ WeierstrassCurve.map_baseChange
baseChange_addY 📖	mathematical	—	addY WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_addY WeierstrassCurve.map_baseChange
baseChange_dblU 📖	mathematical	—	dblU WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_dblU WeierstrassCurve.map_baseChange
baseChange_dblX 📖	mathematical	—	dblX WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_dblX WeierstrassCurve.map_baseChange
baseChange_dblXYZ 📖	mathematical	—	dblXYZ WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_dblXYZ WeierstrassCurve.map_baseChange
baseChange_dblY 📖	mathematical	—	dblY WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_dblY WeierstrassCurve.map_baseChange
baseChange_dblZ 📖	mathematical	—	dblZ WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_dblZ WeierstrassCurve.map_baseChange
baseChange_negAddY 📖	mathematical	—	negAddY WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_negAddY WeierstrassCurve.map_baseChange
baseChange_negDblY 📖	mathematical	—	negDblY WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_negDblY WeierstrassCurve.map_baseChange
baseChange_negY 📖	mathematical	—	negY WeierstrassCurve.toJacobian WeierstrassCurve.baseChange DFunLike.coe AlgHom CommRing.toCommSemiring CommSemiring.toSemiring AlgHom.funLike	—	AlgHomClass.toRingHomClass AlgHom.algHomClass RingHom.coe_coe map_negY WeierstrassCurve.map_baseChange
dblU_eq 📖	mathematical	—	dblU SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing WeierstrassCurve.a₁ Distrib.toAdd instOfNatAtLeastTwo AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Nat.instAtLeastTwoHAddOfNat Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring WeierstrassCurve.a₂ WeierstrassCurve.a₄	—	Nat.instAtLeastTwoHAddOfNat dblU.eq_1 eval_polynomialX
dblU_ne_zero_of_Y_eq 📖	—	Nonsingular EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield negY	—	—	nonsingular_iff_of_Y_eq_negY Y_eq_negY_of_Y_eq IsDomain.to_noZeroDivisors instIsDomain
dblU_of_Z_eq_zero 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	dblU Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing instOfNatAtLeastTwo AddMonoidWithOne.toNatCast AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne Nat.instAtLeastTwoHAddOfNat Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Nat.instAtLeastTwoHAddOfNat dblU_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.cast_zero Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.neg_congr
dblU_smul 📖	mathematical	—	dblU instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Nat.instAtLeastTwoHAddOfNat dblU_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.add_congr Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Meta.NormNum.isNat_mul Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_zero_add
dblXYZ_X 📖	mathematical	—	dblXYZ dblX	—	—
dblXYZ_Y 📖	mathematical	—	dblXYZ dblY	—	—
dblXYZ_Z 📖	mathematical	—	dblXYZ dblZ	—	—
dblXYZ_of_Y_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing EuclideanDomain.toCommRing Field.toEuclideanDomain Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield negY	dblXYZ instSMulForallFinOfNatNat dblU Matrix.vecCons AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Matrix.vecEmpty	—	dblXYZ_of_Y_eq' IsDomain.to_noZeroDivisors instIsDomain mul_one MulZeroClass.mul_zero
dblXYZ_of_Y_eq' 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	dblXYZ Matrix.vecCons dblU MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Matrix.vecEmpty	—	dblXYZ.eq_1 dblX_of_Y_eq dblY_of_Y_eq dblZ_of_Y_eq
dblXYZ_of_Z_eq_zero 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	dblXYZ instSMulForallFinOfNatNat Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Matrix.vecCons AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Matrix.vecEmpty	—	dblX_of_Z_eq_zero dblY_of_Z_eq_zero dblZ_of_Z_eq_zero mul_one MulZeroClass.mul_zero
dblXYZ_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	dblXYZ instSMulForallFinOfNatNat dblZ Matrix.vecCons WeierstrassCurve.Affine.addX toAffine DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing WeierstrassCurve.Affine.slope WeierstrassCurve.Affine.addY AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Matrix.vecEmpty	—	IsUnit.pow isUnit_dblZ_of_Y_ne' dblXYZ.eq_1 smul_fin3 dblX_of_Z_ne_zero IsUnit.mul_div_cancel dblY_of_Z_ne_zero mul_one
dblXYZ_smul 📖	mathematical	—	dblXYZ instSMulForallFinOfNatNat Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	dblXYZ.eq_1 dblX_smul dblY_smul dblZ_smul smul_fin3 dblXYZ_X dblXYZ_Y dblXYZ_Z
dblX_of_Y_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	dblX dblU	—	dblX.eq_1 Y_eq_negY_of_Y_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_one
dblX_of_Z_eq_zero 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	dblX Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.LinearCombination.eq_of_eq Nat.instAtLeastTwoHAddOfNat AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq equation_of_Z_eq_zero Mathlib.Tactic.LinearCombination.eq_rearrange dblX.eq_1 dblU_of_Z_eq_zero negY_of_Z_eq_zero Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit0 Mathlib.Meta.NormNum.natPow_one Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Meta.NormNum.isNat_pow Mathlib.Meta.NormNum.IsNatPowT.run Mathlib.Meta.NormNum.IsNatPowT.bit0 Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero
dblX_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing dblX dblZ WeierstrassCurve.Affine.addX toAffine WeierstrassCurve.Affine.slope	—	dblX.eq_1 dblZ.eq_1 X_eq_iff Nat.instAtLeastTwoHAddOfNat sub_ne_zero Y_ne_negY_of_Y_ne' IsDomain.to_noZeroDivisors instIsDomain
dblX_smul 📖	mathematical	—	dblX instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	dblU_smul negY_smul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Meta.NormNum.instAtLeastTwo
dblY_of_Y_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	dblY dblU	—	dblY.eq_1 negY_eq negDblY_of_Y_eq dblZ_of_Y_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit1 Mathlib.Meta.NormNum.one_natPow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.one_pow
dblY_of_Z_eq_zero 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	dblY Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	dblY.eq_1 negY_eq negDblY_of_Z_eq_zero dblZ_of_Z_eq_zero Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos
dblY_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing dblY dblZ WeierstrassCurve.Affine.addY toAffine WeierstrassCurve.Affine.slope	—	dblY.eq_1 negY_of_Z_ne_zero dblZ_ne_zero_of_Y_ne' IsDomain.to_noZeroDivisors instIsDomain dblX_of_Z_ne_zero negDblY_of_Z_ne_zero WeierstrassCurve.Affine.addY.eq_1
dblY_smul 📖	mathematical	—	dblY instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	dblX_smul negDblY_smul dblZ_smul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add
dblZ_ne_zero_of_Y_ne 📖	—	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—	mul_ne_zero sub_ne_zero Y_ne_negY_of_Y_ne
dblZ_ne_zero_of_Y_ne' 📖	—	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—	mul_ne_zero sub_ne_zero Y_ne_negY_of_Y_ne'
dblZ_of_Y_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	dblZ MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass	—	dblZ.eq_1 Y_eq_negY_of_Y_eq sub_self MulZeroClass.mul_zero
dblZ_of_Z_eq_zero 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	dblZ	—	dblZ.eq_1 MulZeroClass.zero_mul
dblZ_smul 📖	mathematical	—	dblZ instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	negY_smul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add
isUnit_addU_of_Y_ne 📖	mathematical	—	IsUnit MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addU	—	Ne.isUnit addU_ne_zero_of_Y_ne
isUnit_addZ_of_X_ne 📖	mathematical	—	IsUnit MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addZ EuclideanDomain.toCommRing Field.toEuclideanDomain	—	Ne.isUnit addZ_ne_zero_of_X_ne
isUnit_dblU_of_Y_eq 📖	mathematical	Nonsingular EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield negY	IsUnit dblU	—	Ne.isUnit dblU_ne_zero_of_Y_eq
isUnit_dblZ_of_Y_ne 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	IsUnit dblZ	—	Ne.isUnit dblZ_ne_zero_of_Y_ne IsDomain.to_noZeroDivisors instIsDomain
isUnit_dblZ_of_Y_ne' 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	IsUnit dblZ	—	Ne.isUnit dblZ_ne_zero_of_Y_ne' IsDomain.to_noZeroDivisors instIsDomain
map_addU 📖	mathematical	—	addU DFunLike.coe RingHom Semiring.toNonAssocSemiring DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield RingHom.instFunLike	—	map_neg RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_div₀ RingHomClass.toMonoidWithZeroHomClass map_sub map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass
map_addX 📖	mathematical	—	addX WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_add AddMonoidHomClass.toAddHomClass RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_sub map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass map_ofNat
map_addXYZ 📖	mathematical	—	addXYZ WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_addX map_addY map_addZ comp_fin3
map_addY 📖	mathematical	—	addY WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_addX map_negAddY map_addZ map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_neg map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_addZ 📖	mathematical	—	addZ DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_dblU 📖	mathematical	—	dblU WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	Nat.instAtLeastTwoHAddOfNat dblU_eq map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_add AddMonoidHomClass.toAddHomClass map_ofNat map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_dblX 📖	mathematical	—	dblX WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_dblU map_negY map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_ofNat
map_dblXYZ 📖	mathematical	—	dblXYZ WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_dblX map_dblY map_dblZ comp_fin3
map_dblY 📖	mathematical	—	dblY WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_dblX map_negDblY map_dblZ map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_neg map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_dblZ 📖	mathematical	—	dblZ WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass RingHom.instRingHomClass map_sub RingHomClass.toAddMonoidHomClass map_neg map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_negAddY 📖	mathematical	—	negAddY WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_add AddMonoidHomClass.toAddHomClass RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_sub map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_neg map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass map_ofNat
map_negDblY 📖	mathematical	—	negDblY WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_dblU map_dblX map_negY neg_mul map_add AddMonoidHomClass.toAddHomClass RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_neg map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_sub map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
map_negY 📖	mathematical	—	negY WeierstrassCurve.toJacobian WeierstrassCurve.map DFunLike.coe RingHom Semiring.toNonAssocSemiring CommSemiring.toSemiring CommRing.toCommSemiring RingHom.instFunLike	—	map_sub RingHomClass.toAddMonoidHomClass RingHom.instRingHomClass map_neg map_mul NonUnitalRingHomClass.toMulHomClass RingHomClass.toNonUnitalRingHomClass map_pow MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass
negAddY_eq 📖	mathematical	—	negAddY EuclideanDomain.toCommRing Field.toEuclideanDomain DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Distrib.toMul SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addX addZ	—	negAddY_eq' mul_div_cancel_right₀ EuclideanDomain.toMulDivCancelClass pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain mul_ne_zero
negAddY_eq' 📖	mathematical	—	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing negAddY Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Distrib.toAdd SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing addX addZ	—	negAddY.eq_1 addX.eq_1 addZ.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Tactic.Ring.pow_bit1
negAddY_of_X_eq 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	negAddY NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup DivisionRing.toRing Field.toDivisionRing addU	—	addU.eq_1 neg_neg div_pow negAddY_of_X_eq' mul_div_cancel_right₀ EuclideanDomain.toMulDivCancelClass pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain mul_ne_zero
negAddY_of_X_eq' 📖	mathematical	Equation Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	negAddY SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing	—	negAddY_eq' addX_eq' addZ_of_X_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.pow_bit1
negAddY_of_Z_eq_zero_left 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	negAddY Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq equation_of_Z_eq_zero Mathlib.Tactic.LinearCombination.eq_rearrange negAddY.eq_1 negY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero
negAddY_of_Z_eq_zero_right 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	negAddY Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing negY	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq equation_of_Z_eq_zero Mathlib.Tactic.LinearCombination.eq_rearrange negAddY.eq_1 negY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit1 Mathlib.Meta.NormNum.one_natPow Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero
negAddY_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing negAddY Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield addZ WeierstrassCurve.Affine.negAddY toAffine WeierstrassCurve.Affine.slope	—	negAddY_eq addX_eq' addZ_ne_zero_of_X_ne
negAddY_self 📖	mathematical	—	negAddY MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	—	negAddY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
negAddY_smul 📖	mathematical	—	negAddY instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_gt
negDblY_of_Y_eq 📖	mathematical	Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring negY	negDblY NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing dblU	—	negDblY.eq_1 dblX_of_Y_eq Y_eq_negY_of_Y_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.zero_pow Mathlib.Tactic.Ring.const_pos Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.isInt_pow Mathlib.Meta.NormNum.intPow_negOfNat_bit1 Mathlib.Meta.NormNum.one_natPow
negDblY_of_Z_eq_zero 📖	mathematical	Equation MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	negDblY NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.LinearCombination.eq_of_eq Nat.instAtLeastTwoHAddOfNat AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.mul_const_eq equation_of_Z_eq_zero Mathlib.Tactic.LinearCombination.eq_rearrange negDblY.eq_1 dblU_of_Z_eq_zero dblX_of_Z_eq_zero negY_of_Z_eq_zero Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.neg_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isNat_mul Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Meta.NormNum.isNat_pow Mathlib.Meta.NormNum.IsNatPowT.run Mathlib.Meta.NormNum.IsNatPowT.bit0 Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Meta.NormNum.IsNatPowT.bit1 Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
negDblY_of_Z_ne_zero 📖	mathematical	Equation EuclideanDomain.toCommRing Field.toEuclideanDomain Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing negDblY dblZ WeierstrassCurve.Affine.negAddY toAffine WeierstrassCurve.Affine.slope	—	negDblY.eq_1 dblX.eq_1 dblZ.eq_1 X_eq_iff Nat.instAtLeastTwoHAddOfNat sub_ne_zero Y_ne_negY_of_Y_ne' IsDomain.to_noZeroDivisors instIsDomain
negDblY_smul 📖	mathematical	—	negDblY instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	dblU_smul dblX_smul negY_smul Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.sub_congr Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_mul Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.pow_nat Mathlib.Tactic.Ring.coeff_one Mathlib.Tactic.Ring.pow_one_cast Mathlib.Tactic.Ring.pow_bit0 Mathlib.Tactic.Ring.pow_one Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.pow_bit1
negY_eq 📖	mathematical	—	negY Matrix.vecCons Matrix.vecEmpty SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne CommRing.toRing NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing WeierstrassCurve.a₁ WeierstrassCurve.a₃ Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	—
negY_of_Z_eq_zero 📖	mathematical	MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing	negY NegZeroClass.toNeg SubNegZeroMonoid.toNegZeroClass SubtractionMonoid.toSubNegZeroMonoid SubtractionCommMonoid.toSubtractionMonoid AddCommGroup.toDivisionAddCommMonoid Ring.toAddCommGroup CommRing.toRing	—	negY.eq_1 MulZeroClass.mul_zero sub_zero zero_pow three_ne_zero
negY_of_Z_ne_zero 📖	mathematical	—	DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing negY EuclideanDomain.toCommRing Field.toEuclideanDomain Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield WeierstrassCurve.Affine.negY toAffine	—	Mathlib.Tactic.LinearCombination.eq_of_eq AddRightCancelSemigroup.toIsRightCancelAdd Mathlib.Tactic.LinearCombination.add_eq_eq Mathlib.Tactic.LinearCombination.mul_const_eq div_self pow_ne_zero isReduced_of_noZeroDivisors IsDomain.to_noZeroDivisors instIsDomain Mathlib.Tactic.LinearCombination.eq_rearrange negY.eq_1 WeierstrassCurve.Affine.negY.eq_1 Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.div_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.div_pf Mathlib.Tactic.Ring.inv_single Mathlib.Tactic.Ring.inv_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_inv_one Mathlib.Tactic.Ring.mul_one Nat.cast_one Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero
negY_smul 📖	mathematical	—	negY instSMulForallFinOfNatNat Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	—	Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.mul_pp_pf_overlap Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.isNat_add Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add
nonsingular_iff_of_Y_eq_negY 📖	mathematical	negY EuclideanDomain.toCommRing Field.toEuclideanDomain	Nonsingular Equation	—	negY.eq_1 Nat.instAtLeastTwoHAddOfNat eval_polynomialY Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Meta.NormNum.instAtLeastTwo Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_one Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.neg_congr Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.sub_pf Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Tactic.Ring.add_pf_add_overlap Mathlib.Tactic.Ring.add_overlap_pf Mathlib.Meta.NormNum.isNat_add nonsingular_iff_of_Z_ne_zero sub_self

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