Documentation Verification Report

Common

πŸ“ Source: Mathlib/Tactic/Ring/Common.lean

Statistics

MetricCount
DefinitionsCache, czΞ±, dsΞ±, int, nat, rΞ±, ExBase, cast, cmp, eq, evalIntCast, evalNatCast, evalPos, toProd, ExProd, cast, cmp, coeff, eq, evalIntCast, evalInv, evalNatCast, evalPos, mkNNRat, mkNat, mkNegNNRat, mkNegNat, toSum, ExSum, cast, cmp, eq, evalIntCast, evalInv, evalNatCast, evalPos, ExtractCoeff, e', k, p, ve', Overlap, expr, proof, val, eval, evalAdd, evalAddOverlap, evalAtom, evalCast, evalDiv, evalInvAtom, evalMul, evalMulProd, evalMul₁, evalNSMul, evalNeg, evalNegProd, evalPow, evalPowAtom, evalPowNat, evalPowProd, evalPowProdAtom, evalPow₁, evalSub, evalZSMul, extractCoeff, instInhabitedResultOfSigmaQuoted, instInhabitedSigmaQuotedExBase, instInhabitedSigmaQuotedExProd, instInhabitedSigmaQuotedExSum, instOrdRat_mathlib, isAtomOrDerivable, mkCache, sβ„•, sβ„€
76
Theoremsadd_congr, add_mul, add_overlap_pf, add_overlap_pf_zero, add_pf_add_gt, add_pf_add_lt, add_pf_add_overlap, add_pf_add_overlap_zero, add_pf_add_zero, add_pf_zero_add, add_pos_left, add_pos_right, atom_pf, atom_pf', cast_neg, cast_nnrat, cast_pos, cast_rat, cast_zero, coeff_mul, coeff_one, const_pos, div_congr, div_pf, intCast_add, intCast_mul, intCast_negOfNat_Int, intCast_zero, inv_add, inv_congr, inv_mul, inv_single, inv_zero, mul_add, mul_congr, mul_exp_pos, mul_one, mul_pf_left, mul_pf_right, mul_pow, mul_pp_pf_overlap, mul_zero, natCast_add, natCast_int, natCast_mul, natCast_nat, natCast_zero, neg_add, neg_congr, neg_mul, neg_one_mul, neg_zero, nsmul_congr, one_mul, one_pow, pow_add, pow_atom, pow_bit0, pow_bit1, pow_congr, pow_nat, pow_one, pow_one_cast, pow_prod_atom, pow_zero, single_pow, smul_eq_cast, smul_eq_intCast, smul_int, smul_nat, sub_congr, sub_pf, toProd_pf, zero_mul, zero_pow, zsmul_congr
76
Total152

Mathlib.Tactic.Ring

Definitions

NameCategoryTheorems
Cache πŸ“–CompDataβ€”
ExBase πŸ“–CompDataβ€”
ExProd πŸ“–CompDataβ€”
ExSum πŸ“–CompDataβ€”
ExtractCoeff πŸ“–CompDataβ€”
Overlap πŸ“–CompDataβ€”
eval πŸ“–CompOpβ€”
evalAdd πŸ“–CompOpβ€”
evalAddOverlap πŸ“–CompOpβ€”
evalAtom πŸ“–CompOpβ€”
evalCast πŸ“–CompOpβ€”
evalDiv πŸ“–CompOpβ€”
evalInvAtom πŸ“–CompOpβ€”
evalMul πŸ“–CompOpβ€”
evalMulProd πŸ“–CompOpβ€”
evalMul₁ πŸ“–CompOpβ€”
evalNSMul πŸ“–CompOpβ€”
evalNeg πŸ“–CompOpβ€”
evalNegProd πŸ“–CompOpβ€”
evalPow πŸ“–CompOpβ€”
evalPowAtom πŸ“–CompOpβ€”
evalPowNat πŸ“–CompOpβ€”
evalPowProd πŸ“–CompOpβ€”
evalPowProdAtom πŸ“–CompOpβ€”
evalPow₁ πŸ“–CompOpβ€”
evalSub πŸ“–CompOpβ€”
evalZSMul πŸ“–CompOpβ€”
extractCoeff πŸ“–CompOpβ€”
instInhabitedResultOfSigmaQuoted πŸ“–CompOpβ€”
instInhabitedSigmaQuotedExBase πŸ“–CompOpβ€”
instInhabitedSigmaQuotedExProd πŸ“–CompOpβ€”
instInhabitedSigmaQuotedExSum πŸ“–CompOpβ€”
instOrdRat_mathlib πŸ“–CompOpβ€”
isAtomOrDerivable πŸ“–CompOpβ€”
mkCache πŸ“–CompOpβ€”
sβ„• πŸ“–CompOpβ€”
sβ„€ πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
add_congr πŸ“–β€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”β€”
add_mul πŸ“–β€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
β€”β€”add_mul
Distrib.rightDistribClass
add_overlap_pf πŸ“–mathematicalDistrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”mul_add
Distrib.leftDistribClass
add_overlap_pf_zero πŸ“–mathematicalMathlib.Meta.NormNum.IsNat
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”Distrib.leftDistribClass
Nat.cast_zero
MulZeroClass.mul_zero
add_pf_add_gt πŸ“–β€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”add_left_comm
add_pf_add_lt πŸ“–β€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”add_assoc
add_pf_add_overlap πŸ“–β€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”add_left_comm
add_assoc
add_pf_add_overlap_zero πŸ“–β€”Mathlib.Meta.NormNum.IsNat
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”β€”add_add_add_comm
Mathlib.Meta.NormNum.IsNat.out
Nat.cast_zero
add_pf_zero_add
add_pf_add_zero πŸ“–mathematicalβ€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”add_zero
add_pf_zero_add πŸ“–mathematicalβ€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”zero_add
add_pos_left πŸ“–β€”β€”β€”β€”β€”
add_pos_right πŸ“–β€”β€”β€”β€”β€”
atom_pf πŸ“–mathematicalβ€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Nat.rawCast
Nat.instAddMonoidWithOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Nat.cast_one
pow_one
mul_one
add_zero
atom_pf' πŸ“–mathematicalβ€”Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toMul
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Nat.rawCast
Nat.instAddMonoidWithOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Nat.cast_one
pow_one
mul_one
add_zero
cast_neg πŸ“–mathematicalMathlib.Meta.NormNum.IsIntDistrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Int.rawCast
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Int.cast_negOfNat
add_zero
cast_nnrat πŸ“–mathematicalMathlib.Meta.NormNum.IsNNRat
DivisionSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
NNRat.rawCast
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”invOf_eq_inv
div_eq_mul_inv
add_zero
cast_pos πŸ“–mathematicalMathlib.Meta.NormNum.IsNat
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Nat.rawCast
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”add_zero
cast_rat πŸ“–mathematicalMathlib.Meta.NormNum.IsRat
DivisionRing.toRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Rat.rawCast
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”invOf_eq_inv
div_eq_mul_inv
add_zero
cast_zero πŸ“–mathematicalMathlib.Meta.NormNum.IsNat
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”Nat.cast_zero
coeff_mul πŸ“–mathematicalβ€”Monoid.toNatPow
Nat.instMonoid
β€”mul_assoc
coeff_one πŸ“–mathematicalβ€”Nat.rawCast
Nat.instAddMonoidWithOne
β€”Nat.cast_one
one_mul
const_pos πŸ“–mathematicalβ€”Nat.rawCast
Nat.instAddMonoidWithOne
β€”β€”
div_congr πŸ“–β€”DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
DivisionSemiring.toGroupWithZero
Semifield.toDivisionSemiring
β€”β€”β€”
div_pf πŸ“–mathematicalInvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
DivisionSemiring.toGroupWithZero
β€”div_eq_mul_inv
intCast_add πŸ“–mathematicalAddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”Int.cast_add
intCast_mul πŸ“–mathematicalAddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
Monoid.toNatPow
Int.instMonoid
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”Int.cast_mul
Int.cast_pow
intCast_negOfNat_Int πŸ“–mathematicalβ€”AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
Int.rawCast
Int.instRing
β€”Int.cast_negOfNat
Int.cast_neg
Int.cast_natCast
intCast_zero πŸ“–mathematicalβ€”AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”Int.cast_zero
inv_add πŸ“–mathematicalAddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”Nat.cast_add
inv_congr πŸ“–β€”InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
β€”β€”β€”
inv_mul πŸ“–β€”InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”β€”mul_inv_rev
inv_pow
Nat.cast_one
mul_one
inv_single πŸ“–mathematicalInvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”add_zero
inv_zero πŸ“–mathematicalβ€”InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
β€”inv_zero
mul_add πŸ“–β€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”β€”mul_add
Distrib.leftDistribClass
add_zero
mul_congr πŸ“–β€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”β€”
mul_exp_pos πŸ“–mathematicalβ€”Monoid.toNatPow
Nat.instMonoid
β€”β€”
mul_one πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Nat.cast_one
mul_one
mul_pf_left πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”mul_assoc
mul_pf_right πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”mul_left_comm
mul_pow πŸ“–mathematicalMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”mul_pow
pow_mul
mul_pp_pf_overlap πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”pow_add
mul_mul_mul_comm
mul_zero πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”MulZeroClass.mul_zero
natCast_add πŸ“–mathematicalAddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”Nat.cast_add
natCast_int πŸ“–mathematicalβ€”AddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
Nat.rawCast
AddGroupWithOne.toAddMonoidWithOne
Int.instRing
β€”Int.cast_natCast
natCast_mul πŸ“–mathematicalAddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Monoid.toNatPow
Nat.instMonoid
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
β€”Nat.cast_mul
Nat.cast_pow
natCast_nat πŸ“–mathematicalβ€”AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Nat.rawCast
Nat.instAddMonoidWithOne
β€”β€”
natCast_zero πŸ“–mathematicalβ€”AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
β€”Nat.cast_zero
neg_add πŸ“–mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”neg_add_rev
add_comm
neg_congr πŸ“–β€”NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
β€”β€”β€”
neg_mul πŸ“–mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
β€”mul_neg
neg_one_mul πŸ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Int.rawCast
CommRing.toRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
β€”Int.cast_neg
Int.cast_one
neg_mul
one_mul
neg_zero πŸ“–mathematicalβ€”NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
β€”neg_zero
nsmul_congr πŸ“–β€”AddMonoid.toNatSMul
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
β€”β€”β€”
one_mul πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Nat.cast_one
one_mul
one_pow πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
β€”Nat.cast_one
one_pow
pow_add πŸ“–β€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”β€”pow_add
pow_atom πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”Nat.cast_one
mul_one
add_zero
pow_bit0 πŸ“–β€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”β€”one_mul
pow_add
pow_bit1 πŸ“–β€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”β€”one_mul
pow_add
pow_one
pow_congr πŸ“–β€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
β€”β€”β€”
pow_nat πŸ“–β€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
β€”β€”pow_mul
pow_one πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
β€”pow_one
pow_one_cast πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Nat.rawCast
Nat.instAddMonoidWithOne
β€”Nat.cast_one
pow_one
pow_prod_atom πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toAdd
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”add_zero
Nat.cast_one
mul_one
pow_zero πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Nat.rawCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”pow_zero
Nat.cast_one
add_zero
single_pow πŸ“–mathematicalMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”add_zero
smul_eq_cast πŸ“–mathematicalAddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
AddMonoid.toNatSMul
AddMonoidWithOne.toAddMonoid
β€”nsmul_eq_mul
smul_eq_intCast πŸ“–mathematicalAddGroupWithOne.toIntCast
Ring.toAddGroupWithOne
CommRing.toRing
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
SubNegMonoid.toZSMul
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
β€”zsmul_eq_mul
smul_int πŸ“–mathematicalβ€”SubNegMonoid.toZSMul
AddGroup.toSubNegMonoid
Int.instAddGroup
β€”β€”
smul_nat πŸ“–mathematicalβ€”AddMonoid.toNatSMul
Nat.instAddMonoid
β€”β€”
sub_congr πŸ“–β€”SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
β€”β€”β€”
sub_pf πŸ“–mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
CommRing.toRing
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
β€”sub_eq_add_neg
toProd_pf πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Nat.rawCast
Nat.instAddMonoidWithOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Nat.cast_one
pow_one
mul_one
zero_mul πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
β€”MulZeroClass.zero_mul
zero_pow πŸ“–mathematicalβ€”Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
β€”pow_succ
MulZeroClass.mul_zero
zsmul_congr πŸ“–β€”SubNegMonoid.toZSMul
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
β€”β€”β€”

Mathlib.Tactic.Ring.Cache

Definitions

NameCategoryTheorems
czΞ± πŸ“–CompOpβ€”
dsΞ± πŸ“–CompOpβ€”
int πŸ“–CompOpβ€”
nat πŸ“–CompOpβ€”
rΞ± πŸ“–CompOpβ€”

Mathlib.Tactic.Ring.ExBase

Definitions

NameCategoryTheorems
cast πŸ“–CompOpβ€”
cmp πŸ“–CompOpβ€”
eq πŸ“–CompOpβ€”
evalIntCast πŸ“–CompOpβ€”
evalNatCast πŸ“–CompOpβ€”
evalPos πŸ“–CompOpβ€”
toProd πŸ“–CompOpβ€”

Mathlib.Tactic.Ring.ExProd

Definitions

NameCategoryTheorems
cast πŸ“–CompOpβ€”
cmp πŸ“–CompOpβ€”
coeff πŸ“–CompOpβ€”
eq πŸ“–CompOpβ€”
evalIntCast πŸ“–CompOpβ€”
evalInv πŸ“–CompOpβ€”
evalNatCast πŸ“–CompOpβ€”
evalPos πŸ“–CompOpβ€”
mkNNRat πŸ“–CompOpβ€”
mkNat πŸ“–CompOpβ€”
mkNegNNRat πŸ“–CompOpβ€”
mkNegNat πŸ“–CompOpβ€”
toSum πŸ“–CompOpβ€”

Mathlib.Tactic.Ring.ExSum

Definitions

NameCategoryTheorems
cast πŸ“–CompOpβ€”
cmp πŸ“–CompOpβ€”
eq πŸ“–CompOpβ€”
evalIntCast πŸ“–CompOpβ€”
evalInv πŸ“–CompOpβ€”
evalNatCast πŸ“–CompOpβ€”
evalPos πŸ“–CompOpβ€”

Mathlib.Tactic.Ring.ExtractCoeff

Definitions

NameCategoryTheorems
e' πŸ“–CompOpβ€”
k πŸ“–CompOpβ€”
p πŸ“–CompOpβ€”
ve' πŸ“–CompOpβ€”

Mathlib.Tactic.Ring.Result

Definitions

NameCategoryTheorems
expr πŸ“–CompOpβ€”
proof πŸ“–CompOpβ€”
val πŸ“–CompOpβ€”

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