Documentation Verification Report

Defs

📁 Source: Mathlib/Algebra/Group/Invertible/Defs.lean

Statistics

MetricCount
Definitionscopy, copy', invOf, mul, invertibleInvOf, invertibleMul, invertibleOfGroup, invertibleOfLeftInverse, invertibleOfRightInverse, invertibleOne, «term⅟_»
11
TheoremsinvOf_mul_self, mul_invOf_self, subsingleton, invOf_eq_group_inv, invOf_eq_left_inv, invOf_eq_right_inv, invOf_inj, invOf_invOf, invOf_mul, invOf_mul_cancel_left, invOf_mul_cancel_left', invOf_mul_cancel_right, invOf_mul_cancel_right', invOf_mul_eq_iff_eq_mul_left, invOf_mul_self, invOf_mul_self', invOf_one, invOf_one', invertible_unique, mul_invOf_cancel_left, mul_invOf_cancel_left', mul_invOf_cancel_right, mul_invOf_cancel_right', mul_invOf_eq_iff_eq_mul_right, mul_invOf_self, mul_invOf_self', mul_left_eq_iff_eq_invOf_mul, mul_left_inj_of_invertible, mul_right_eq_iff_eq_mul_invOf, mul_right_inj_of_invertible
30
Total41

Invertible

Definitions

NameCategoryTheorems
copy 📖CompOp
copy' 📖CompOp
invOf 📖CompOp
166 mathmath: vsub_midpoint, Matrix.invOf_fromBlocks₂₂_eq, Matrix.add_mul_mul_invOf_mul_eq_one, invOf_one', WeierstrassCurve.toCharNeTwoNF_t, CliffordAlgebra.ι_mul_ι_mul_invOf_ι, NormedSpace.invOf_exp_of_mem_ball, Matrix.mul_invOf_eq_iff_eq_mul_right, invOf_pos, Polynomial.Chebyshev.S_eq_U_comp_half_mul_X, invOf_one, IsAlgebraic.invOf, congr, invOf_mul_cancel_left, invOf_nonneg, Matrix.fromBlocks_eq_of_invertible₁₁, commute_invOf, SymAlg.unsym_mul, Ring.inverse_invertible, Polynomial.eval₂_reflect_eq_zero_iff, mul_left_eq_iff_eq_invOf_mul, invOf_mul_self, LaurentPolynomial.invOf_T, Polynomial.dvd_comp_C_mul_X_add_C_iff, Polynomial.algEquivCMulXAddC_symm_eq, TrivSqZeroExt.fst_invOf, QuadraticForm.polarBilin_tmul, Commute.invOf_right, mul_invOf_self, QuadraticMap.associated_apply, invOf_eq_right_inv, Matrix.toLinearEquiv'_symm_apply, mul_invOf_cancel_right, WeierstrassCurve.toCharNeTwoNF_s, invOf_lt_zero, midpoint_eq_smul_add, midpoint_sub_right, invOf_mul_eq_iff_eq_mul_left, xInTermsOfW_eq, TrivSqZeroExt.invertibleEquivInvertibleFst_symm_apply_invOf, invOf_eq_group_inv, Matrix.invOf_eq_nonsing_inv, Matrix.inv_smul, invOf_invOf, invOf_sub_invOf, ExteriorAlgebra.invertibleAlgebraMapEquiv_apply_invOf, Polynomial.eval₂_reflect_mul_pow, Matrix.invOf_mul_eq_iff_eq_mul_left, FDRep.average_char_eq_finrank_invariants, invOf_mul_self, Set.invOf_mem_center, mul_invOf_eq_iff_eq_mul_right, CliffordAlgebra.invOf_ι_mul_ι_mul_ι, sup_eq_half_smul_add_add_abs_sub, QuadraticMap.associated_toQuadraticMap, Set.mem_invOf_smul_set, TrivSqZeroExt.invertibleEquivInvertibleFst_apply_invOf, mul_invOf_self, SymAlg.invOf_sym, TrivSqZeroExt.invOf_eq_inv, Matrix.add_mul_mul_invOf_mul_eq_one', Matrix.det_fromBlocks₁₁, Matrix.add_mul_mul_mul_invOf_eq_one, NormedSpace.invOf_exp, one_sub_invOf_two, Matrix.invOf_fromBlocks_zero₁₂_eq, midpoint_vsub_left, Matrix.transpose_invOf, PowerSeries.derivative_invOf, invOf_two_smul_add_invOf_two_smul, Matrix.isUnit_fromBlocks_iff_of_invertible₂₂, Matrix.mul_invOf_cancel_right, QuadraticMap.half_moduleEnd_apply_eq_half_smul, Matrix.fromBlocks_eq_of_invertible₂₂, TrivSqZeroExt.snd_invOf, Commute.invOf_left, Matrix.invOf_add_mul_mul, Matrix.isUnit_fromBlocks_iff_of_invertible₁₁, invOf_neg, neg_one_eq_invOf_mul_add_invOf_mul_iff, homothety_invOf_two, invOf_smul_smul, Matrix.add_mul_mul_mul_invOf_eq_one', midpoint_vsub_right, CliffordAlgebra.invOf_ι, skewAdjointPart_apply_coe, Matrix.mul_right_eq_iff_eq_mul_invOf, selfAdjointPartL_apply_coe, Polynomial.dickson_one_one_eq_chebyshev_T, Polynomial.chebyshev_T_eq_dickson_one_one, Matrix.invOf_diagonal_eq, ofLeftInverse_invOf, Matrix.det_fromBlocks₂₂, invOf_nonpos, Matrix.mul_left_eq_iff_eq_invOf_mul, mul_invOf_cancel_left, QuadraticMap.associated_linMulLin, invertible_unique, invOf_mul_cancel_left', Algebra.exists_aeval_invOf_eq_zero_of_idealMap_adjoin_sup_span_eq_top, selfAdjointPart_apply_coe, skewAdjointPartL_apply_coe, Matrix.invOf_mul_cancel_right, Matrix.mul_invOf_cancel_left, pos_invOf_of_invertible_cast, Matrix.invOf_add_mul_mul', Polynomial.dickson_two_one_eq_chebyshev_U, inf_eq_half_smul_add_sub_abs_sub, Matrix.invOf_fromBlocks_zero₂₁_eq, FDRep.char_orthonormal, Matrix.invOf_submatrix_equiv_eq, midpoint_sub_left, midpoint_vsub, Polynomial.Chebyshev.C_eq_two_mul_T_comp_half_mul_X, invOf_inj, IsAlgebraic.invOf_iff, Polynomial.algEquivCMulXAddC_symm_apply, Polynomial.Chebyshev.T_eq_half_mul_C_comp_two_mul_X, invOf_eq_inv, invOf_div, smul_invOf_smul, mul_right_eq_iff_eq_mul_invOf, invOf_smul_eq_iff, invOf_mul_self', Polynomial.eval₂_reverse_mul_pow, invOf_eq_of_coprime, smul_eq_iff_eq_invOf_smul, mul_invOf_self', IsLocalization.invertible_mk'_one_invOf, right_sub_midpoint, mul_invOf_cancel_left', Mathlib.Meta.NormNum.Rat.invOf_denom_swap, invOf_eq_left_inv, LieAlgebra.Orthogonal.pb_inv, Matrix.invOf_eq, invOf_mul_cancel_right, midpoint_vsub_midpoint_same_left, star_invOf, Mathlib.Meta.NormNum.NNRat.invOf_denom_swap, right_vsub_midpoint, Derivation.leibniz_invOf, invOf_units, map_invOf, FDRep.scalar_product_char_eq_finrank_equivariant, ExteriorAlgebra.invertibleAlgebraMapEquiv_symm_apply_invOf_toQuot, Matrix.invOf_fromBlocks₁₁_eq, SymAlg.sym_mul_sym, invOf_pow, invOf_mul_cancel_right', invOf_le_one, Matrix.invOf_mul_cancel_left, mul_invOf_cancel_right', Matrix.det_invOf, left_sub_midpoint, neg_add_eq_mul_invOf_mul_same_iff, midpoint_vsub_midpoint_same_right, TrivSqZeroExt.eq_smul_exp_of_invertible, SymAlg.mul_def, invOf_add_invOf, invOf_two_add_invOf_two, LieAlgebra.Orthogonal.pd_inv, val_inv_unitOfInvertible, left_vsub_midpoint, Matrix.conjTranspose_invOf, Polynomial.eval₂_reverse_eq_zero_iff, invOf_mul
mul 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
invOf_mul_self 📖mathematicalinvOf
mul_invOf_self 📖mathematicalinvOf
subsingleton 📖mathematicalInvertible
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
left_inv_eq_right_inv

(root)

Definitions

NameCategoryTheorems
invertibleInvOf 📖CompOp
1 mathmath: Polynomial.algEquivCMulXAddC_symm_eq
invertibleMul 📖CompOp
2 mathmath: Invertible.mulRight_apply, Invertible.mulLeft_apply
invertibleOfGroup 📖CompOp
invertibleOfLeftInverse 📖CompOp
invertibleOfRightInverse 📖CompOp
invertibleOne 📖CompOp
«term⅟_» 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
invOf_eq_group_inv 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MulOne.toOne
DivInvMonoid.toInv
invOf_eq_right_inv
mul_inv_cancel
invOf_eq_left_inv 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Invertible.invOfleft_inv_eq_right_inv
mul_invOf_self
invOf_eq_right_inv 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Invertible.invOfleft_inv_eq_right_inv
invOf_mul_self
invOf_inj 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invertible_unique
invOf_invOf 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invOf_eq_right_inv
invOf_mul_self
invOf_mul 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invOf_eq_right_inv
mul_invOf_cancel_right'
mul_invOf_self'
invOf_mul_cancel_left 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
invOf_mul_cancel_left'
invOf_mul_cancel_left' 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_assoc
invOf_mul_self
one_mul
invOf_mul_cancel_right 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
invOf_mul_cancel_right'
invOf_mul_cancel_right' 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_assoc
invOf_mul_self'
mul_one
invOf_mul_eq_iff_eq_mul_left 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_right_inj_of_invertible
mul_invOf_cancel_left
invOf_mul_self 📖mathematicalInvertible.invOfinvOf_mul_self'
invOf_mul_self' 📖mathematicalInvertible.invOfInvertible.invOf_mul_self
invOf_one 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invOf_one'
invOf_one' 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invOf_eq_right_inv
mul_one
invertible_unique 📖mathematicalInvertible.invOf
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
invOf_eq_right_inv
mul_invOf_self
mul_invOf_cancel_left 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_invOf_cancel_left'
mul_invOf_cancel_left' 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_assoc
mul_invOf_self
one_mul
mul_invOf_cancel_right 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_invOf_cancel_right'
mul_invOf_cancel_right' 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_assoc
mul_invOf_self'
mul_one
mul_invOf_eq_iff_eq_mul_right 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_left_inj_of_invertible
invOf_mul_cancel_right
mul_invOf_self 📖mathematicalInvertible.invOfmul_invOf_self'
mul_invOf_self' 📖mathematicalInvertible.invOfInvertible.mul_invOf_self
mul_left_eq_iff_eq_invOf_mul 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_right_inj_of_invertible
invOf_mul_cancel_left
mul_left_inj_of_invertible 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
mul_invOf_cancel_right'
mul_right_eq_iff_eq_mul_invOf 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Invertible.invOf
MulOne.toOne
mul_left_inj_of_invertible
mul_invOf_cancel_right
mul_right_inj_of_invertible 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
invOf_mul_cancel_left'

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