Theorems · Theorem · ring theory
Invertible.congr
∀ {α : Type u} [inst : Monoid α] (a b : α) [inst_1 : Invertible a] [inst_2 : Invertible b], a = b → ⅟a = ⅟bIf a is invertible and a = b, then ⅟a = ⅟b.
- Defined in
- Mathlib.Algebra.Group.Invertible.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- MonoidInvertibleInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement · cited by 268
- invertible_uniqueproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- lipschitzGroup.conjAct_smul_ι_mem_range_ιproof · cited by 3
- CliffordAlgebra.invOf_ιproof · cited by 2
- lipschitzGroup.involute_act_ι_mem_range_ιproof · cited by 2
- Matrix.invOf_add_mul_mulproof · cited by 1
- Matrix.invOf_add_mul_mul'proof · cited by 1
- Matrix.invOf_diagonal_eqproof · cited by 1
- Matrix.invOf_eqproof · cited by 1
- Matrix.invOf_fromBlocks_zero₁₂_eqproof · cited by 1
- Matrix.invOf_fromBlocks_zero₂₁_eqproof · cited by 1
- Matrix.invOf_submatrix_equiv_eqproof · cited by 1
- TrivSqZeroExt.snd_invOfproof · cited by 1
- Matrix.det_invOfproof · cited by 1