Theorems · Theorem · ring theory
invOf_mul_self
∀ {α : Type u} [inst : Mul α] [inst_1 : One α] (a : α) [inst_2 : Invertible a], ⅟a * a = 1- Defined in
- Mathlib.Algebra.Group.Invertible.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulOneInvertible
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Invertiblestatement and proof · cited by 549
- Invertible.invOfstatement · cited by 268
- invOf_mul_self'proof · cited by 8
Cited by20
Results whose statement or proof uses this declaration.
- Matrix.nonsing_inv_mulproof · cited by 12
- invOf_eq_right_invproof · cited by 10
- invOf_mul_cancel_left'proof · cited by 6
- Polynomial.eval₂_reflect_mul_powproof · cited by 3
- CliffordAlgebra.invOf_ι_mul_ι_mul_ιproof · cited by 2
- invOf_add_invOfproof · cited by 2
- Matrix.invOf_mul_cancel_rightproof · cited by 2
- Matrix.fromBlocks_eq_of_invertible₁₁proof · cited by 2
- xInTermsOfW_auxproof · cited by 2
- CliffordAlgebra.ι_mul_ι_mul_invOf_ιproof · cited by 2
- invOf_sub_invOfproof · cited by 2
- sup_eq_half_smul_add_add_abs_subproof · cited by 1