Theorems · Theorem · ring theory
mul_invOf_self
∀ {α : Type u} [inst : Mul α] [inst_1 : One α] (a : α) [inst_2 : Invertible a], a * ⅟a = 1- Defined in
- Mathlib.Algebra.Group.Invertible.Defs
- Cited by
- 28 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
- mul_invOf_self'proof · cited by 16
Cited by28
Results whose statement or proof uses this declaration.
- Matrix.mul_nonsing_invproof · cited by 11
- midpoint_eq_smul_addproof · cited by 6
- AffineEquiv.pointReflection_midpoint_leftproof · cited by 5
- mul_invOf_cancel_left'proof · cited by 4
- bind₁_wittPolynomial_xInTermsOfWproof · cited by 3
- invertible_uniqueproof · cited by 3
- invOf_posproof · cited by 3
- invOf_two_add_invOf_twoproof · cited by 3
- star_invOfproof · cited by 2
- Matrix.mul_invOf_cancel_leftproof · cited by 2
- Matrix.mul_invOf_cancel_rightproof · cited by 2
- invOf_add_invOfproof · cited by 2