Theorems · Theorem · group theory
inv_ne_one
∀ {α : Type u_1} [inst : DivisionMonoid α] {a : α}, a⁻¹ ≠ 1 ↔ a ≠ 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- DivisionMonoid
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.
- Iff.notproof · cited by 489
- DivisionMonoidstatement and proof · cited by 201
- inv_eq_oneproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Function.mulSupport_fun_invproof · cited by 5
- Monoid.CoprodI.lift_word_prod_nontrivial_of_head_cardproof · cited by 1
- jacobiSum_mul_jacobiSum_invproof · cited by 0