Theorems · Theorem · group theory
inv_eq_one
∀ {α : Type u_1} [inst : DivisionMonoid α] {a : α}, a⁻¹ = 1 ↔ a = 1- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 11 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.
- inv_oneproof · cited by 301
- DivisionMonoidstatement and proof · cited by 201
- inv_injectiveproof · cited by 17
Cited by10
Results whose statement or proof uses this declaration.
- inv_ne_oneproof · cited by 3
- orderOf_dvd_iff_zpow_eq_oneproof · cited by 2
- Subgroup.exists_smul_eqproof · cited by 1
- IsDiscrete.exists_nhds_eq_one_of_image_mulRight_inter_nonemptyproof · cited by 1
- Monoid.CoprodI.NeWord.inv.eq_defproof · cited by 0
- isOfFinOrder_iff_zpow_eq_oneproof · cited by 0
- Equiv.Perm.monotone_iffproof · cited by 0
- IsFreeGroupoid.SpanningTree.endIsFreeproof · cited by 0
- one_eq_invproof · cited by 0
- div_eq_selfproof · cited by 0