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Theorems · Definition · group theory

Function.Injective.invOneClass

{M₁ : Type u_1} →
  {M₂ : Type u_2} →
    [inst : One M₁] →
      [inst_1 : Inv M₁] →
        [inst_2 : InvOneClass M₂] →
          (f : M₁ → M₂) → Function.Injective f → f 1 = 1 → (∀ (x : M₁), f x⁻¹ = (f x)⁻¹) → InvOneClass M₁

A type endowed with 1 and ⁻¹ is a InvOneClass, if it admits an injective map that preserves 1 and ⁻¹ to a InvOneClass. See note [reducible non-instances].

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
OneInvInvOneClass
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Around this declaration

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Function.Injective.divInvOneMonoid · cited by 0Injective.divInvOneMonoidFunLike.invOneClass · cited by 0FunLike.invOneClassInvOneClass · cited by 5InvOneClassInjective.invOneClassCITED BYCITES

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