Mathlib Map

Theorems · Definition · group theory

Function.Injective.rightCancelSemigroup

{M₁ : Type u_1} →
  {M₂ : Type u_2} →
    [inst : Mul M₁] →
      [inst_1 : RightCancelSemigroup M₂] →
        (f : M₁ → M₂) → Function.Injective f → (∀ (x y : M₁), f (x * y) = f x * f y) → RightCancelSemigroup M₁

A type endowed with * is a right cancel semigroup, if it admits an injective map that preserves * to a right cancel semigroup. See note [reducible non-instances].

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
MulRightCancelSemigroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Function.Injective.rightCancelMonoid · cited by 0Injective.rightCancelMono…FunLike.rightCancelSemigroup · cited by 0FunLike.rightCancelSemigr…Semigroup · cited by 202SemigroupIsRightCancelMul · cited by 43IsRightCancelMulRightCancelSemigroup · cited by 3RightCancelSemigroupFunction.Injective.semigroup · cited by 0Injective.semigroupInjective.rightCancelSemigroupCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.