Mathlib Map

Theorems · Theorem · group theory

Function.Injective.isRightCancelMul

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

A type has right-cancellative multiplication, if it admits an injective map that preserves * to another type with right-cancellative multiplication.

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MulMulIsRightCancelMul
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Around this declaration

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

Function.Injective.isCancelMul · cited by 2Injective.isCancelMulFunLike.isRightCancelMul · cited by 0FunLike.isRightCancelMulEquiv.isRightCancelMul · cited by 0Equiv.isRightCancelMulIsRightCancelMul · cited by 43IsRightCancelMulmul_right_cancel · cited by 14mul_right_cancelInjective.isRightCancelMulCITED BYCITES

Cites2

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Cited by3

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