Mathlib Map

Theorems · Theorem · group theory

Function.Injective.isLeftCancelMul

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

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

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MulMulIsLeftCancelMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Function.Injective.isCancelMul · cited by 2Injective.isCancelMulEquiv.isLeftCancelMul · cited by 0Equiv.isLeftCancelMulFunLike.isLeftCancelMul · cited by 0FunLike.isLeftCancelMulIsLeftCancelMul · cited by 51IsLeftCancelMulmul_left_cancel · cited by 16mul_left_cancelInjective.isLeftCancelMulCITED BYCITES

Cites2

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Cited by3

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