Mathlib Map

Theorems · Theorem · group theory

Function.Injective.isCancelMul

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

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

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

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

Equiv.isCancelMul · cited by 0Equiv.isCancelMulFunLike.isCancelMul · cited by 0FunLike.isCancelMulIsLeftCancelMul · cited by 51IsLeftCancelMulIsRightCancelMul · cited by 43IsRightCancelMulIsCancelMul · cited by 32IsCancelMulFunction.Injective.isRightCancelMul · cited by 3Injective.isRightCancelMulFunction.Injective.isLeftCancelMul · cited by 3Injective.isLeftCancelMulInjective.isCancelMulCITED BYCITES

Cites5

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Cited by2

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