Mathlib Map

Theorems · Theorem · group theory

Function.Injective.isRightCancelMulZero

∀ {M₀ : Type u_1} {M₀' : Type u_3} [inst : Mul M₀] [inst_1 : Zero M₀] [inst_2 : Mul M₀'] [inst_3 : Zero M₀']
  (f : M₀ → M₀'),
  Function.Injective f →
    f 0 = 0 → (∀ (x y : M₀), f (x * y) = f x * f y) → ∀ [IsRightCancelMulZero M₀'], IsRightCancelMulZero M₀
Defined in
Mathlib.Algebra.GroupWithZero.InjSurj
Cited by
4 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MulZeroMulZeroIsRightCancelMulZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulEquiv.isDomain · cited by 8MulEquiv.isDomainFunction.Injective.isCancelMulZero · cited by 4Injective.isCancelMulZeroMulOpposite.isLeftCancelMulZero_iff · cited by 1MulOpposite.isLeftCancelM…MulEquiv.isRightCancelMulZero_iff · cited by 0MulEquiv.isRightCancelMul…IsRightCancelMulZero · cited by 33IsRightCancelMulZeromul_right_cancel₀ · cited by 22mul_right_cancel₀Injective.isRightCancelMulZeroCITED BYCITES

Cites2

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

Cited by4

Results whose statement or proof uses this declaration.