Theorems · Theorem · group theory
Function.Injective.isCancelMulZero
∀ {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) → ∀ [IsCancelMulZero M₀'], IsCancelMulZero M₀- Defined in
- Mathlib.Algebra.GroupWithZero.InjSurj
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsCancelMulZerostatement and proof · cited by 177
- IsLeftCancelMulZeroproof · cited by 48
- IsRightCancelMulZeroproof · cited by 33
- Function.Injective.isLeftCancelMulZeroproof · cited by 5
- Function.Injective.isRightCancelMulZeroproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Function.Injective.isDomainproof · cited by 27
- MulEquiv.isCancelMulZero_iffproof · cited by 1
- MulOpposite.isCancelMulZero_iffproof · cited by 0
- IsCancelMulZero.of_faithfulSMulproof · cited by 0