Theorems · Definition · group theory

Function.Injective.mulZeroOneClass

{M₀ : Type u_1} →
  {M₀' : Type u_3} →
    [inst : MulZeroOneClass M₀] →
      [inst_1 : Mul M₀'] →
        [inst_2 : Zero M₀'] →
          [inst_3 : One M₀'] →
            (f : M₀' → M₀) →
              Function.Injective f → f 0 = 0 → f 1 = 1 → (∀ (a b : M₀'), f (a * b) = f a * f b) → MulZeroOneClass M₀'

Pull back a MulZeroOneClass instance along an injective function. See note [reducible non-instances].

Defined in

Mathlib.Algebra.GroupWithZero.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext

Assumes

MulZeroOneClassMulZeroOne