Theorems · Theorem · commutative algebra

Function.Surjective.leftDistribClass

∀ {R : Type u_1} {S : Type u_2} (f : R → S),
  Function.Surjective f →
    ∀ [inst : Add S] [inst_1 : Mul S] [inst_2 : Mul R] [inst_3 : Add R] [LeftDistribClass R],
      (∀ (x y : R), f (x + y) = f x + f y) → (∀ (x y : R), f (x * y) = f x * f y) → LeftDistribClass S

Pushforward a LeftDistribClass instance along a surjective function.

Defined in: Mathlib.Algebra.Ring.InjSurj
Cited by: 0 results in Mathlib
Foundations: Depth 8 from the axioms · uses propext
Assumes: Add Mul Mul Add LeftDistribClass

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left_distribproof · cited by 19
LeftDistribClassstatement and proof · cited by 12
Function.Surjective.forall₃proof · cited by 3

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