Theorems · Theorem · group theory

map_sub

∀ {G : Type u_7} {H : Type u_8} {F : Type u_9} [inst : FunLike F G H] [inst_1 : AddGroup G]
  [inst_2 : SubtractionMonoid H] [AddMonoidHomClass F G H] (f : F) (a b : G), f (a - b) = f a - f b

Additive group homomorphisms preserve subtraction.

Defined in

Mathlib.Algebra.Group.Hom.Defs

Cited by

565 results in Mathlib

Foundations

Depth 15 from the axioms, rests on 97 definitions · uses propext, Classical.choice, Quot.sound

Assumes

FunLikeAddGroupSubtractionMonoidAddMonoidHomClass