Theorems · Theorem · group theory

AddEquiv.map_zero

∀ {M : Type u_4} {N : Type u_5} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] (h : M ≃+ N), h 0 = 0

An additive isomorphism of additive monoids sends 0 to 0 (and is hence an additive monoid isomorphism).

Defined in

Mathlib.Algebra.Group.Equiv.Defs

Cited by

9 results in Mathlib

Foundations

Depth 18 from the axioms · uses Quot.sound

Assumes

AddZeroClassAddZeroClass