Theorems · Theorem · group theory
map_add_eq_zero
∀ {M : Type u_4} {N : Type u_5} {F : Type u_9} [inst : AddZero M] [inst_1 : AddZero N] [inst_2 : FunLike F M N]
[AddMonoidHomClass F M N] (f : F) {a b : M}, a + b = 0 → f a + f b = 0- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- map_zeroproof · cited by 1,614
- map_addproof · cited by 964
- AddMonoidHomClassstatement and proof · cited by 252
- AddZerostatement and proof · cited by 87
Cited by5
Results whose statement or proof uses this declaration.
- map_negproof · cited by 378
- AddMonoid.Coprod.mk_of_neg_addproof · cited by 1
- IsAddUnit.eq_on_negproof · cited by 1
- AddMonoidHom.map_exists_left_negproof · cited by 0
- AddMonoidHom.map_exists_right_negproof · cited by 0