Theorems · Theorem · group theory
FreeAbelianGroup.lift_add_apply
∀ {α : Type u} {G : Type u_1} [inst : AddCommGroup G] (f g : α → G) (a : FreeAbelianGroup α),
(FreeAbelianGroup.lift (f + g)) a = (FreeAbelianGroup.lift f) a + (FreeAbelianGroup.lift g) a- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- zero_addproof · cited by 2,366
- map_negproof · cited by 378
- FreeAbelianGroupstatement and proof · cited by 82
- neg_addproof · cited by 69
- add_add_add_commproof · cited by 56
- AddMonoidHom.map_addproof · cited by 48
- AddMonoidHom.map_zeroproof · cited by 47
- FreeAbelianGroup.ofproof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- FreeAbelianGroup.liftAddGroupHomproof · cited by 1
- FreeAbelianGroup.lift_addproof · cited by 0