Theorems · Theorem · group theory
FreeAbelianGroup.lift_neg
∀ {α : Type u} {G : Type u_1} [inst : AddCommGroup G] (f : α → G), FreeAbelianGroup.lift (-f) = -FreeAbelianGroup.lift f- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommGroupstatement and proof · cited by 12,871
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- FreeAbelianGroupstatement · cited by 82
- FreeAbelianGroup.liftstatement · cited by 33
- AddEquiv.map_negproof · cited by 9
- FreeAbelianGroup.liftAddEquivproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- FreeAbelianGroup.lift_neg_applyproof · cited by 0