Theorems · Theorem · group theory
FreeAbelianGroup.lift_apply_of
∀ {α : Type u} {β : Type v} [inst : AddCommGroup β] (f : α → β) (x : α),
(FreeAbelianGroup.lift f) (FreeAbelianGroup.of x) = f x- Defined in
- Mathlib.GroupTheory.FreeAbelianGroup
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 85 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.
Cites14
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
- Multiplicativeproof · cited by 875
- FreeAbelianGroupstatement · cited by 82
- FreeAbelianGroup.ofstatement and proof · cited by 40
- FreeGroup.ofproof · cited by 39
- FreeAbelianGroup.liftstatement and proof · cited by 33
- FreeGroup.liftproof · cited by 32
- Abelianization.ofproof · cited by 20
- Abelianization.liftproof · cited by 9
Cited by12
Results whose statement or proof uses this declaration.
- FreeCommRing.lift_ofproof · cited by 9
- FreeAbelianGroup.of_injectiveproof · cited by 6
- FreeAbelianGroup.of_ne_zeroproof · cited by 3
- FreeAbelianGroup.toFinsupp_ofproof · cited by 2
- FreeAbelianGroup.of_mul_ofproof · cited by 2
- FreeAbelianGroup.pure_bindproof · cited by 1
- FreeAbelianGroup.map_compproof · cited by 1
- FreeAbelianGroup.lift_add_applyproof · cited by 1
- Finsupp.toFreeAbelianGroup_comp_toFinsuppproof · cited by 1
- FreeRing.coe_eqproof · cited by 0
- FreeAbelianGroup.lift_compproof · cited by 0
- FreeAbelianGroup.lift_comp_applyproof · cited by 0