Theorems · Theorem · group theory
FreeAddGroup.range_lift_le
∀ {α : Type u} {β : Type v} [inst : AddGroup β] {f : α → β} {s : AddSubgroup β},
Set.range f ⊆ ↑s → (FreeAddGroup.lift f).range ≤ s- Defined in
- Mathlib.GroupTheory.FreeGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- AddMonoidHom.rangestatement and proof · cited by 142
- FreeAddGroupstatement and proof · cited by 90
- FreeAddGroup.Red.Stepproof · cited by 41
- AddSubgroup.zero_memproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- FreeAddGroup.range_lift_eq_closureproof · cited by 5