Theorems · Theorem · group theory
alternatingGroup.range_ofSubtype
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (s : Finset α),
(alternatingGroup.ofSubtype s).range = Equiv.Perm.ofSubtype.range.subgroupOf (alternatingGroup α)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- MonoidHomproof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Equiv.Permstatement and proof · cited by 1,375
- MonoidHom.rangestatement and proof · cited by 314
- Subgroup.mapproof · cited by 301
- Subgroup.subtypeproof · cited by 185
- Subgroup.subgroupOfstatement and proof · cited by 122
- alternatingGroupstatement and proof · cited by 96
- Equiv.Perm.ofSubtypestatement and proof · cited by 41
- Subgroup.range_subtypeproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.mem_range_ofSubtype_iffproof · cited by 1