Theorems · Theorem · group theory
Equiv.Perm.notMem_support
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α} {x : α}, x ∉ f.support ↔ f x = x- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
Cited by20
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.Basis.ofPermHomFun_apply_of_mem_fixedPointsproof · cited by 5
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.cycle_is_cycleOfproof · cited by 4
- Equiv.Perm.OnCycleFactors.kerParam_range_eqproof · cited by 3
- Equiv.Perm.eq_on_support_mem_disjointproof · cited by 2
- Equiv.Perm.isInvariant_of_support_leproof · cited by 2
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- Equiv.Perm.IsCycle.commute_iff'proof · cited by 2
- Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iffproof · cited by 1
- Equiv.Perm.Basis.ofPermHom_supportproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_applyproof · cited by 1