Theorems · Theorem · group theory
Equiv.Perm.IsCycle.nonempty_support
∀ {α : Type u_2} [inst : Fintype α] [inst_1 : DecidableEq α] {g : Equiv.Perm α}, g.IsCycle → g.support.NonemptySupport of a cycle is nonempty
- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Finset.Nonemptystatement · cited by 1,001
- Equiv.Perm.supportstatement and proof · cited by 230
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Finset.nonempty_iff_ne_emptyproof · cited by 34
- Equiv.Perm.IsCycle.ne_oneproof · cited by 11
- Equiv.Perm.support_eq_empty_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.commute_iff'proof · cited by 2
- Equiv.Perm.Basis.nonemptyproof · cited by 2
- Equiv.Perm.closure_cycleType_eq_two_two_eq_alternatingGroupproof · cited by 2
- Equiv.Perm.isCycleOn_support_of_mem_cycleFactorsFinsetproof · cited by 1