Theorems · Theorem · group theory
Equiv.Perm.mem_toCycle_iff_support
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {x : α} (f : Equiv.Perm α) (hf : f.IsCycle),
x ∈ f.toCycle hf ↔ f x ≠ x- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Concrete
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
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Cites16
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
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- pow_zeroproof · cited by 1,094
- Equiv.Perm.supportproof · cited by 230
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
- Cyclestatement · cited by 79
- Equiv.Perm.mem_supportproof · cited by 51
- Cycle.ofListproof · cited by 38
- Equiv.Perm.toListproof · cited by 24
- Equiv.Perm.toCyclestatement and proof · cited by 7
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