Theorems · Theorem · group theory
Equiv.Perm.IsCycle.ne_one
∀ {α : Type u_2} {f : Equiv.Perm α}, f.IsCycle → f ≠ 1- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.SameCycleproof · cited by 116
- Equiv.Perm.IsCyclestatement and proof · cited by 108
Cited by11
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsCycle.nonempty_supportproof · cited by 4
- Equiv.Perm.IsCycle.support_pow_eq_iffproof · cited by 4
- Equiv.Perm.nodup_of_pairwise_disjoint_cyclesproof · cited by 3
- Equiv.Perm.IsCycle.two_le_card_supportproof · cited by 3
- Equiv.Perm.swap_isSwap_iffproof · cited by 3
- Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_supportproof · cited by 1
- Equiv.Perm.IsCycle.pow_iffproof · cited by 1
- Equiv.Perm.eq_cycleOf_of_mem_cycleFactorsFinset_iffproof · cited by 1
- Equiv.Perm.IsCycle.existsUnique_cycle_nontrivial_subtypeproof · cited by 0
- Equiv.Perm.isCycle_cycleOf_iffproof · cited by 0
- Equiv.Perm.not_isCycle_oneproof · cited by 0