Theorems · Theorem · group theory
Equiv.Perm.one_lt_of_mem_cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α} {n : ℕ}, n ∈ σ.cycleType → 1 < n- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 96 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.
Cites5
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
- Multisetstatement · cited by 2,627
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Equiv.Perm.two_le_of_mem_cycleTypeproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- Equiv.Perm.pow_prime_eq_one_iffproof · cited by 2
- alternatingGroup.mem_kleinFour_of_order_two_powproof · cited by 1
- Equiv.Perm.cycleType_prime_orderproof · cited by 1