Theorems · Theorem · group theory
Equiv.Perm.le_card_support_of_mem_cycleType
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {n : ℕ} {σ : Equiv.Perm α},
n ∈ σ.cycleType → n ≤ σ.support.card- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 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.
Cites10
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
- LE.le.transproof · cited by 3,151
- Multisetstatement · cited by 2,627
- Finset.cardstatement · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- le_of_eqproof · cited by 366
- Equiv.Perm.supportstatement · cited by 230
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Equiv.Perm.sum_cycleTypeproof · cited by 14
- Multiset.le_sum_of_memproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.isThreeCycle_sq_of_three_mem_cycleType_fiveproof · cited by 0