Theorems · Theorem · group theory
card_support_eq_three_iff
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ : Equiv.Perm α}, σ.support.card = 3 ↔ σ.IsThreeCycle- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 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.
Cites22
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
- Multisetproof · cited by 2,627
- Finset.cardstatement and proof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.sumproof · cited by 388
- Multiset.consproof · cited by 313
- Equiv.Perm.supportstatement and proof · cited by 230
- ne_of_ltproof · cited by 203
- Multiset.eraseproof · cited by 93
- Equiv.Perm.cycleTypeproof · cited by 87
- Multiset.sum_consproof · cited by 45
- Equiv.Perm.IsThreeCyclestatement and proof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.IsThreeCycle.isThreeCycle_sqproof · cited by 2
- Equiv.Perm.isThreeCycle_swap_mul_swap_sameproof · cited by 2
- Equiv.Perm.isThreeCycle_sq_of_three_mem_cycleType_fiveproof · cited by 0