Theorems · Theorem · group theory
Equiv.Perm.card_fixedPoints
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] (σ : Equiv.Perm α),
Fintype.card ↑(Function.fixedPoints ⇑σ) = Fintype.card α - σ.cycleType.sum- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 4 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.
Cites21
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
- Setstatement · cited by 53,352
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Finset.univproof · cited by 3,473
- Compl.complproof · cited by 2,925
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- Equiv.Permstatement and proof · cited by 1,375
- Finset.filterproof · cited by 949
- Finset.extproof · cited by 565
Cited by4
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_of_cycleType_eq_replicateproof · cited by 1
- Equiv.Perm.card_le_of_centralizer_le_alternatingproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_range_cardproof · cited by 1
- Equiv.Perm.centralizer_le_alternating_iffproof · cited by 0