Theorems · Theorem · group theory
Equiv.Perm.Disjoint.cycleFactorsFinset_mul_eq_union
∀ {α : Type u_2} [inst : DecidableEq α] [inst_1 : Fintype α] {f g : Equiv.Perm α},
f.Disjoint g → (f * g).cycleFactorsFinset = f.cycleFactorsFinset ∪ g.cycleFactorsFinset- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Factors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Set.Pairwiseproof · cited by 321
- Equiv.Perm.IsCycleproof · cited by 108
- Equiv.Perm.cycleFactorsFinsetstatement and proof · cited by 96
- Finset.coe_subsetproof · cited by 93
- Equiv.Perm.Disjointstatement and proof · cited by 81
- Finset.coe_unionproof · cited by 78
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.Disjoint.cycleType_mulproof · cited by 14
- Equiv.Perm.cycleFactorsFinset_mul_inv_mem_eq_sdiffproof · cited by 0