Theorems · Theorem · group theory
Equiv.Perm.Disjoint.cycleType_mul
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] {σ τ : Equiv.Perm α},
σ.Disjoint τ → (σ * τ).cycleType = σ.cycleType + τ.cycleType- Defined in
- Mathlib.GroupTheory.Perm.Cycle.Type
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 99 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Multisetstatement and proof · cited by 2,627
- Finset.cardproof · cited by 2,327
- Equiv.Permstatement and proof · cited by 1,375
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Equiv.Perm.supportproof · cited by 230
- Equiv.Perm.cycleFactorsFinsetproof · cited by 96
- Equiv.Perm.cycleTypestatement and proof · cited by 87
- Equiv.Perm.Disjointstatement and proof · cited by 81
- Multiset.map_addproof · cited by 26
Cited by14
Results whose statement or proof uses this declaration.
- Equiv.Perm.sum_cycleTypeproof · cited by 14
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.cycleType_extendDomainproof · cited by 3
- Equiv.Perm.sign_of_cycleType'proof · cited by 2
- Equiv.Perm.cycleType_conjproof · cited by 2
- Equiv.Perm.mem_cycleType_iffproof · cited by 2
- Equiv.Perm.isConj_of_cycleType_eqproof · cited by 1
- Equiv.Perm.Disjoint.cycleType_noncommProdproof · cited by 1
- Equiv.Perm.cycleType_invproof · cited by 1
- Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_subproof · cited by 1
- Equiv.Perm.cycleType_swap_mul_swap_of_nodupproof · cited by 1
- alternatingGroup.isConj_swap_mul_swap_of_cycleType_twoproof · cited by 0