Theorems · Definition · group theory
Equiv.Perm.Disjoint
{α : Type u_1} → Equiv.Perm α → Equiv.Perm α → PropTwo permutations f and g are Disjoint if their supports are disjoint, i.e.,
every element is fixed either by f, or by g.
- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equiv.Permstatement and proof · cited by 1,375
Cited by86
Results whose statement or proof uses this declaration.
- Equiv.Perm.cycleFactorsFinsetproof · cited by 96
- Equiv.Perm.Disjoint.commutestatement and proof · cited by 23
- Equiv.Perm.sum_cycleTypeproof · cited by 14
- Equiv.Perm.Disjoint.cycleType_mulstatement and proof · cited by 14
- Equiv.Perm.IsCycle.cycleTypeproof · cited by 12
- Equiv.Perm.disjoint_iff_disjoint_supportstatement · cited by 11
- Equiv.Perm.cycleFactorsFinset_pairwise_disjointstatement · cited by 10
- Equiv.Perm.Disjoint.symmstatement · cited by 9
- Equiv.Perm.cycle_induction_onstatement and proof · cited by 8
- Equiv.Perm.lcm_cycleTypeproof · cited by 7
- Equiv.Perm.pairwise_commute_of_mem_zpowersproof · cited by 7
- Equiv.Perm.cycleFactorsFinset_eq_finsetstatement and proof · cited by 5