Theorems · Theorem · group theory
Equiv.Perm.mem_support
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α} {x : α}, x ∈ f.support ↔ f x ≠ x- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 56 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.
Cites7
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
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Finset.mem_univproof · cited by 361
- Equiv.Perm.supportstatement · cited by 230
- Finset.mem_filterproof · cited by 185
Cited by51
Results whose statement or proof uses this declaration.
- Equiv.Perm.apply_mem_supportproof · cited by 8
- Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iffproof · cited by 7
- Equiv.Perm.mem_cycleFactorsFinset_support_leproof · cited by 7
- Equiv.Perm.support_mul_leproof · cited by 6
- Equiv.Perm.nodup_toListproof · cited by 5
- Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eqproof · cited by 5
- Equiv.Perm.support_pow_leproof · cited by 5
- Equiv.Perm.IsCycle.support_pow_eq_iffproof · cited by 4
- Equiv.Perm.cycle_is_cycleOfproof · cited by 4
- Equiv.Perm.support_zpow_leproof · cited by 4
- Equiv.Perm.Disjoint.support_mulproof · cited by 4
- Equiv.Perm.IsCycle.pow_eq_one_iffproof · cited by 3