Theorems · Theorem · group theory
Equiv.Perm.Basis.nonempty
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] (g : Equiv.Perm α), Nonempty g.Basis- Defined in
- Mathlib.GroupTheory.Perm.Centralizer
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Finset.Nonemptyproof · cited by 1,001
- Subtype.propproof · cited by 505
- Equiv.Perm.supportproof · cited by 230
- Equiv.Perm.cycleFactorsFinsetproof · cited by 96
- Equiv.Perm.Basisstatement · cited by 25
- Equiv.Perm.mem_cycleFactorsFinset_iffproof · cited by 17
- Equiv.Perm.IsCycle.nonempty_supportproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iffproof · cited by 3
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1