Theorems · Theorem · group theory
Equiv.Perm.support_eq_empty_iff
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : Fintype α] {σ : Equiv.Perm α}, σ.support = ∅ ↔ σ = 1- Defined in
- Mathlib.GroupTheory.Perm.Support
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 58 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.Perm.supportstatement · cited by 230
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.support_oneproof · cited by 10
- Equiv.Perm.IsCycle.nonempty_supportproof · cited by 4
- Equiv.Perm.IsCycle.support_pow_eq_iffproof · cited by 4
- Equiv.Perm.card_support_eq_zeroproof · cited by 3
- Equiv.Perm.disjoint_of_disjoint_supportproof · cited by 1