Theorems · Theorem · group theory
Equiv.Perm.IsSwap.sign_eq
∀ {α : Type u} [inst : DecidableEq α] [inst_1 : Fintype α] {f : Equiv.Perm α}, f.IsSwap → Equiv.Perm.sign f = -1- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 79 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.
- DFunLike.coestatement and proof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.swapproof · cited by 197
- Equiv.Perm.signstatement and proof · cited by 138
- Equiv.Perm.IsSwapstatement and proof · cited by 35
- Equiv.Perm.sign_swapproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_prod_list_swapproof · cited by 3
- alternatingGroup.stabilizer.surjective_toPermproof · cited by 2
- Equiv.Perm.mul_mem_alternatingGroup_of_isSwapproof · cited by 0