Theorems · Theorem · group theory
Equiv.Perm.sign_swap
∀ {α : Type u} [inst : DecidableEq α] [inst_1 : Fintype α] {x y : α}, x ≠ y → Equiv.Perm.sign (Equiv.swap x y) = -1- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 78 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Finset.univproof · cited by 3,473
- Unitsstatement · cited by 2,804
- Equiv.Permstatement · cited by 1,375
- Finset.valproof · cited by 438
- Finset.mem_univproof · cited by 361
- Equiv.swapstatement · cited by 197
- Equiv.Perm.signstatement · cited by 138
- Equiv.Perm.signAux3_mul_and_swapproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_swap'proof · cited by 10
- Equiv.Perm.sign_sumCongrproof · cited by 3
- Equiv.Perm.IsSwap.sign_eqproof · cited by 3
- Equiv.Perm.sign_eq_prod_prod_Iioproof · cited by 2
- alternatingGroup.isConj_ofproof · cited by 1
- Matrix.detp_mulproof · cited by 1
- Equiv.Perm.sign_surjectiveproof · cited by 1
- Matrix.det_mul_auxproof · cited by 1
- Equiv.Perm.eq_alternatingGroup_of_index_eq_twoproof · cited by 1
- AlternatingMap.domCoprod.summand_add_swap_smul_eq_zeroproof · cited by 0