Theorems · Definition · group theory
Equiv.Perm.truncSwapFactors
{α : Type u} → [inst : DecidableEq α] → [Fintype α] → (f : Equiv.Perm α) → Trunc { l // l.prod = f ∧ ∀ g ∈ l, g.IsSwap }This computably represents the fact that any permutation can be represented as the product of a list of transpositions.
- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 57 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.coeproof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- Equiv.Permstatement and proof · cited by 1,375
- Finset.valproof · cited by 438
- Truncstatement · cited by 39
- Equiv.Perm.IsSwapstatement · cited by 35
- Trunc.mkproof · cited by 21
- Equiv.Perm.swapFactorsAuxproof · cited by 0
Cited by5
Results whose statement or proof uses this declaration.
- Equiv.Perm.swap_induction_onproof · cited by 5
- Equiv.Perm.closure_three_cycles_eq_alternatingproof · cited by 3
- Equiv.Perm.mclosure_isSwapproof · cited by 2
- Equiv.Perm.sign_subtypePermproof · cited by 1
- Equiv.Perm.eq_sign_of_surjective_homproof · cited by 0