Theorems · Definition · group theory
Equiv.Perm.decomposeFin
{n : ℕ} → Equiv.Perm (Fin n.succ) ≃ Fin n.succ × Equiv.Perm (Fin n)Permutations of Fin (n + 1) are equivalent to fixing a single
Fin (n + 1) and permuting the remaining with a Perm (Fin n).
The fixed Fin (n + 1) is swapped with 0.
- Defined in
- Mathlib.GroupTheory.Perm.Fin
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Equivstatement · cited by 8,337
- Equiv.symmproof · cited by 3,681
- Equiv.Permstatement and proof · cited by 1,375
- Equiv.transproof · cited by 337
- Equiv.reflproof · cited by 274
- finSuccEquivproof · cited by 28
- Equiv.permCongrproof · cited by 27
- Equiv.prodCongrproof · cited by 24
- Equiv.Perm.decomposeOptionproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Equiv.Perm.decomposeFin_symm_apply_succstatement · cited by 3
- Equiv.Perm.decomposeFin_symm_apply_zerostatement · cited by 2
- Equiv.Perm.decomposeFin_symm_of_reflstatement · cited by 2
- Equiv.Perm.decomposeFin.symm_signstatement · cited by 2
- finRotate_succ_eq_decomposeFinstatement and proof · cited by 1
- Matrix.det_succ_column_zeroproof · cited by 1
- Finset.univ_perm_fin_succstatement and proof · cited by 1
- Equiv.Perm.decomposeFin_symm_of_onestatement · cited by 0
- Equiv.Perm.decomposeFin_symm_apply_onestatement and proof · cited by 0