Theorems · Theorem · combinatorics
Tuple.sort_eq_refl_iff_monotone
∀ {n : ℕ} {α : Type u_1} [inst : LinearOrder α] {f : Fin n → α}, Tuple.sort f = Equiv.refl (Fin n) ↔ Monotone fThe permutation that sorts f is the identity if and only if f is monotone.
- Defined in
- Mathlib.Data.Fin.Tuple.Sort
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Monotonestatement and proof · cited by 1,397
- Equiv.Permstatement · cited by 1,375
- Equiv.reflstatement · cited by 274
- Tuple.sortstatement · cited by 19
- Equiv.coe_reflproof · cited by 7
- Tuple.eq_sort_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Equiv.Perm.monotone_iffproof · cited by 0