Theorems · Definition · order theory
Fin.orderIsoTriple
{α : Type u_1} → [inst : Preorder α] → [inst_1 : DecidableEq α] → (a b c : α) → a < b → b < c → Fin 3 ≃o ↥{a, b, c}This is the order isomorphism from Fin 3
to a finset {a, b, c} when a < b and b < c.
- Defined in
- Mathlib.Order.Fin.Finset
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- OrderIsostatement · cited by 874
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- StrictMono.orderIsoOfSurjectiveproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Fin.orderIsoTriple_zerostatement · cited by 0
- Fin.orderIsoTriple_onestatement · cited by 0
- Fin.orderIsoTriple_twostatement · cited by 0