Theorems · Definition · order theory
linearOrderOfSTO
{α : Type u} → (r : α → α → Prop) → [IsStrictTotalOrder α r] → [DecidableRel r] → LinearOrder αConstruct a linear order from an IsStrictTotalOrder relation.
See note [reducible non-instances].
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- LinearOrderstatement · cited by 8,572
- PartialOrderproof · cited by 6,410
- IsStrictTotalOrderstatement and proof · cited by 10
- decidableEqOfDecidableLEproof · cited by 0
- decidableLTOfDecidableLEproof · cited by 0
- partialOrderOfSOproof · cited by 0
Cited by13
Results whose statement or proof uses this declaration.
- Cardinal.exists_ord_eq_type_ltproof · cited by 3
- IsWellOrder.linearOrderproof · cited by 3
- Ordinal.inductionOnWellOrderproof · cited by 2
- exteriorPower.finrank_eqproof · cited by 1
- monovaryOn_iff_exists_monotoneOnproof · cited by 1
- BumpCovering.sum_toPOUFun_eqproof · cited by 1
- Ordinal.liftOnWellOrderproof · cited by 1
- Ordinal.liftOnWellOrder_typeproof · cited by 1
- exists_wellFoundedGTproof · cited by 1
- exists_wellFoundedLTproof · cited by 1
- Cardinal.mk_subset_mk_lt_cofproof · cited by 0
- IsWellFounded.rank_eq_typeinproof · cited by 0