Theorems · Inductive type · order theory
IsStrictOrder
(α : Sort u_1) → (α → α → Prop) → Prop
IsStrictOrder X r means that the binary relation r on X is a strict order, that is,
Std.Irrefl r and IsTrans X r.
- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by37
Results whose statement or proof uses this declaration.
- RelEmbedding.natGTstatement and proof · cited by 6
- RelEmbedding.not_wellFoundedstatement and proof · cited by 5
- RelEmbedding.wellFounded_iff_isEmptystatement and proof · cited by 4
- RelEmbedding.natLTstatement and proof · cited by 4
- Set.Finite.wellFoundedOnstatement and proof · cited by 3
- Set.wellFoundedOn_iff_no_descending_seqstatement and proof · cited by 3
- Set.wellFoundedOn_sdiff_singletonstatement and proof · cited by 3
- DFinsupp.lex_lt_of_lt_of_preorderstatement and proof · cited by 3
- RelEmbedding.acc_iff_isEmpty_subtype_mem_rangestatement and proof · cited by 2
- Finset.wellFoundedOn_supstatement and proof · cited by 2
- Set.WellFoundedOn.unionstatement and proof · cited by 2
- Set.wellFoundedOn_insertstatement and proof · cited by 2