Theorems · Inductive type · order theory
IsOrderConnected
(α : Type u) → (α → α → Prop) → Prop
A connected order is one satisfying the condition a < c → a < b ∨ b < c.
This is recognizable as an intuitionistic substitute for a ≤ b ∨ b ≤ a on
the constructive reals, and is also known as negative transitivity,
since the contrapositive asserts transitivity of the relation ¬ a < b.
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 3 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 by5
Results whose statement or proof uses this declaration.
- IsOrderConnected.connstatement and proof · cited by 1
- IsOrderConnected.neg_transstatement and proof · cited by 1
- isStrictWeakOrder_of_isOrderConnectedstatement and proof · cited by 0
- IsOrderConnected.casesOnstatement and proof · cited by 0
- IsOrderConnected.recOnstatement and proof · cited by 0