Theorems · Theorem · order theory
IsOrderConnected.conn
∀ {α : Type u} {lt : α → α → Prop} [self : IsOrderConnected α lt] (a b c : α), lt a c → lt a b ∨ lt b cA connected order is one satisfying the condition a < c → a < b ∨ b < c.
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- IsOrderConnected
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsOrderConnectedstatement and proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsOrderConnected.neg_transproof · cited by 1