Theorems · Theorem · order theory
IsOrderConnected.neg_trans
∀ {α : Type u} {r : α → α → Prop} [IsOrderConnected α r] {a b c : α}, ¬r a b → ¬r b c → ¬r a c- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- IsOrderConnected
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsOrderConnectedstatement and proof · cited by 3
- IsOrderConnected.connproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isStrictWeakOrder_of_isOrderConnectedproof · cited by 0