Theorems · Theorem · order theory
Preorder.lt_iff_le_not_ge
∀ {α : Type u_2} [self : Preorder α] (a b : α), a < b ↔ a ≤ b ∧ ¬b ≤ a- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
Cited by2
Results whose statement or proof uses this declaration.
- lt_iff_le_not_geproof · cited by 35
- specializationPreorderproof · cited by 2