Theorems · Theorem · order theory
inf_lt_sup
∀ {α : Type u} [inst : Lattice α] {a b : α}, a ⊓ b < a ⊔ b ↔ a ≠ b- Defined in
- Mathlib.Order.Lattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- LE.le.lt_iff_neproof · cited by 34
- inf_le_supproof · cited by 14
- inf_eq_supproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- min_lt_maxproof · cited by 3
- Convex.nontrivial_iff_nonempty_interiorproof · cited by 2