Theorems · Theorem · order theory
left_lt_sup
∀ {α : Type u} [inst : SemilatticeSup α] {a b : α}, a < a ⊔ b ↔ ¬b ≤ a- Defined in
- Mathlib.Order.Lattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- SemilatticeSup
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.
- SemilatticeSupstatement and proof · cited by 785
- le_sup_leftproof · cited by 265
- LE.le.lt_iff_neproof · cited by 34
- left_eq_supproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.finite_minimalPrimes_of_isNoetherianRingproof · cited by 3
- SimpleGraph.exists_isTutteViolatorproof · cited by 1
- Ne.lt_sup_or_lt_supproof · cited by 1
- SimpleGraph.lt_sup_edgeproof · cited by 1
- FractionalIdeal.isPrincipal.of_finite_maximals_of_invproof · cited by 1
- Set.ssubset_union_left_iffproof · cited by 0
- left_or_right_lt_supproof · cited by 0