Theorems · Theorem · order theory
sup_le
∀ {α : Type u} [inst : SemilatticeSup α] {a b c : α}, a ≤ c → b ≤ c → a ⊔ b ≤ c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 159 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- SemilatticeSup
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.
- SemilatticeSupstatement and proof · cited by 785
- SemilatticeSup.sup_leproof · cited by 1
Cited by159
Results whose statement or proof uses this declaration.
- sup_le_iffproof · cited by 58
- sup_le_supproof · cited by 48
- Ideal.comap_map_of_surjectiveproof · cited by 30
- Finset.union_subsetproof · cited by 28
- Submodule.comap_map_eqproof · cited by 23
- abs_add_leproof · cited by 17
- codisjoint_iff_le_supproof · cited by 15
- MeasureTheory.lintegral_add_measureproof · cited by 13
- Monotone.le_map_supproof · cited by 11
- Ideal.map_isPrime_of_surjectiveproof · cited by 11
- Subgroup.comap_map_eqproof · cited by 9
- Measurable.prodproof · cited by 9