Theorems · Theorem · order theory
sup_le_sup
∀ {α : Type u} [inst : SemilatticeSup α] {a b c d : α}, a ≤ b → c ≤ d → a ⊔ c ≤ b ⊔ d- Defined in
- Mathlib.Order.Lattice
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- 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
- sup_leproof · cited by 159
- le_sup_of_le_leftproof · cited by 26
- le_sup_of_le_rightproof · cited by 17
Cited by48
Results whose statement or proof uses this declaration.
- Set.union_subset_unionproof · cited by 29
- max_le_maxproof · cited by 23
- sup_le_sup_leftproof · cited by 20
- sup_le_sup_rightproof · cited by 14
- Finset.union_subset_unionproof · cited by 8
- iSup_sup_eqproof · cited by 7
- ClosureOperator.closure_sup_closure_leftproof · cited by 5
- symmDiff_triangleproof · cited by 5
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- iInf_sup_of_monotoneproof · cited by 3
- Filter.IsBoundedUnder.supproof · cited by 3
- symmDiff_le_supproof · cited by 3