Theorems · Theorem · order theory
sSup_pair
∀ {α : Type u_1} [inst : CompleteLattice α] {a b : α}, sSup {a, b} = a ⊔ b- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- IsLUB.sSup_eqproof · cited by 17
- isLUB_pairproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- iSup_bool_eqproof · cited by 12
- Set.sUnion_pairproof · cited by 2
- Filter.ker_supproof · cited by 2
- DirectSum.IsInternal.isComplproof · cited by 1
- AddQuantale.add_sup_distribproof · cited by 0
- Quantale.mul_sup_distribproof · cited by 0
- Quantale.sup_mul_distribproof · cited by 0
- Submodule.annihilator_supproof · cited by 0
- CompleteLattice.ωScottContinuous.supproof · cited by 0
- AddQuantale.sup_add_distribproof · cited by 0
- DirectSum.isInternal_submodule_iff_isComplproof · cited by 0