Theorems · Theorem · order theory
sup_eq_iSup
∀ {α : Type u_1} [inst : CompleteLattice α] (x y : α), x ⊔ y = ⨆ b, bif b then x else y- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_bool_eqproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- Set.union_eq_iUnionproof · cited by 28
- Filter.comap_supproof · cited by 5
- Metric.hausdorffEDist_union_leproof · cited by 4
- Lattice.BicartSq.multicoequalizerDiagramproof · cited by 1
- Filter.totallyBounded_supproof · cited by 1
- Topology.IsGeneratedBy.supproof · cited by 1
- SequentialSpace.supproof · cited by 0