Theorems · Theorem · order theory
iSup_and
∀ {α : Type u_1} [inst : CompleteLattice α] {p q : Prop} {s : p ∧ q → α}, iSup s = ⨆ (h₁ : p), ⨆ (h₂ : q), s ⋯- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- CompleteLatticestatement and proof · cited by 1,048
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- iSup₂_leproof · cited by 96
- le_iSup₂proof · cited by 56
Cited by13
Results whose statement or proof uses this declaration.
- biSup_prodproof · cited by 5
- iSup_and'proof · cited by 4
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- Set.iUnion_andproof · cited by 4
- sSupIndep_iffproof · cited by 3
- iSupIndep_comp_coe_iff_supIndepproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- Filter.blimsup_eq_iInf_biSup_of_natproof · cited by 3
- Filter.HasBasis.blimsup_eq_iInf_iSupproof · cited by 2
- Finset.iSup_biUnionproof · cited by 1
- UniformOnFun.edist_def'proof · cited by 1
- Metric.exists_set_encard_eq_packingNumberproof · cited by 0