Theorems · Theorem · order theory
iSup_subtype
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {p : ι → Prop} {f : Subtype p → α},
iSup f = ⨆ i, ⨆ (h : p i), f ⟨i, h⟩- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 26 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 by26
Results whose statement or proof uses this declaration.
- iSup_subtype'proof · cited by 44
- iSup_subtype''proof · cited by 18
- Set.iUnion_subtypeproof · cited by 14
- partialSups_eq_biSupproof · cited by 4
- Set.finite_sdiff_iUnion_Ioo'proof · cited by 3
- sSupIndep_iffproof · cited by 3
- iSupIndep_comp_coe_iff_supIndepproof · cited by 3
- Module.End.genEigenspace_eq_iSup_genEigenspace_natproof · cited by 2
- UniformOnFun.edist_continuousRestrict_of_singletonproof · cited by 2
- AlgebraicGeometry.mono_pushoutSection_of_isCompact_of_flat_rightproof · cited by 2
- AlgebraicGeometry.isCompact_basicOpenproof · cited by 1