Theorems · Theorem · order theory
ciSup_subtype
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {p : ι → Prop} {f : Subtype p → α},
BddAbove (Set.range f) → sSup ∅ ≤ iSup f → iSup f = ⨆ i, ⨆ (h : p i), f ⟨i, h⟩- Cited by
- 4 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- SupSet.sSupstatement and proof · cited by 954
- IsEmptyproof · cited by 759
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isEmpty_or_nonemptyproof · cited by 269
- iSup_congr_Propproof · cited by 247
- isEmptyElimproof · cited by 59
- le_ciSupproof · cited by 57
Cited by4
Results whose statement or proof uses this declaration.
- cbiSup_eq_of_not_forallproof · cited by 2
- ciSup_subtype_funproof · cited by 2
- ciInf_subtypeproof · cited by 2
- cbiSup_eq_ciSup_subtypeproof · cited by 1