Theorems · Theorem · order theory
ciInf_subtype
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {p : ι → Prop} {f : Subtype p → α},
BddBelow (Set.range f) → iInf f ≤ sInf ∅ → iInf f = ⨅ i, ⨅ (h : p i), f ⟨i, h⟩- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 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.
Cites7
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
- iInfstatement and proof · cited by 1,690
- InfSet.sInfstatement and proof · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- ciSup_subtypeproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- cbiInf_eq_ciInf_subtypeproof · cited by 1
- ciInf_subtype_funproof · cited by 1