Theorems · Theorem · order theory
csInf_le_csInf
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s t : Set α},
BddBelow t → s.Nonempty → s ⊆ t → sInf t ≤ sInf s- Cited by
- 9 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- 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 and proof · cited by 53,352
- Set.Nonemptystatement and proof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- csInf_leproof · cited by 51
- le_csInfproof · cited by 36
Cited by9
Results whose statement or proof uses this declaration.
- Filter.limsSup_le_limsSupproof · cited by 4
- gauge_monoproof · cited by 4
- MeasureTheory.hittingBtwn_eq_hittingBtwn_of_existsproof · cited by 3
- csInf_le_csInf'proof · cited by 2
- MeasureTheory.hittingAfter_antiproof · cited by 1
- MeasureTheory.hittingBtwn_mono_leftproof · cited by 1
- MeasureTheory.hittingAfter_monoproof · cited by 1
- MeasureTheory.hittingBtwn_antiproof · cited by 1
- MonotoneOn.csInf_eq_of_subset_of_forall_exists_leproof · cited by 1