Theorems · Theorem · order theory
csInf_le_of_le
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a b : α}, BddBelow s → b ∈ s → b ≤ a → sInf s ≤ a- Cited by
- 6 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.
Cites6
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
- InfSet.sInfstatement · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- csInf_leproof · cited by 51
- ge_transproof · cited by 34
Cited by6
Results whose statement or proof uses this declaration.
- upperClosure_eq_Ici_csInfproof · cited by 2
- Real.sInf_nonpos'proof · cited by 2
- MeasureTheory.hittingBtwn_antiproof · cited by 1
- MonotoneOn.csInf_eq_of_subset_of_forall_exists_leproof · cited by 1
- MeasureTheory.hittingBtwn_mono_leftproof · cited by 1
- ConvexOn.monotoneOn_rightDerivproof · cited by 0