Theorems · Theorem · order theory
csInf_le
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α}, BddBelow s → a ∈ s → sInf s ≤ a- Cited by
- 51 results in Mathlib
- Foundations
- Depth 10 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
- isGLB_csInfproof · cited by 24
- Set.nonempty_of_memproof · cited by 19
Cited by51
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.opNorm_le_boundproof · cited by 59
- ContinuousMultilinearMap.opNorm_le_boundproof · cited by 21
- ContinuousLinearMap.opNorm_comp_leproof · cited by 16
- NormedAddGroupHom.opNorm_le_boundproof · cited by 12
- BoundedContinuousFunction.dist_leproof · cited by 11
- Filter.limsup_le_of_leproof · cited by 11
- SimpleGraph.Colorable.chromaticNumber_leproof · cited by 11
- csInf_le'proof · cited by 9
- csInf_le_csInfproof · cited by 9
- gauge_le_of_memproof · cited by 8
- MeasureTheory.hittingBtwn_leproof · cited by 8
- csInf_le_of_leproof · cited by 6