Theorems · Theorem · order theory
le_csInf
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α}, s.Nonempty → (∀ b ∈ s, a ≤ b) → a ≤ sInf s- Cited by
- 36 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.
Cites5
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
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isGLB_csInfproof · cited by 24
Cited by36
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.dist_coe_le_distproof · cited by 18
- exists_lt_of_csInf_ltproof · cited by 10
- NormedAddGroupHom.le_opNormproof · cited by 9
- csInf_le_csInfproof · cited by 9
- MeasureTheory.le_hittingBtwnproof · cited by 6
- NormedAddGroupHom.opNorm_nonnegproof · cited by 5
- Filter.le_limsup_of_leproof · cited by 5
- geometric_hahn_banach_openproof · cited by 4
- MeasureTheory.hittingBtwn_eq_hittingBtwn_of_existsproof · cited by 3
- SimpleGraph.Colorable.chromaticNumber_posproof · cited by 2
- csInf_eq_of_forall_ge_of_forall_gt_exists_ltproof · cited by 2
- rieszContentAux_unionproof · cited by 2