Theorems · Theorem · order theory
le_ciSup_of_le
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLattice α] {a : α} {f : ι → α},
BddAbove (Set.range f) → ∀ (c : ι), a ≤ f c → a ≤ iSup f- Cited by
- 22 results in Mathlib
- Foundations
- Depth 12 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.
Cited by22
Results whose statement or proof uses this declaration.
- Finite.le_ciSup_of_leproof · cited by 17
- ciSup_monoproof · cited by 9
- ciInf_le_of_leproof · cited by 8
- AlgebraicIndependent.lift_cardinalMk_le_trdegproof · cited by 4
- ciSup_mono_of_forall_exists'proof · cited by 4
- Module.rank_top_le_rank_of_isScalarTowerproof · cited by 3
- le_ciSup₂proof · cited by 3
- trdeg_subsingletonproof · cited by 2
- spectralNorm_nonnegproof · cited by 2
- IsUltrametricDist.norm_tprod_leproof · cited by 2
- IsUltrametricDist.norm_tsum_leproof · cited by 2
- seminormFromBounded_isNonarchimedeanproof · cited by 1