Theorems · Theorem · order theory
le_csSup_of_le
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a b : α}, BddAbove s → b ∈ s → a ≤ b → a ≤ sSup s- Cited by
- 7 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
- le_transproof · cited by 985
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- le_csSupproof · cited by 66
Cited by7
Results whose statement or proof uses this declaration.
- seminormFromBounded_nonnegproof · cited by 2
- Real.sSup_nonneg'proof · cited by 2
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- MonotoneOn.csSup_eq_of_subset_of_forall_exists_leproof · cited by 1
- ConvexOn.monotoneOn_leftDerivproof · cited by 0
- CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁proof · cited by 0
- CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₁₂proof · cited by 0