Theorems · Theorem · order theory
le_csSup
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α} {a : α}, BddAbove s → a ∈ s → a ≤ sSup s- Cited by
- 66 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
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- isLUB_csSupproof · cited by 34
- Set.nonempty_of_memproof · cited by 19
Cited by66
Results whose statement or proof uses this declaration.
- le_ciSupproof · cited by 57
- Monotone.le_leftLimproof · cited by 9
- Filter.le_liminf_of_leproof · cited by 9
- csSup_eq_of_forall_le_of_forall_lt_exists_gtproof · cited by 8
- le_csSup_of_leproof · cited by 7
- csSup_le_csSupproof · cited by 6
- RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependentproof · cited by 5
- cauchySeq_iff_le_tendsto_0proof · cited by 5
- subset_Icc_csInf_csSupproof · cited by 4
- lt_csSup_of_ltproof · cited by 4
- SimpleGraph.IsClique.card_le_cliqueNumproof · cited by 4
- IsCompact.sSup_lt_iff_of_continuousproof · cited by 3