Theorems · Theorem · order theory
subset_Icc_csInf_csSup
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α},
BddBelow s → BddAbove s → s ⊆ Set.Icc (sInf s) (sSup s)- Cited by
- 4 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.
Cites9
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.Iccstatement · cited by 1,702
- SupSet.sSupstatement · cited by 954
- InfSet.sInfstatement · cited by 935
- BddAbovestatement and proof · cited by 620
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- le_csSupproof · cited by 66
- csInf_leproof · cited by 51
Cited by4
Results whose statement or proof uses this declaration.
- Set.Nonempty.ordConnected_iff_of_bddproof · cited by 3
- Bornology.IsBounded.subset_Icc_sInf_sSupproof · cited by 3
- IsPreconnected.mem_intervalsproof · cited by 1
- eq_Icc_csInf_csSup_of_connected_bdd_closedproof · cited by 1