Theorems · Theorem · order theory
isLUB_csSup
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α},
s.Nonempty → autoParam (BddAbove s) isLUB_csSup._auto_1 → IsLUB s (sSup s)- Cited by
- 34 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- IsLUBstatement · cited by 280
- ConditionallyCompleteLattice.isLUB_csSupproof · cited by 1
Cited by34
Results whose statement or proof uses this declaration.
- le_csSupproof · cited by 66
- csSup_leproof · cited by 35
- IsLUB.csSup_eqproof · cited by 19
- isLUB_ciSupproof · cited by 10
- Order.IsNormal.map_sSupproof · cited by 5
- csSup_image2_eq_csSup_csSupproof · cited by 5
- GaloisConnection.l_csSupproof · cited by 4
- lt_csSup_iffproof · cited by 4
- MonotoneOn.map_csSup_of_continuousWithinAtproof · cited by 4
- isLUB_csSup'proof · cited by 4
- csSup_mem_closureproof · cited by 4
- isLUB_ciSup_setproof · cited by 3