Theorems · Theorem · order theory
csSup_add
∀ {M : Type u_1} [inst : ConditionallyCompleteLattice M] [inst_1 : AddGroup M] [AddLeftMono M] [AddRightMono M]
{s t : Set M}, s.Nonempty → BddAbove s → t.Nonempty → BddAbove t → sSup (s + t) = sSup s + sSup t- Cited by
- 3 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- AddLeftMonostatement and proof · cited by 687
- BddAbovestatement and proof · cited by 620
- AddRightMonostatement and proof · cited by 367
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.addstatement · cited by 338
- OrderIso.to_galoisConnectionproof · cited by 32
- OrderIso.addLeftproof · cited by 18
- OrderIso.addRightproof · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- ConditionallyCompleteLinearOrderedField.inducedMap_addproof · cited by 1
- Archimedean.embedRealFun_addproof · cited by 1
- csSup_subproof · cited by 0