Theorems · Theorem · order theory
csInf_add
∀ {M : Type u_1} [inst : ConditionallyCompleteLattice M] [inst_1 : AddGroup M] [AddLeftMono M] [AddRightMono M]
{s t : Set M}, s.Nonempty → BddBelow s → t.Nonempty → BddBelow t → sInf (s + t) = sInf s + sInf t- Cited by
- 1 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.
Cites14
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
- InfSet.sInfstatement · cited by 935
- AddLeftMonostatement and proof · cited by 687
- OrderIso.symmproof · cited by 475
- BddBelowstatement and proof · cited by 401
- 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
Cited by1
Results whose statement or proof uses this declaration.
- csInf_subproof · cited by 0