Theorems · Theorem · order theory
csInf_sub
∀ {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 → BddAbove t → sInf (s - t) = sInf s - sSup t- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
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
- sub_eq_add_negproof · cited by 1,023
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- AddLeftMonostatement and proof · cited by 687
- BddAbovestatement and proof · cited by 620
- BddBelowstatement and proof · cited by 401
- AddRightMonostatement and proof · cited by 367
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.substatement · cited by 136
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