Theorems · Theorem · order theory
csSup_div
∀ {M : Type u_1} [inst : ConditionallyCompleteLattice M] [inst_1 : Group M] [MulLeftMono M] [MulRightMono M]
{s t : Set M}, s.Nonempty → BddAbove s → t.Nonempty → BddBelow t → sSup (s / t) = sSup s / sInf t- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Groupstatement and proof · cited by 6,238
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- div_eq_mul_invproof · cited by 715
- BddAbovestatement and proof · cited by 620
- MulLeftMonostatement and proof · cited by 410
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- MulRightMonostatement and proof · cited by 263
- Set.divstatement · cited by 112
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.