Theorems · Theorem · order theory
csSup_mul
∀ {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 → BddAbove t → sSup (s * t) = sSup s * sSup 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.
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
- Groupstatement and proof · cited by 6,238
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- MulLeftMonostatement and proof · cited by 410
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.mulstatement · cited by 297
- MulRightMonostatement and proof · cited by 263
- OrderIso.to_galoisConnectionproof · cited by 32
- OrderIso.mulLeftproof · cited by 18
- OrderIso.mulRightproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- csSup_divproof · cited by 0