Theorems · Theorem · order theory
sSup_mul_distrib
∀ {α : Type u_1} {x : α} {s : Set α} [inst : Semigroup α] [inst_1 : CompleteLattice α] [IsQuantale α],
sSup s * x = ⨆ y ∈ s, y * x- Defined in
- Mathlib.Algebra.Order.Quantale
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- Semigroupstatement and proof · cited by 202
- IsQuantalestatement and proof · cited by 13
- IsQuantale.sSup_mul_distribproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Quantale.leftMulResiduation_le_iff_mul_leproof · cited by 0
- Quantale.bot_mulproof · cited by 0
- Quantale.sup_mul_distribproof · cited by 0
- Quantale.iSup_mul_distribproof · cited by 0