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Theorems · Theorem · order theory

IsQuantale.mul_sSup_distrib

∀ {α : Type u_1} {inst : Semigroup α} {inst_1 : CompleteLattice α} [self : IsQuantale α] (x : α) (s : Set α),
  x * sSup s = ⨆ y ∈ s, x * y

Multiplication is distributive over join in a quantale

Defined in
Mathlib.Algebra.Order.Quantale
Cited by
1 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
IsQuantale
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mul_sSup_distrib · cited by 4mul_sSup_distribSet · cited by 53352SetiSup · cited by 2415iSupCompleteLattice · cited by 1048CompleteLatticeSupSet.sSup · cited by 954SupSet.sSupSemigroup · cited by 202SemigroupIsQuantale · cited by 13IsQuantaleIsQuantale.mul_sSup_distribCITED BYCITES

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Cited by1

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