Mathlib Map

Theorems · Inductive type · order theory

Quantale

(α : Type u_1) → [inst : Semigroup α] → [inst_1 : CompleteLattice α] → [IsQuantale α] → Type

A quantale is a semigroup distributing over a complete lattice.

Defined in
Mathlib.Algebra.Order.Quantale
Cited by
1 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
SemigroupCompleteLatticeIsQuantale
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quantale.casesOn · cited by 0Quantale.casesOnQuantale.ctorIdx · cited by 0Quantale.ctorIdxQuantale.noConfusion · cited by 0Quantale.noConfusionQuantale.noConfusionType · cited by 0Quantale.noConfusionTypeQuantale.recOn · cited by 0Quantale.recOnQuantale.mk.sizeOf_spec · cited by 0mk.sizeOf_specCompleteLattice · cited by 1048CompleteLatticeSemigroup · cited by 202SemigroupIsQuantale · cited by 13IsQuantaleQuantaleCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.