Theorems · Inductive type · order theory
IsAddQuantale
(α : Type u_1) → [AddSemigroup α] → [CompleteLattice α] → Prop
An additive quantale is an additive semigroup distributing over a complete lattice.
- Defined in
- Mathlib.Algebra.Order.Quantale
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- AddSemigroupCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteLatticestatement · cited by 1,048
- AddSemigroupstatement · cited by 136
Cited by21
Results whose statement or proof uses this declaration.
- add_sSup_distribstatement and proof · cited by 4
- sSup_add_distribstatement and proof · cited by 4
- IsAddQuantale.add_sSup_distribstatement and proof · cited by 1
- IsAddQuantale.sSup_add_distribstatement and proof · cited by 1
- AddQuantalestatement · cited by 1
- IsAddQuantale.casesOnstatement and proof · cited by 0
- IsAddQuantale.recOnstatement and proof · cited by 0
- AddQuantale.add_botstatement and proof · cited by 0
- AddQuantale.add_iSup_distribstatement and proof · cited by 0
- AddQuantale.add_sup_distribstatement and proof · cited by 0
- AddQuantale.bot_addstatement and proof · cited by 0
- AddQuantale.casesOnstatement and proof · cited by 0