Theorems · Inductive type · order theory
IsQuantale
(α : Type u_1) → [Semigroup α] → [CompleteLattice α] → Prop
A quantale is a 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
- SemigroupCompleteLattice
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
- Semigroupstatement · cited by 202
Cited by21
Results whose statement or proof uses this declaration.
- mul_sSup_distribstatement and proof · cited by 4
- sSup_mul_distribstatement and proof · cited by 4
- IsQuantale.mul_sSup_distribstatement and proof · cited by 1
- IsQuantale.sSup_mul_distribstatement and proof · cited by 1
- Quantalestatement · cited by 1
- IsQuantale.casesOnstatement and proof · cited by 0
- IsQuantale.recOnstatement and proof · cited by 0
- Quantale.bot_mulstatement and proof · cited by 0
- Quantale.casesOnstatement and proof · cited by 0
- Quantale.ctorIdxstatement and proof · cited by 0
- Quantale.iSup_mul_distribstatement and proof · cited by 0
- Quantale.leftMulResiduation_le_iff_mul_lestatement and proof · cited by 0