Structures · Order
CompletelyDistribLattice
A completely distributive lattice is a complete lattice whose ⨅ and ⨆
distribute over each other.
- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Shape
- One type argument · adds le_himp_iff, himp_bot, sdiff_le_iff, top_sdiff, iInf_iSup_eq
Extends2
Extended by2
Forgetful instances
Every CompletelyDistribLattice is also a
Provided automatically by
Concrete types that are instances6
- UpperSet
- LowerSet
- SimpleGraph.Subgraph
- SimpleGraph.Finsubgraph
- Prod
- OrderDual
How is a type an instance?
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Assumed by21
- CompletelyDistribLattice.toHImp
- CompletelyDistribLattice.toSDiff
- CompletelyDistribLattice.MinimalAxioms.of
- CompletelyDistribLattice.toHNot
- biSup_iInter_of_pairwise_disjoint
- CompletelyDistribLattice.toCompl
- CompletelyDistribLattice.iInf_iSup_eq
- iInf_iSup_eq
- CompletelyDistribLattice.top_sdiff
- Equiv.completelyDistribLattice
- OrderDual.instCompletelyDistribLattice
- CompletelyDistribLattice.toBiheytingAlgebra
- Prod.instCompletelyDistribLattice
- CompletelyDistribLattice.toCompleteDistribLattice
- Pi.instCompletelyDistribLattice
- CompletelyDistribLattice.le_himp_iff
- Function.Injective.completelyDistribLattice
- CompletelyDistribLattice.sdiff_le_iff
- iSup_iInf_eq
- CompletelyDistribLattice.toCompleteLattice
- CompletelyDistribLattice.himp_bot
Ancestors44
- BiheytingAlgebra
- Bot
- BoundedOrder
- ChainCompletePartialOrder
- CoheytingAlgebra
- Compl
- CompleteDistribLattice
- CompleteLattice
- CompletePartialOrder
- CompleteSemilatticeInf
- CompleteSemilatticeSup
- ConditionallyCompleteLattice
- ConditionallyCompletePartialOrder
- ConditionallyCompletePartialOrderInf
- ConditionallyCompletePartialOrderSup
- DistribLattice
- GeneralizedCoheytingAlgebra
- GeneralizedHeytingAlgebra
- GradeBoundedOrder
- GradeMaxOrder
- GradeMinOrder
- GradeOrder
- HImp
- HNot
- HeytingAlgebra
- InfSet
- LE
- LT
- Lattice
- Max
- Min
- Nonempty
- OmegaCompletePartialOrder
- Order.Coframe
- Order.Frame
- OrderBot
- OrderTop
- PartialOrder
- Preorder
- SDiff
- SemilatticeInf
- SemilatticeSup
- SupSet
- Top