Structures · Order
CompleteSemilatticeSup
Note that we rarely use CompleteSemilatticeSup
(in fact, any such object is always a CompleteLattice, so it's usually best to start there).
Nevertheless it is sometimes a useful intermediate step in constructions.
- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Shape
- One type argument · adds isLUB_sSup
Extends2
Extended by1
Concrete types that are instances7
- AlgebraicGeometry.Scheme.IdealSheafData
- ClosedSubmodule
- TwoSidedIdeal
- CategoryTheory.Subobject
- AbstractSimplicialComplex
- PreAbstractSimplicialComplex
- OrderDual
How is a type an instance?
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Assumed by24
- le_sSup
- sSup_le
- sSup_le_sSup
- isLUB_sSup
- IsLUB.sSup_eq
- le_iSup_iff
- sSup_singleton
- sSup_le_iff
- isLUB_iff_sSup_eq
- iSup_lt_iff
- le_sSup_of_le
- sSup_lt_iff
- CompleteSemilatticeSup.isLUB_sSup
- sSup_mem_upperBounds
- gc_sSup_Iic
- le_sSup_iff
- sSup_le_sSup_of_isCofinalFor
- isOrderRightAdjoint_sSup
- giSSupIic
- CompleteSemilatticeSup.toSupSet
- completeLatticeOfCompleteSemilatticeSup
- gi_sSup_Iic
- CompleteSemilatticeSup.toPartialOrder
- instCompleteSemilatticeInfOrderDualOfCompleteSemilatticeSup