[Add] Properties for DCPOs in Relation.Binary.Properties.Domain
#2734
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jmougeot
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Relation.Binary.Properties.DomainRelation.Binary.Properties.Domain
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This pull request introduces new modules and properties for directed complete partial orders (DCPOs) in the Agda standard library. These additions are adapted from the 1Lab library.
The first part of this pull request is available at [Add] Initial files for Domain theory #2721 .
Please comment only on the
src/Relation/Binary/Properties/Domain.agdafile hereKey Changes:
1. Properties of Least Upper Bounds:
uniqueLub:Proves the uniqueness of least upper bounds.IsLub-cong: Demonstrates congruence of least upper bounds under equivalence.2. Scott Continuity and Monotonicity:
DirectedCompletePartialOrder+scott→monotone: Proves that Scott continuous functions are monotone.3. Scott Continuous Functions:
ScottId: Identity function as a Scott continuous function.scott-∘: Composition of Scott continuous functions.4. Suprema and Pointwise Ordering:
⋃-pointwise: Proves pointwise ordering of suprema in directed families.5. Scott Continuity Module:
pres-⋁: Proves preservation of least upper bounds under Scott continuous functions.6. Conversion to Scott Continuity:
-Added
to-scott: Converts monotone functions with preservation of least upper bounds into Scott continuous functions.Source :
1Lab library