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Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > subCollection
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subCollection comparison table
Subject have domain2 have domain1 be first domain of documentation have axiom is a kind of is an instance of
BinaryPredicate  singleValuedA Predicate relating two items - its valence is two
(=>
 	(instance ?REL BinaryPredicate)
 	(valence ?REL 2))
Predicate 
IrreflexiveRelation  trichotomizingOnRelation ?REL is irreflexive if (?REL ?INST ?INST) holds for no value of ?INST
(=>
    (instance ?REL IrreflexiveRelation)
    (forall (?INST)
       (not 
          (holds ?REL ?INST ?INST))))
BinaryRelation 
TransitiveRelation  trichotomizingOnA BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
BinaryRelation 
subCollectionCollectionCollectionsingleValued(subCollection ?COLL1 ?COLL2) means that the Collection ?COLL1 is a proper part of the Collection ?COLL2
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
 TransitiveRelation

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