[MONOiD]

2.17 IsPreOrder

IsPreOrder( rel )

IsPreOrder returns true if the binary relation rel is a preoder and false otherwise. 

    gap> IsPreOrder( Relation( [ [  ], [ 1 ], [ 1, 2 ] ] ) );      
    false
    gap> IsPreOrder( Relation( [ [ 1, 2 ], [ 1, 2 ], [ 1, 2, 3 ] ] ) ); 
    true
A relation rel is called a preorder if rel is reflexive and transitive.

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Version 2.4 (May 1998)
[MONOiD]