A relation-extended-to-quantities is a relation that, when it is true on a sequence of arguments that are magnitudes (e.g., real numbers or tensors), then it is also true on a sequence of constant quantites with those magnitudes in some units.For example, the < relation is extended to quantities. That means that for all pairs of quantities q1 and q2, (< q1 q2) if and only if (< (magnitude q1 ?u) (magnitude q2 ?u)) for all units on which the two magnitudes are defined.
There may be relations that are not instances of this class that nonetheless hold for quantity arguments. To be a relation-extended-to-quantities means that the relation holds when all the arguments are of the same physical dimension.
(<=> (Relation-Extended-To-Quantities ?R)
(And (Relation ?R)
(Forall (@Args)
(<=> (And (Holds ?R @Args)
(=> (Item ?Q (Listof @Args))
(Constant-Quantity ?Q)))
(Forall (?Unit ?Q)
(=> (And (Unit-Of-Measure ?Unit)
(=> (Item ?Q (Listof @Args))
(Compatible-Quantities
?Q
?Unit)))
(Member (Map (Lambda
(?Q)
(Magnitude ?Q
?Unit))
(Listof @Args))
?R)))))))