[isabelle] Monotonicity rules for function application

Dear all,

In the HOL library, many rules for reasoning about predicates which are closed under function composition (such as monotonicity, continuity and measurability) follow a common format:

1. There is a rule for the identity function: "P (%x. x)"
2. All the rules for function constants F are lifted over function composition, i.e., we use the rule
  "P ?f ==> P (%x. F (?f x))"
rather than
  "P F"

This way, "P <some complicated expression>" can be proved by resolving with the rules if all the constituent parts satisfy P.

For monotonicity rules as used by the partial_function package, there is one exception to this format, namely the rule call_mono:

  monotone (fun_ord ?ord) ?ord (Îf. f ?t)

Now, monotonicity proofs by resolution with the rules fail in my applications, because in my goal, I would need the lifted version of call_mono, namely

  monotone ?orda (fun_ord ?ord) ?F â monotone ?orda ?ord (Îf. ?F x ?y)    (***)

because my goal looks has the form

  monotone (fun_ord ord) ord (%f. G f x)

for some HOL term G, which is monotone, too.

My problem is that I don't know how to control resolution with (***). If I add (***) to the intro rules, then it also matches when there is no ?y that should be removed, i.e., the HO unifier has the form ?F = (%x y. ?F' x). Is there anything in the ML library that would only yield unifiers which do not discard the second argument to ?F? Do you have any suggestions how to solve this problem?


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