PairRules.FILTER_PSTRIP

Stripping apart a goal in a more careful way than is done by PSTRIP_TAC may be necessary when dealing with quantified terms and implications. FILTER_PSTRIP_TAC behaves like PSTRIP_TAC, but it does not strip apart a goal if it contains a given term.

If u is a term, then FILTER_PSTRIP_TAC u is a tactic that removes one outermost occurrence of one of the connectives !, ==>, ~ or /\ from the conclusion of the goal t, provided the term being stripped does not contain u. FILTER_PSTRIP_TAC will strip paired universal quantifications. A negation ~t is treated as the implication t ==> F. FILTER_PSTRIP_TAC also breaks apart conjunctions without applying any filtering.

If t is a universally quantified term, FILTER_PSTRIP_TAC u strips off the quantifier:

      A ?- !p. v
   ================  FILTER_PSTRIP_TAC "u"       [where p is not u]
     A ?- v[p'/p]

where p' is a primed variant of the pair p that does not contain any variables that appear free in the assumptions A. If t is a conjunction, no filtering is done and FILTER_PSTRIP_TAC simply splits the conjunction:

      A ?- v /\ w
   =================  FILTER_PSTRIP_TAC "u"
    A ?- v   A ?- w

If t is an implication and the antecedent does not contain a free instance of u, then FILTER_PSTRIP_TAC u moves the antecedent into the assumptions and recursively splits the antecedent according to the following rules (see PSTRIP_ASSUME_TAC):

    A ?- v1 /\ ... /\ vn ==> v            A ?- v1 \/ ... \/ vn ==> v
   ============================        =================================
       A u {v1,...,vn} ?- v             A u {v1} ?- v ... A u {vn} ?- v

     A ?- (?p. w) ==> v
   ====================
    A u {w[p'/p]} ?- v

where p' is a variant of the pair p.