PairRules.PSTRIP_GOAL

STRUCTURE

LIBRARY

pair

SYNOPSIS

Splits a goal by eliminating one outermost connective, applying the given theorem-tactic to the antecedents of implications.

DESCRIPTION

Given a theorem-tactic ttac and a goal (A,t), PSTRIP_GOAL_THEN removes one outermost occurrence of one of the connectives !, ==>, ~ or /\ from the conclusion of the goal t. If t is a universally quantified term, then STRIP_GOAL_THEN strips off the quantifier. Note that PSTRIP_GOAL_THEN will strip off paired universal quantifications.

      A ?- !p. u
   ==============  PSTRIP_GOAL_THEN ttac
    A ?- u[p'/p]

where p' is a primed variant that contains no variables that appear free in the assumptions A. If t is a conjunction, then PSTRIP_GOAL_THEN simply splits the conjunction into two subgoals:

      A ?- v /\ w
   =================  PSTRIP_GOAL_THEN ttac
    A ?- v   A ?- w

If t is an implication "u ==> v" and if:

      A ?- v
  ===============  ttac (u |- u)
     A' ?- v'

then:

      A ?- u ==> v
  ====================  PSTRIP_GOAL_THEN ttac
        A' ?- v'

Finally, a negation ~t is treated as the implication t ==> F.

FAILURE

PSTRIP_GOAL_THEN ttac (A,t) fails if t is not a paired universally quantified term, an implication, a negation or a conjunction. Failure also occurs if the application of ttac fails, after stripping the goal.

USES

PSTRIP_GOAL_THEN is used when manipulating intermediate results (obtained by stripping outer connectives from a goal) directly, rather than as assumptions.

SEEALSO

PGEN_TAC, STRIP_GOAL_THEN, FILTER_PSTRIP_THEN, PSTRIP_TAC, FILTER_PSTRIP_TAC