STRIP_THM_THEN : thm_tactical

SYNOPSIS

STRIP_THM_THEN applies the given theorem-tactic using the result of stripping off one outer connective from the given theorem.

DESCRIPTION

Given a theorem-tactic ttac, a theorem th whose conclusion is a conjunction, a disjunction or an existentially quantified term, and a goal (A,t), STRIP_THM_THEN ttac th first strips apart the conclusion of th, next applies ttac to the theorem(s) resulting from the stripping and then applies the resulting tactic to the goal. In particular, when stripping a conjunctive theorem A' |- u /\ v, the tactic

   ttac(u |- u) THEN ttac(v |- v)

resulting from applying ttac to the conjuncts, is applied to the goal. When stripping a disjunctive theorem A' |- u \/ v, the tactics resulting from applying ttac to the disjuncts, are applied to split the goal into two cases. That is, if

    A ?- t                           A ?- t
   =========  ttac (u |- u)    and    =========  ttac (v |- v)
    A ?- t1                          A ?- t2

then:

         A ?- t
   ==================  STRIP_THM_THEN ttac (A' |- u \/ v)
    A ?- t1  A ?- t2

When stripping an existentially quantified theorem A' |- ?x.u, the tactic ttac(u |- u), resulting from applying ttac to the body of the existential quantification, is applied to the goal. That is, if:

    A ?- t
   =========  ttac (u |- u)
    A ?- t1

then:

      A ?- t
   =============  STRIP_THM_THEN ttac (A' |- ?x. u)
      A ?- t1

The assumptions of the theorem being split are not added to the assumptions of the goal(s) but are recorded in the proof. If A' is not a subset of the assumptions A of the goal (up to alpha-conversion), STRIP_THM_THEN ttac th results in an invalid tactic.

FAILURE CONDITIONS

STRIP_THM_THEN ttac th fails if the conclusion of th is not a conjunction, a disjunction or an existentially quantified term. Failure also occurs if the application of ttac fails, after stripping the outer connective from the conclusion of th.

USES

STRIP_THM_THEN is used enrich the assumptions of a goal with a stripped version of a previously-proved theorem.