STRIP_GOAL_THEN : thm_tactic -> tactic

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), STRIP_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:

      A ?- !x.u
   ==============  STRIP_GOAL_THEN ttac
     A ?- u[x'/x]

where x' is a primed variant that does not appear free in the assumptions A. If t is a conjunction, then STRIP_GOAL_THEN simply splits the conjunction into two subgoals:

      A ?- v /\ w
   =================  STRIP_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
  ====================  STRIP_GOAL_THEN ttac
        A' ?- v'

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

FAILURE CONDITIONS

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

EXAMPLE

When solving the goal

  # g `n = 1 ==> n * n = n`;;
  Warning: Free variables in goal: n
  val it : goalstack = 1 subgoal (1 total)

  `n = 1 ==> n * n = n`

a possible initial step is to apply

  # e(STRIP_GOAL_THEN SUBST1_TAC);;
  val it : goalstack = 1 subgoal (1 total)

  `1 * 1 = 1`

which is immediate by ARITH_TAC, for example.

USES

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