CHOOSE_TAC : thm_tactic

SYNOPSIS

Adds the body of an existentially quantified theorem to the assumptions of a goal.

DESCRIPTION

When applied to a theorem A' |- ?x. t and a goal, CHOOSE_TAC adds t[x'/x] to the assumptions of the goal, where x' is a variant of x which is not free in the assumption list; normally x' is just x.

         A ?- u
   ====================  CHOOSE_TAC (A' |- ?x. t)
    A u {t[x'/x]} ?- u

Unless A' is a subset of A, this is not a valid tactic.

FAILURE CONDITIONS

Fails unless the given theorem is existentially quantified.

EXAMPLE

Suppose we have a goal asserting that the output of an electrical circuit (represented as a boolean-valued function) will become high at some time:

   ?- ?t. output(t)

and we have the following theorems available:

   t1 = |- ?t. input(t)
   t2 = !t. input(t) ==> output(t+1)

Then the goal can be solved by the application of:

   CHOOSE_TAC t1 THEN EXISTS_TAC `t+1` THEN
   UNDISCH_TAC `input (t:num) :bool` THEN MATCH_ACCEPT_TAC t2

SEE ALSO

CHOOSE_THEN, X_CHOOSE_TAC.