Thm_cont.CHOOSE

STRUCTURE

SYNOPSIS

Applies a tactic generated from the body of existentially quantified theorem.

DESCRIPTION

When applied to a theorem-tactic ttac, an existentially quantified theorem A' |- ?x. t, and a goal, CHOOSE_THEN applies the tactic ttac (t[x'/x] |- t[x'/x]) to the goal, where x' is a variant of x chosen not to be free in the assumption list of the goal. Thus if:

    A ?- s1
   =========  ttac (t[x'/x] |- t[x'/x])
    B ?- s2

then

    A ?- s1
   ==========  CHOOSE_THEN ttac (A' |- ?x. t)
    B ?- s2

This is invalid unless A' is a subset of A.

FAILURE

Fails unless the given theorem is existentially quantified, or if the resulting tactic fails when applied to the goal.

EXAMPLE

This theorem-tactical and its relatives are very useful for using existentially quantified theorems. For example one might use the inbuilt theorem

   LESS_ADD_1 = |- !m n. n < m ==> (?p. m = n + (p + 1))

to help solve the goal

   ?- x < y ==> 0 < y * y

by starting with the following tactic

   DISCH_THEN (CHOOSE_THEN SUBST1_TAC o MATCH_MP LESS_ADD_1)

which reduces the goal to

   ?- 0 < ((x + (p + 1)) * (x + (p + 1)))

which can then be finished off quite easily, by, for example:

   REWRITE_TAC[ADD_ASSOC, SYM (SPEC_ALL ADD1),
               MULT_CLAUSES, ADD_CLAUSES, LESS_0]

SEEALSO

CHOOSE_TAC, X_CHOOSE_THEN