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CHOOSE_THEN                                                 (Thm_cont)
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CHOOSE_THEN : thm_tactical

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

KEYWORDS
theorem-tactic, existential.

DESCRIBE
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
Tactic.CHOOSE_TAC, Thm_cont.X_CHOOSE_THEN.

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