`CHOOSE_THEN : thm_tactical`
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),