`CHOOSE_THEN : thm_tactical`

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 CONDITIONS
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
```  LT_EXISTS = |- !m n. m < n <=> (?d. n = m + SUC d)
```
to help solve the goal
```  # g `x < y ==> 0 < y * y`;;
```
by starting with the following tactic
```  # e(DISCH_THEN(CHOOSE_THEN SUBST1_TAC o REWRITE_RULE[LT_EXISTS]));;
```
reducing the goal to
```  val it : goalstack = 1 subgoal (1 total)

`0 < (x + SUC d) * (x + SUC d)`
```
which can then be finished off quite easily, by, for example just ARITH_TAC, or
```  # e(REWRITE_TAC[ADD_CLAUSES; MULT_CLAUSES; LT_0]);;
```