X_CHOOSE_THEN : (term -> thm_tactical)
Replaces existentially quantified variable with given witness, and passes it to a theorem-tactic.
X_CHOOSE_THEN expects a variable y, a tactic-generating function f:thm->tactic, and a theorem of the form (A1 |- ?x. w) as arguments. A new theorem is created by introducing the given variable y as a witness for the object x whose existence is asserted in the original theorem, (w[y/x] |- w[y/x]). If the tactic-generating function f applied to this theorem produces results as follows when applied to a goal (A ?- t):
    A ?- t
   =========  f ({w[y/x]} |- w[y/x])
    A ?- t1
then applying (X_CHOOSE_THEN "y" f (A1 |- ?x. w)) to the goal (A ?- t) produces the subgoal:
    A ?- t
   =========  X_CHOOSE_THEN y f (A1 |- ?x. w)
    A ?- t1         (y not free anywhere)

Fails if the theorem’s conclusion is not existentially quantified, or if the first argument is not a variable. Failures may arise in the tactic-generating function. An invalid tactic is produced if the introduced variable is free in w, t or A, or if the theorem has any hypothesis which is not alpha-convertible to an assumption of the goal.
Given a goal of the form
   {n < m} ?- ?x. m = n + (x + 1)
the following theorem may be applied:
   th = [n < m] |- ?p. m = n + p
by the tactic (X_CHOOSE_THEN (Term`q:num`) SUBST1_TAC th) giving the subgoal:
   {n < m} ?- ?x. n + q = n + (x + 1)

HOL  Kananaskis-14