X_CHOOSE_TAC : term -> thm_tactic
Assumes a theorem, with existentially quantified variable replaced by a given witness.
X_CHOOSE_TAC expects a variable y and theorem with an existentially quantified conclusion. When applied to a goal, it adds a new assumption obtained by introducing the variable y as a witness for the object x whose existence is asserted in the theorem.
           A ?- t
   ===================  X_CHOOSE_TAC y (A1 |- ?x. w)
    A u {w[y/x]} ?- t         (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_TAC (Term`q:num`) th) giving the subgoal:
   {n < m, m = n + q} ?- ?x. m = n + (x + 1)

HOL  Kananaskis-14