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

Fails if the theorem’s conclusion is not existentially quantified, or if the first argument is not a paired structure of variables. Failures may arise in the tactic-generating function. An invalid tactic is produced if the introduced variable is free in u or t, or if the theorem has any hypothesis which is not alpha-convertible to an assumption of the goal.
HOL  Kananaskis-14