DEEP_INTRO_TAC : thm -> tactic
Applies an introduction-rule backwards; instantiating a predicate variable.
The function DEEP_INTRO_TAC expects a theorem of the form
   antecedents ==> P (term-pattern)
where P is a variable, and term-pattern is a pattern describing the form of an expected sub-term in the goal. When th is of this form, the tactic DEEP_INTRO_TAC th finds a higher-order instantiation for the variable P and a first order instantiation for the variables in term-pattern such that the instantiated conclusion of th is identical to the goal. It then applies MATCH_MP_TAC to turn the goal into an instantiation of the antecedents of th.
Fails if there is no (free) instance of term-pattern in the goal. Also fails if th is not of the required form.
The theorem SELECT_ELIM_THM states
   |- !P Q. (?x. P x) /\ (!x. P x ==> Q x) ==> Q ($@ P)
This is of the required form for use by DEEP_INTRO_TAC, and can be used to transform a goal mentioning Hilbert Choice (the @ operator) into one that doesn’t. Indeed, this is how SELECT_ELIM_TAC is implemented.
HOL  Kananaskis-14