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DEEP_INTRO_TAC                                                (Tactic)
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DEEP_INTRO_TAC : thm -> tactic

SYNOPSIS
Applies an introduction-rule backwards; instantiating a predicate variable.

KEYWORDS
matching

DESCRIBE
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}.

FAILURE
Fails if there is no (free) instance of {term-pattern} in the goal.
Also fails if {th} is not of the required form.

EXAMPLE
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.

SEEALSO
Tactic.MATCH_MP_TAC, Tactic.SELECT_ELIM_TAC.

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