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PMATCH_MP_TAC                                              (PairRules)
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PMATCH_MP_TAC : thm_tactic

KEYWORDS
tactic, modus ponens, implication.

LIBRARY
pair

SYNOPSIS
Reduces the goal using a supplied implication, with matching.

DESCRIBE
When applied to a theorem of the form

   A' |- !p1...pn. s ==> !q1...qm. t

{PMATCH_MP_TAC} produces a tactic that reduces a goal whose
conclusion {t'} is a substitution and/or type instance of {t} to the
corresponding instance of {s}. Any variables free in {s} but not in {t} will
be existentially quantified in the resulting subgoal:

     A ?- !u1...ui. t'
  ======================  PMATCH_MP_TAC (A' |- !p1...pn. s ==> !q1...qm. t)
     A ?- ?w1...wp. s'

where {w1}, ..., {wp} are (type instances of) those pairs among
{p1}, ..., {pn} having variables that do not occur free in {t}.
Note that this is not a valid tactic unless {A'} is a subset of {A}.

FAILURE
Fails unless the theorem is an (optionally paired universally quantified)
implication whose consequent can be instantiated to match the goal.
The generalized pairs {u1}, ..., {ui} must occur in {s'} in order for the
conclusion {t} of the supplied theorem to match {t'}.

SEEALSO
Tactic.MATCH_MP_TAC.

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