PART_MATCH : (term -> term) -> thm -> term -> thm
Instantiates a theorem by matching part of it to a term.
When applied to a ‘selector’ function of type term -> term, a theorem and a term:
   PART_MATCH fn (A |- !x1...xn. t) tm
the function PART_MATCH applies fn to t' (the result of specializing universally quantified variables in the conclusion of the theorem), and attempts to match the resulting term to the argument term tm. If it succeeds, the appropriately instantiated version of the theorem is returned.
Fails if the selector function fn fails when applied to the instantiated theorem, or if the match fails with the term it has provided.

Since PART_MATCH will not instantiate variables which appear in the hypotheses of the given theorem, it fails if the attempted match would require instantiating these variables. To allow instantiation of these variables, use PART_MATCH_A.

Suppose that we have the following theorem:
   th = |- !x. x==>x
then the following:
   PART_MATCH (fst o dest_imp) th "T"
results in the theorem:
   |- T ==> T
because the selector function picks the antecedent of the implication (the inbuilt specialization gets rid of the universal quantifier), and matches it to T.
HOL  Kananaskis-14