PairRules.PSTRIP_ASSUME

Given a theorem th and a goal (A,t), PSTRIP_ASSUME_TAC th splits th into a list of theorems. This is done by recursively breaking conjunctions into separate conjuncts, cases-splitting disjunctions, and eliminating paired existential quantifiers by choosing arbitrary variables. Schematically, the following rules are applied:

           A ?- t
   ======================  PSTRIP_ASSUME_TAC (A' |- v1 /\ ... /\ vn)
    A u {v1,...,vn} ?- t

                A ?- t
   =================================  PSTRIP_ASSUME_TAC (A' |- v1 \/ ... \/ vn)
    A u {v1} ?- t ... A u {vn} ?- t

          A ?- t
   ====================  PSTRIP_ASSUME_TAC (A' |- ?p. v)
    A u {v[p'/p]} ?- t

where p' is a variant of the pair p.

If the conclusion of th is not a conjunction, a disjunction or a paired existentially quantified term, the whole theorem th is added to the assumptions.

As assumptions are generated, they are examined to see if they solve the goal (either by being alpha-equivalent to the conclusion of the goal or by deriving a contradiction).

The assumptions of the theorem being split are not added to the assumptions of the goal(s), but they are recorded in the proof. This means that if A' is not a subset of the assumptions A of the goal (up to alpha-conversion), PSTRIP_ASSUME_TAC (A'|-v) results in an invalid tactic.