Tactic.IMP_RES

Given a theorem th, the theorem-tactic IMP_RES_TAC uses RES_CANON to derive a canonical list of implications, each of which has the form:

   A |- u1 ==> u2 ==> ... ==> un ==> v

IMP_RES_TAC then tries to repeatedly ‘resolve’ these theorems against the assumptions of a goal by attempting to match the antecedents u1, u2, ..., un (in that order) to some assumption of the goal (i.e. to some candidate antecedents among the assumptions). If all the antecedents can be matched to assumptions of the goal, then an instance of the theorem

   A u {a1,...,an} |- v

called a ‘final resolvent’ is obtained by repeated specialization of the variables in the implicative theorem, type instantiation, and applications of modus ponens. If only the first i antecedents u1, ..., ui can be matched to assumptions and then no further matching is possible, then the final resolvent is an instance of the theorem:

   A u {a1,...,ai} |- u(i+1) ==> ... ==> v

All the final resolvents obtained in this way (there may be several, since an antecedent ui may match several assumptions) are added to the assumptions of the goal, in the stripped form produced by using STRIP_ASSUME_TAC. If the conclusion of any final resolvent is a contradiction ‘F’ or is alpha-equivalent to the conclusion of the goal, then IMP_RES_TAC solves the goal.