formal/hol/Help/ANTE_RES_THEN.doc

\DOC ANTE_RES_THEN

\TYPE {ANTE_RES_THEN : thm_tactical}

\SYNOPSIS
Resolves implicative assumptions with an antecedent.

\KEYWORDS
theorem-tactic, resolution.

\DESCRIBE
Given a theorem-tactic {ttac} and a theorem {A |- t}, the function
{ANTE_RES_THEN} produces a tactic that attempts to match {t} to the antecedent
of each implication
{
   Ai |- !x1...xn. ui ==> vi
}
\noindent (where {Ai} is just {!x1...xn. ui ==> vi}) that occurs among the
assumptions of a goal. If the antecedent {ui} of any implication matches {t},
then an instance of {Ai u A |- vi} is obtained by specialization of the
variables {x1}, ..., {xn} and type instantiation, followed by an application of
modus ponens.  Because all implicative assumptions are tried, this may result
in several modus-ponens consequences of the supplied theorem and the
assumptions.  Tactics are produced using {ttac} from all these theorems, and
these tactics are applied in sequence to the goal.  That is,
{
   ANTE_RES_THEN ttac (A |- t) g
}
\noindent has the effect of:
{
   MAP_EVERY ttac [A1 u A |- v1; ...; Am u A |- vm] g
}
\noindent where the theorems {Ai u A |- vi} are all the consequences that can
be drawn by a (single) matching modus-ponens inference from the implications
that occur among the assumptions of the goal {g} and the supplied theorem
{A |- t}.

\FAILURE
{ANTE_RES_THEN ttac (A |- t)} fails when applied to a goal {g} if any of the
tactics produced by {ttac (Ai u A |- vi)}, where {Ai u A |- vi} is the {i}th
resolvent obtained from the theorem {A |- t} and the assumptions of {g}, fails
when applied in sequence to {g}.

\SEEALSO
IMP_RES_THEN, MATCH_MP, MATCH_MP_TAC.

\ENDDOC