Drule.MATCH

STRUCTURE

SYNOPSIS

Modus Ponens inference rule with automatic matching.

DESCRIPTION

When applied to theorems A1 |- !x1...xn. t1 ==> t2 and A2 |- t1', the inference rule MATCH_MP matches t1 to t1' by instantiating free or universally quantified variables in the first theorem (only), and returns a theorem A1 u A2 |- !xa..xk. t2', where t2' is a correspondingly instantiated version of t2. Polymorphic types are also instantiated if necessary.

Variables free in the consequent but not the antecedent of the first argument theorem will be replaced by variants if this is necessary to maintain the full generality of the theorem, and any which were universally quantified over in the first argument theorem will be universally quantified over in the result, and in the same order.

    A1 |- !x1..xn. t1 ==> t2   A2 |- t1'
   --------------------------------------  MATCH_MP
          A1 u A2 |- !xa..xk. t2'

As with MP and the underlying syntactic function dest_imp, negated terms (of the form ~p) are treated as if they were implications from the argument of the negation to falsity.

FAILURE

Fails unless the first theorem is a (possibly repeatedly universally quantified) implication (in the sense of dest_imp) whose antecedent can be instantiated to match the conclusion of the second theorem, without instantiating any variables which are free in A1, the first theorem’s assumption list.

EXAMPLE

In this example, automatic renaming occurs to maintain the most general form of the theorem, and the variant corresponding to z is universally quantified over, since it was universally quantified over in the first argument theorem.

   - val ith = (GENL [Term `x:num`, Term `z:num`]
                  o DISCH_ALL
                  o AP_TERM (Term `$+ (w + z)`))
               (ASSUME (Term `x:num = y`));
   > val ith = |- !x z. (x = y) ==> (w + z + x = w + z + y) : thm

   - val th = ASSUME (Term `w:num = z`);
   > val th = [w = z] |- w = z : thm

   - MATCH_MP ith th;
   > val it =  [w = z] |- !z'. w' + z' + w = w' + z' + z : thm

SEEALSO

dest_imp, EQ_MP, MATCH_MP_TAC, MP, MP_TAC, CONSEQ_REWRITE_CONV