MATCH_MP
Drule.MATCH_MP : thm -> thm -> thm
Modus Ponens inference rule with automatic matching.
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
See also
boolSyntax.dest_imp,
Thm.EQ_MP,
Tactic.MATCH_MP_TAC, Thm.MP,
Tactic.MP_TAC,
ConseqConv.CONSEQ_REWRITE_CONV