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
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'
A1 u A2 |- !xa..xk. t2'
- FAILURE CONDITIONS
Fails unless the first theorem is a (possibly repeatedly universally
quantified) implication 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.
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.
# let ith = ARITH_RULE `!x z:num. x = y ==> (w + z) + x = (w + z) + y`;;
val ith : thm = |- !x z. x = y ==> (w + z) + x = (w + z) + y
# let th = ASSUME `w:num = z`;;
val th : thm = w = z |- w = z
# MATCH_MP ith th;;
val it : thm = w = z |- !z'. (w + z') + w = (w + z') + z
- SEE ALSO
EQ_MP, MATCH_MP_TAC, MP, MP_TAC.