(SUBSETP (APPEND (FOO A) (BAR B)) (MUM C))
Major Section: INTRODUCTION-TO-THE-THEOREM-PROVER
What rules come to mind when looking at the following subterm of a Key Checkpoint? Think of strong rules (see strong-rewrite-rules).
(SUBSETP (APPEND (FOO A) (BAR B)) (MUM C))
When is (append x y) a subset of z? When everything in
x is in z and everything in y is in z. We would
make it a rewrite rule:
(defthm subsetp-append-1-strong
(equal (subsetp (append x y) z)
(and (subsetp x z)
(subsetp y z))))
We put the ``-1-'' in the name because there is a comparable
theorem for when the append is in the second argument of the subsetp;
see practice-formulating-strong-rules-5.
This strong rule is better than the conditional rule;
(defthm subsetp-append-1-weak
(implies (and (subsetp x z)
(subsetp y z))
(subsetp (append x y) z)))
for all the usual reasons.Use your browser's Back Button now to return to practice-formulating-strong-rules.