The WARNING about the Trivial Consequence

This Warning alerts us to the fact that when treated as a rewrite rule, the new rule TRIVIAL-CONSEQUENCE, rewrites terms of the same form as a rule we have already proved, namely ASSOCIATIVITY-OF-APP.

When you see this warning you should think about your rules!

In the current case, it would be a good idea not to make TRIVIAL-CONSEQUENCE a rule at all. We could do this with :rule-classes nil.

ACL2 proceeds to try to prove the theorem, even though it printed some warnings. The basic assumption in ACL2 is that the user understands what he or she is doing but may need a little reminding just to manage a complicated set of facts.