Abstract
Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a ``difference matching'' procedure. The critic then proposes lemmas and generalizations which ``ripple'' these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.
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