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A Unified View of Induction Reasoning for First-Order Logic

Induction is a powerful proof technique adapted to reason on sets with an unbounded number of elements. In a first-order setting, two different methods are distinguished: the conventional induction, based on explicit induction schemas, and the implicit induction, based on reductive procedures. We propose a new cycle-based induction method that keeps their best features, i.e., performs local and non-reductive reasoning, and naturally fits for mutual and lazy induction. The heart of the method is a proof strategy that identifies in the proof script the subset of formulas contributing to validate the application of induction hypotheses. The conventional and implicit induction are particular cases of our method.