A Unified View of Induction Reasoning for First-Order Logic

Induction is a powerful proof technique adapted to reason on setswith an unbounded number of elements. In a first-order setting, twodifferent methods are distinguished: the conventional induction,based on explicit induction schemas, and the implicit induction,based on reductive procedures. We propose a new cycle-basedinduction method that keeps their best features, i.e. i) performslazy induction, ii) naturally fits for mutual induction, and iii) isfree of reductive constraints. The heart of the method is a proofstrategy that identifies in the proof script the subset of formulascontributing to validate the application of induction hypotheses.The conventional and implicit induction are particular cases of ourmethod.