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Performing Implicit Induction Reasoning with Certifying Proof Environments

Abstract : Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers allow for lazy and mutual induction reasoning. In this paper, we present a new tactic for the Coq proof assistant able to perform automatically implicit induction reasoning. By using an automatic black-box approach, conjectures intended to be manually proved by the certifying proof environment that integrates Coq are proved instead by the Spike implicit induction theorem prover. The resulting proofs are translated afterwards into certified Coq scripts.
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https://hal.inria.fr/hal-00764909
Contributor : Sorin Stratulat <>
Submitted on : Thursday, December 13, 2012 - 4:01:20 PM
Last modification on : Tuesday, December 18, 2018 - 4:38:25 PM
Long-term archiving on: : Sunday, December 18, 2016 - 12:50:53 AM

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Amira Henaien, Sorin Stratulat. Performing Implicit Induction Reasoning with Certifying Proof Environments. SCSS'2012 - 4th International Symposium on Symbolic Computation in Software Science, Dec 2012, Gammarth, Tunisia. ⟨hal-00764909⟩

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