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This book constitutes the refereed proceedings of the 9th International Conference on Tests and Proofs, TAP 2015, held in L` Aquila, Italy, in July 2015, as part of the STAF 2015 Federated Conferences. The 11 revised full papers and 1 short papers presented together with 3 invited talks were carefully reviewed and selected from 21 submissions.

This book constitutes the refereed proceedings of the 7th International Conference on Interactive Theorem Proving, ITP 2016, held in Nancy, France, in August 2016.
The 27 full papers and 5 short papers presented were carefully reviewed and selected from 55 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematical theories.