Formal Verification of Robertson-Type Uncertainty Relation

Formal verification using interactive theorem provers have been noticed as a method of verifica-tion of proofs that are too big for humans to check the validity of them. The purpose of this work is to verify the validity of Robertson-type uncertainty relation toward verifying unconditional secu-rity of quantum key distributions. We verify the validity of the relation by using proof assistant Coq and it is turned out that the theorem regarding the relation formally holds. The source code for Coq which represents the validity of the theorem is printed in Appendix