Z-modules
Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Formalization of Orthogonal Complements of Normed Spaces
Okazaki, Hiroyuki
Gaussian Integers
Futa, Yuichi, Okazaki, Hiroyuki, Mizushima, Daichi, Shidama, Yasunari
Formalization of the Data Encryption Standard
Okazaki, Hiroyuki, Shidama, Yasunari
Difference of Function on Vector Space over F
Arai, Kenichi, Wakabayashi, Ken, Okazaki, Hiroyuki
Probability on Finite Set and Real-Valued Random Variables
Okazaki, Hiroyuki, Shidama, Yasunari
Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module
Nakasho, Kazuhisa, Futa, Yuichi, Okazaki, Hiroyuki, Shidama, Yasunari
Real Vector Space and Related Notions
Nakasho, Kazuhisa, Okazaki, Hiroyuki, Shidama, Yasunari
Banach Algebra of Bounded Complex-Valued Functionals
Kanazashi, Katuhiko, Okazaki, Hiroyuki, Shidama, Yasunari
Equivalent Expressions of Direct Sum Decomposition of Groups1
Nakasho, Kazuhisa, Okazaki, Hiroyuki, Yamazaki, Hiroshi, Shidama, Yasunari
Extended Euclidean Algorithm and CRT Algorithm
Okazaki, Hiroyuki, Aoki, Yosiki, Shidama, Yasunari
Normal Subgroup of Product of Groups
Okazaki, Hiroyuki, Arai, Kenichi, Shidama, Yasunari