Description
Please use the Coq file hw2-2.v[1] to show the following instance of the Chinese remainder theorem:
Theorem 1. Let m,n ∈ Z and m,n be relatively prime. For every a,b ∈Z, there is an x ∈Z such that
x ≡ a (m) x ≡ b (n).
Hints:
- Bezout’s coefficients in the Coq standard library Znumtheory[2]will be useful.
- A useful on-line information is Software Foundations[3].
- Another useful on-line information is Certified Programming with Dependent Types[4].
- Send me emails if you have any question.
1
[1] http://www.iis.sinica.edu.tw/~bywang/courses/comp-logic/hw2-2.v
[2] https://coq.inria.fr/distrib/current/stdlib/
[3] https://softwarefoundations.cis.upenn.edu/current/index.html
