Thm* r: , s:{s': | CoPrime(r,s') }, a,b: .
Thm*  x: . ((x = a mod r) & (x = b mod s)) | [chrem_exists_a] |
Thm* r,s: . CoPrime(r,s)  ( a,b: . x: . (x = a mod r) & (x = b mod s)) | [chrem_exists] |
Thm* r: , s:{s': | CoPrime(r,s') }.  x: . ((x = 1 mod r) & (x = 0 mod s)) | [chrem_exists_aux_a] |
Thm* r,s: . CoPrime(r,s)  ( x: . (x = 1 mod r) & (x = 0 mod s)) | [chrem_exists_aux] |
Thm* m,a,a',b,b': . (a = a' mod m)  (b = b' mod m)  ((a b) = (a' b') mod m) | [multiply_functionality_wrt_eqmod] |
Thm* m,a,a',b,b': . (a = a' mod m)  (b = b' mod m)  ((a+b) = (a'+b') mod m) | [add_functionality_wrt_eqmod] |
Thm* m,a,a',b,b': .
Thm* (a = a' mod m)  (b = b' mod m)  ((a = b mod m)  (a' = b' mod m)) | [eqmod_fun] |
Thm* m,m',a,a',b,b': .
Thm* m = m'
Thm* 
Thm* (a = a' mod m)  (b = b' mod m)  ((a = b mod m)  (a' = b' mod m')) | [eqmod_functionality_wrt_eqmod] |
Thm* m,a,b: . (a = b mod m)  (b = a mod m) | [eqmod_inversion] |
Thm* m,a,b,c: . (a = b mod m)  (b = c mod m)  (a = c mod m) | [eqmod_transitivity] |
Thm* m,a,b: . a = b  (a = b mod m) | [eqmod_weakening] |