Thm* r,s: . CoPrime(r,s)  ( a,b: . x: . (x = a mod r) & (x = b mod s)) | [chrem_exists] |
Thm* r,s: . CoPrime(r,s)  ( x: . (x = 1 mod r) & (x = 0 mod s)) | [chrem_exists_aux] |
Thm* a,b: . CoPrime(a,b)  ( x,y: . a x+b y = 1) | [coprime_bezout_id] |
Thm* a,b: . ( x,y: . a x+b y = 1)  CoPrime(a,b) | [coprime_bezout_id2] |
Thm* a,b: . CoPrime(a,b)  ( x,y: . a x+b y = 1) | [coprime_bezout_id1] |
Thm* a,b: . CoPrime(a,b)  ( x,y: . (a x+b y) ~ 1) | [coprime_bezout_id0] |
Thm* a,b: . u,v: . GCD(a;b;u a+v b) | [bezout_ident] |
Thm* b: , a: . u,v: . GCD(a;b;u a+v b) | [bezout_ident_n] |
Thm* a,b: . y: . GCD(a;b;y) | [gcd_exists] |
Thm* b: , a: . y: . GCD(a;b;y) | [gcd_exists_n] |
Thm* a: , b: . q: , r: b. a = q b+r | [quot_rem_exists] |
Thm* a: , b: . q: , r: b. a = q b+r | [quot_rem_exists_n] |
Thm* a,b: . y: . GCD(a;b;y) & gcd(a;b) = y | [gcd_elim] |
Thm* a,b: . a | b  ( c: . b = a c  ) | [divides_nchar] |
Def reducible(a) == b,c:  . (b ~ 1) & (c ~ 1) & a = b c | [reducible] |
Def b | a == c: . a = b c | [divides] |