theorem Th42: :: INT_4:42

for m1, m2, c1, c2 being Integer st m1 <> 0 & m2 <> 0 & m1 gcd m2 divides c2 - c1 holds
ex r being Integer st
( ( for x being Integer st (x - c1) mod m1 = 0 & (x - c2) mod m2 = 0 holds
x,c1 + (m1 * r) are_congruent_mod m1 lcm m2 ) & (((m1 div (m1 gcd m2)) * r) - ((c2 - c1) div (m1 gcd m2))) mod (m2 div (m1 gcd m2)) = 0 )