theorem Th12: :: NTALGO_1:12

for x, y being Integer
for b, m being non empty FinSequence of INT st 2 <= len b & ( for i, j being Nat st i in Seg (len b) & j in Seg (len b) & i <> j holds
b . i,b . j are_coprime ) & ( for i being Nat st i in Seg (len b) holds
x mod (b . i) = y mod (b . i) ) & m . 1 = 1 holds
for k being Element of NAT st 1 <= k & k <= len b & ( for i being Nat st 1 <= i & i <= k holds
m . (i + 1) = (m . i) * (b . i) ) holds
x mod (m . (k + 1)) = y mod (m . (k + 1))