
theorem Th31:
  for u being INT-valued FinSequence, m being CR_Sequence st
  len m = len u holds 0 <= to_int(u,m) & to_int(u,m) < Product(m)
proof
  let u be INT-valued FinSequence, m be CR_Sequence;
  set z = to_int(u,m);
  set c = the CR_coefficients of m;
  assume len u = len m;
  then z = Sum(u(#)c) mod Product(m) by Def5;
  hence thesis by NAT_D:62;
end;
