
theorem Th22:
  for i,j being Integer st i,j are_coprime holds ex s being
  Integer st s*i,1 are_congruent_mod j
proof
  let i,j be Integer;
  assume i gcd j = 1;
  then consider s,t being Integer such that
A1: 1 = s * i + t * j by NAT_D:68;
  take s;
  s * i - 1 = (-t) * j by A1;
  then j divides (s*i - 1) by INT_1:def 3;
  hence thesis by INT_2:15;
end;
