theorem Th40:
  a*b,c*d are_coprime implies a,c are_coprime
  proof
    assume
    A1: a*b, c*d are_coprime;
    A3: a gcd c divides a*b by INT_2:2,21;
    a gcd c divides c*d by INT_2:2,21;
    hence a, c are_coprime by A1,A3,WSIERP_1:15,INT_2:22;
  end;
