reserve a,b,c,d,x,j,k,l,m,n for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

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;
