reserve x,y,z for Real,
  a,b,c,d,e,f,g,h for Nat,
  k,l,m,n,m1,n1,m2,n2 for Integer,
  q for Rational;

theorem Th6:
  m gcd n = 1 & k gcd n = 1 implies m*k gcd n = 1
proof
  assume (m gcd n)=1 & (k gcd n)=1;
  then m,n are_coprime & k,n are_coprime by INT_2:def 3;
  then m*k,n are_coprime by INT_2:26;
  hence thesis by INT_2:def 3;
end;
