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 Th5:
  k divides m & k divides n implies k divides m*m1+n*n1
proof
  assume k divides m & k divides n;
  then k divides m*m1 & k divides n*n1 by INT_2:2;
  hence thesis by Th4;
end;
