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 Th4:
  k divides m & k divides n implies k divides m+n
proof
  assume that
A1: k divides m and
A2: k divides n;
  consider m1 such that
A3: m=k*m1 by A1;
  consider n1 such that
A4: n=k*n1 by A2;
  m+n=k*(m1+n1) by A3,A4;
  hence thesis;
end;
