reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;

theorem
  a + b = k*a + k*b & a*b > 0 implies k = 1
  proof
    assume
    A0: a + b = k*a + k*b & a*b > 0; then
    (k-1)*(a + b) = 0; then
    a + b = 0 or k -1 = 0; then
    a = 0 or k = 1;
    hence thesis by A0;
  end;
