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 Th1:
  a1|^2 - b1|^2 = (a1-b1)*(a1+b1)
  proof
    a1|^2 = a1^2 & b1|^2 = b1^2 by NEWTON:81;
    hence thesis by SQUARE_1:8;
  end;
