reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem RI3:
  a1|^(m+2) + b1|^(m+2) =
    (a1+b1)*(a1|^(m+1) + b1|^(m+1)) - a1*b1*(a1|^(m)+ b1|^(m))
proof
  a1|^((m+1)+1) = a1*a1|^(m+1) & b1|^((m+1)+1) = b1*b1|^(m+1) &
  a1|^((m)+1) = a1*a1|^(m) & b1|^((m)+1) = b1*b1|^(m) by NEWTON:6;
  hence thesis;
end;
