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 Th14:
  a|^(m+1)-b|^(m+1)=(a-b)*(t*(a+b)+a|^m+b|^m)/2 iff
  a|^m - b|^m = (a-b)*t
  proof
    a+b = 0 implies a|^m - b|^m = (a-b)*t
    proof
      assume a+b = 0; then
      a = 0 & b =0;
      hence thesis;
    end;
    hence thesis by Lm16,Lm17;
  end;
