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 is odd & b is odd & m is even implies a|^m + b|^m <> c|^m
  proof
    a is odd & b is odd implies a|^(2*n) + b|^(2*n) <> c|^(2*n)
    proof
  A1: a|^(2*n) = (a|^n)|^2 & b|^(2*n) = (b|^n)|^2 & c|^(2*n) = (c|^n)|^2
        by NEWTON:9;
      assume a is odd & b is odd;
      hence thesis by A1,Lm40;
    end;
    hence thesis;
  end;
