reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem
  (No_omega^ x)" == No_omega^ (-x)
proof
  set X = No_omega^ x;
A1:not No_omega^ x == 0_No by SURREALI:def 8;
  x - x == 0_No by SURREALR:39;
  then
A2: No_omega^ (x-x) == No_omega^ (0_No) = 1_No by Th26,Lm5;
  (No_omega^ x) * (No_omega^ (-x)) == No_omega^ (x-x) by Th27;
  then (No_omega^ x) * (No_omega^ (-x)) == No_omega^ (0_No) = 1_No
  by A2,SURREALO:4;
  hence thesis by SURREALI:42,A1;
end;
