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

theorem Th56:
  not x == 0_No implies omega-y x = omega-y - x
proof
  assume
A1: not x == 0_No;
  then
A2: |.x.|, No_omega^ omega-y x are_commensurate by Def7;
A3: |.x.| =|.-x.| by A1,Th39;
  not - x == 0_No by A1,SURREALR:24;
  hence thesis by A2,A3,Def7;
end;
