reserve A,B,O for Ordinal,
        o for object,
        x,y,z for Surreal,
        n,m for Nat;
reserve d,d1,d2 for Dyadic;
reserve i,j for Integer,
        n,m,p for Nat;
reserve r,r1,r2 for Real;

theorem Th56:
  - uReal.r == uReal.-r
proof
A1: uReal.r = Unique_No sReal.r &
  uReal.-r = Unique_No sReal.-r by Def7;
  then
A2: sReal.r == uReal.r & sReal.-r == uReal.-r &
  - sReal.r == sReal.-r by Lm14,SURREALO:def 10;
  - uReal.r == - sReal.r by A1,SURREALR:65,SURREALO:def 10;
  then - uReal.r == sReal.-r by A2,SURREALO:4;
  hence thesis by A2,SURREALO:4;
end;
