theorem Th55:
  uReal.r1 + uReal.r2 == uReal.(r1+r2)
proof
  uReal.r1 = Unique_No sReal.r1 &
  uReal.r2 = Unique_No sReal.r2 by Def7;
  then sReal.r1 == uReal.r1 & sReal.r2 == uReal.r2 by SURREALO:def 10;
  then uReal.r1 + uReal.r2 == sReal.r1 + sReal.r2 ==
  sReal.(r1+r2) by SURREALR:43,Lm13;
  then A1:uReal.r1 + uReal.r2 == sReal.(r1+r2) by SURREALO:4;
  uReal.(r1+r2) = Unique_No sReal.(r1+r2) by Def7;
  then sReal.(r1+r2) == uReal.(r1+r2) by SURREALO:def 10;
  hence thesis by A1,SURREALO:4;
end;
