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

theorem Th42:
  |.x.| infinitely< z implies |. -x .| infinitely< z
proof
  assume
A1: |.x.| infinitely< z;
  let r be positive Real;
  |. -x .| * uReal.r == |.x.| * uReal.r < z by Th40,A1,SURREALR:51;
  hence thesis by SURREALO:4;
end;
