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

theorem Th14:
  for x,y,z be Surreal st x infinitely< y infinitely< z
    holds x infinitely< z
proof
  let x,y,z be Surreal such that
A1: x infinitely< y infinitely< z;
  let r be positive Real;
  y * uReal.1 < z by A1;
  then y <= z by SURREALN:48;
  hence thesis by A1,SURREALO:4;
end;
