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

theorem Th17:
  x == y & y infinitely< z implies x infinitely< z
proof
  assume
A1:x==y & y infinitely< z;
  let r be positive Real;
  x*uReal.r == y*uReal.r < z by A1,SURREALR:51;
  hence thesis by SURREALO:4;
end;
