 reserve n,m for Nat,
      o for object,
      p for pair object,
      x,y,z for Surreal;

theorem
  ex x,y be Surreal st x == y < 0_No & sqrt x < sqrt y
proof
  consider y be Surreal such that
A1: -1_No == y & sqrt y < -1_No &
  y = [{},{0_No,(sqrt(1_No*1_No+1_No)-1_No) *(sqrt(1_No*1_No+1_No)-1_No)}]
    by Th31,SURREALI:def 8;
  take y, -1_No;
  -1_No < -0_No by SURREALI:def 8,SURREALR:10;
  hence thesis by A1;
end;
