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

theorem Th6:
  sqrtL(p,o).0 = L_p & sqrtR(p,o).0=R_p
proof
  sqrtL(p,o).0 = L_((transitions_of(p,o)).0) &
  (sqrtR(p,o)).0 = R_((transitions_of(p,o)).0) by Def4,Def5;
  hence thesis by Def3;
end;
