reserve A,B,C for Ordinal,
        o for object,
        x,y,z,t,r,l for Surreal,
        X,Y for set;

theorem Th56:
  x * 0_No = 0_No
proof
  A1: comp(L_x,x,0_No,L_0_No) ={} & comp(R_x,x,0_No,R_0_No) = {} by Th49;
  x * 0_No = [comp(L_x,x,0_No,L_0_No) \/ comp(R_x,x,0_No,R_0_No),
              comp(L_x,x,0_No,L_0_No) \/ comp(R_x,x,0_No,L_0_No)] by Th50;
  hence thesis by A1;
end;
