 reserve A,B,O for Ordinal,
      n,m for Nat,
      a,b,o for object,
      x,y,z for Surreal,
      X,Y,Z for set,
      Inv,I1,I2 for Function;

theorem Th7:
   divs(o,x,X,Inv) = divs(o,x,X\{0_No},Inv)
proof
  thus divs(o,x,X,Inv) c= divs(o,x,X\{0_No},Inv)
  proof
    let a;
    assume a in divs(o,x,X,Inv);
    then consider xL be object such that
A1: xL in X & xL <> 0_No &
    a = (1_No +'(xL +' -' x) *' o) *' (Inv.xL) by Def2;
    xL in X\{0_No} by A1,ZFMISC_1:56;
    hence thesis by A1,Def2;
  end;
  let a;
  assume a in divs(o,x,X\{0_No},Inv);
  then consider xL be object such that
A2: xL in X\{0_No} & xL <> 0_No &
  a = (1_No +'(xL +' -' x) *' o) *' (Inv.xL) by Def2;
  thus thesis by A2,Def2;
end;
