theorem Th1:
  divL(o,Inv).0 = {0_No} & divR(o,Inv).0={}
proof
  divL(o,Inv).0 = L_(transitions_of(o,Inv).0) &
    divR(o,Inv).0 = R_(transitions_of(o,Inv).0) by Def5,Def6;
  then divL(o,Inv).0 = L_1_No & divR(o,Inv).0 = R_1_No by Def4;
  hence thesis;
end;
