theorem Th122:
  H + a + b c= (H + a) + (H + b)
proof
  let x be object;
A1: 0_G + b in H + b by Th46,Th104;
  assume x in H + a + b;
  then x in H + (a + b) by ThB34;
  then consider g such that
A2: x = g + (a + b) and
A3: g in H by Th104;
A4: x = g + a + b by A2,RLVECT_1:def 3
    .= g + a + (0_G + b) by Def4;
  g + a in H + a by A3,Th104;
  hence thesis by A1,A4;
end;
