theorem Th104:
  x in H + a iff ex g st x = g + a & g in H
proof
  thus x in H + a implies ex g st x = g + a & g in H
  proof
    assume x in H + a;
    then consider g such that
A1: x = g + a & g in carr(H) by Th28;
    take g;
    thus thesis by A1;
  end;
  given g such that
A2: x = g + a and
A3: g in H;
  thus thesis by A2,A3,Th28;
end;
