theorem Th94:
  x in A + H iff ex g1,g2 st x = g1 + g2 & g1 in A & g2 in H
proof
  thus x in A + H implies ex g1,g2 st x = g1 + g2 & g1 in A & g2 in H
  proof
    assume x in A + H;
    then consider g1,g2 such that
A1: x = g1 + g2 & g1 in A and
A2: g2 in carr H;
    g2 in H by A2;
    hence thesis by A1;
  end;
  given g1,g2 such that
A3: x = g1 + g2 & g1 in A and
A4: g2 in H;
  thus thesis by A3,A4;
end;
