theorem Th36:
  r in X /\ Y /\ dom (h1+h2) implies r in X /\ dom h1 & r in Y /\ dom h2
proof
  assume
A1: r in X /\ Y /\ dom (h1+h2);
  then r in dom (h1+h2) by XBOOLE_0:def 4;
  then r in dom h1 /\ dom h2 by VALUED_1:def 1;
  then
A2: r in dom h1 & r in dom h2 by XBOOLE_0:def 4;
  r in X /\ Y by A1,XBOOLE_0:def 4;
  then r in X & r in Y by XBOOLE_0:def 4;
  hence thesis by A2,XBOOLE_0:def 4;
end;
