reserve x, y for object, X, X1, X2 for set;
reserve Y, Y1, Y2 for complex-functions-membered set,
  c, c1, c2 for Complex,
  f for PartFunc of X,Y,
  f1 for PartFunc of X1,Y1,
  f2 for PartFunc of X2, Y2,
  g, h, k for complex-valued Function;

theorem Th21:
  g /" h /" k = g /" (h (#) k)
proof
A1: dom(g /" h /" k) = dom(g /" h) /\ dom k & dom(g /" (h (#) k)) = dom g /\
  dom (h (#) k) by VALUED_1:16;
  dom(g /" h) = dom g /\ dom h & dom(h (#) k) = dom h /\ dom k by VALUED_1:16
,def 4;
  hence dom(g /" h /" k) = dom(g /" (h (#) k)) by A1,XBOOLE_1:16;
  let x be object;
  assume x in dom(g /" h /" k);
  thus (g /" h /" k).x = (g /" h).x / k.x by VALUED_1:17
    .= g.x / h.x / k.x by VALUED_1:17
    .= g.x / (h.x * k.x) by XCMPLX_1:78
    .= g.x / (h (#) k).x by VALUED_1:5
    .= (g /" (h (#) k)).x by VALUED_1:17;
end;
