theorem Th39:
  ex f,T1,T2 st m = [[T1,T2],f] & (T2`2 = {} implies T1`2 = {}) &
  f is Function of T1`2,T2`2 & for x,y st [x,y] in T1`1 holds [f.x,f.y] in T2`1
proof
  m in {[[T1,T2],f]: (T2`2={} implies T1`2={}) & f is Function of T1`2,T2
  `2 & for x,y st [x,y] in T1`1 holds [f.x,f.y] in T2`1};
  then ex T1,T2,f st m = [[T1,T2],f] & (T2`2={} implies T1`2={}) & f is
  Function of T1`2,T2`2 & for x,y st [x,y] in T1`1 holds [f.x,f.y] in T2`1;
  hence thesis;
end;
