
theorem Th2:
  for G being non void non empty ManySortedSign, v being Vertex of
  G st v in InputVertices G holds not ex o being OperSymbol of G st
  the_result_sort_of o = v
proof
  let G be non void non empty ManySortedSign, v be Vertex of G;
  assume
A1: v in InputVertices G;
  let o be OperSymbol of G such that
A2: the_result_sort_of o = v;
  o in the carrier' of G;
  then o in dom the ResultSort of G by FUNCT_2:def 1;
  then v in rng the ResultSort of G by A2,FUNCT_1:def 3;
  hence contradiction by A1,XBOOLE_0:def 5;
end;
