theorem Th45:
  for f,g being Assign of BASSModel(R,BASSIGN), H1,H2 being Subset
of S holds H1 c= H2 implies SigFoaxTau(g,f,H1,R,BASSIGN) c= SigFoaxTau(g,f,H2,R
  ,BASSIGN)
proof
  let f,g be Assign of BASSModel(R,BASSIGN);
  let H1,H2 be Subset of S;
  assume H1 c= H2;
  then
  for s being Element of S holds s|= Tau(H1,R,BASSIGN) implies s|= Tau(H2,
  R,BASSIGN) by Th34;
  then
  for s being Element of S holds s|= Foax(g,f,Tau(H1,R,BASSIGN)) implies s
  |= Foax(g,f,Tau(H2,R,BASSIGN)) by Th44;
  hence thesis by Th35;
end;
