reserve P for non empty Poset,
  i, j, k for Element of P;
reserve S for non void non empty ManySortedSign;
reserve OAF for OrderedAlgFam of P, S;
reserve B for Binding of OAF;

theorem Th2:
  for P,S,OAF,B,i,j st i >= j for f be ManySortedFunction of OAF.i,
  OAF.j st f = bind (B,i,j) holds f is_homomorphism OAF.i,OAF.j
proof
  let P,S,OAF,B,i,j;
  assume
A1: i >= j;
  let f be ManySortedFunction of OAF.i,OAF.j;
  assume
A2: f = bind (B,i,j);
  j >= j by ORDERS_2:1;
  then
  ex f1 be ManySortedFunction of OAF.i, OAF.j, f2 be ManySortedFunction of
  OAF.j, OAF.j st f1 = B.(j,i) & f2 = B.(j,j) & B.(j,i) = f2 ** f1 & f1
  is_homomorphism OAF.i, OAF.j by A1,Def2;
  hence thesis by A1,A2,Def3;
end;
