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 Th3:
  for i, j st i >= j & i <> j holds B.(j,i) = (Normalized B).(j,i)
proof
  let i, j;
  assume that
A1: i >= j and
A2: i <> j;
  (Normalized B).(j,i) = IFEQ (j, i, id (the Sorts of OAF.i), bind (B,i,j)
** id (the Sorts of OAF.i) ) & IFEQ (j, i, id (the Sorts of OAF.i), bind (B,i,j
) ** id (the Sorts of OAF.i) ) = bind (B,i,j) ** id (the Sorts of OAF.i) by A1
,A2,Def5,FUNCOP_1:def 8;
  then (Normalized B).(j,i) = bind (B,i,j) by MSUALG_3:3;
  hence thesis by A1,Def3;
end;
