theorem Th60:
  for v,w holds (v|still_not-bound_in (P!ll) = w|
  still_not-bound_in (P!ll) implies (J,v |= P!ll iff J,w |= P!ll))
proof
  let v,w;
  assume
A1: v|still_not-bound_in (P!ll) = w|still_not-bound_in (P!ll);
A2: still_not-bound_in (P!ll) = still_not-bound_in ll by QC_LANG3:5;
A3: w*'ll in J.P iff Valid(P!ll,J).w = TRUE by VALUAT_1:7;
A4: Valid(P!ll,J).v = TRUE iff v*'ll in J.P by VALUAT_1:7;
  ll*(w|still_not-bound_in ll) in J.P iff w*'ll in J.P by Th59;
  hence thesis by A1,A2,A4,A3,Th59,VALUAT_1:def 7;
end;
