theorem Th75:
  for v,vS,vS1,vS2 st (for y st y in dom vS1 holds not y in
still_not-bound_in (P!ll)) & (for y st y in dom vS2 holds vS2.y = v.y) & dom vS
  misses dom vS2 holds J,v.vS |= P!ll iff J,v.(vS+*vS1+*vS2) |= P!ll
proof
  let v,vS,vS1,vS2 such that
A1: for y st y in dom vS1 holds not y in still_not-bound_in (P!ll) and
A2: ( for y st y in dom vS2 holds vS2.y = v.y)& dom vS misses dom vS2;
A3: for y st y in dom vS1 holds not y in still_not-bound_in ll
  proof
    let y;
    assume y in dom vS1;
    then not y in still_not-bound_in (P!ll) by A1;
    hence thesis by QC_LANG3:5;
  end;
A4: (v.(vS+*vS1+*vS2))*'ll in J.P iff Valid(P!ll,J).(v.(vS+*vS1+*vS2)) =
  TRUE by VALUAT_1:7;
  Valid(P!ll,J).(v.vS) = TRUE iff (v.vS)*'ll in J.P by VALUAT_1:7;
  hence thesis by A2,A3,A4,Th74,VALUAT_1:def 7;
end;
