theorem Th76:
  (for v,vS,vS1,vS2 st (for y st y in dom vS1 holds not y in
  still_not-bound_in p) & (for y st y in dom vS2 holds vS2.y = v.y) & dom vS
misses dom vS2 holds J,v.vS |= p iff J,v.(vS+*vS1+*vS2) |= p) implies for v,vS,
vS1,vS2 st (for y st y in dom vS1 holds not y in still_not-bound_in 'not' p) &
(for y st y in dom vS2 holds vS2.y = v.y) & dom vS misses dom vS2 holds J,v.vS
  |= 'not' p iff J,v.(vS+*vS1+*vS2) |= 'not' p
proof
  assume
A1: for v,vS,vS1,vS2 st (for y st y in dom vS1 holds not y in
  still_not-bound_in p) & (for y st y in dom vS2 holds vS2.y = v.y) & dom vS
  misses dom vS2 holds J,v.vS |= p iff J,v.(vS+*vS1+*vS2) |= p;
  let v,vS,vS1,vS2 such that
A2: for y st y in dom vS1 holds not y in still_not-bound_in 'not' p and
A3: ( for y st y in dom vS2 holds vS2.y = v.y)& dom vS misses dom vS2;
  for y st y in dom vS1 holds not y in still_not-bound_in p
  proof
    let y;
    assume y in dom vS1;
    then not y in still_not-bound_in 'not' p by A2;
    hence thesis by QC_LANG3:7;
  end;
  then not J,v.vS |= p iff not J,v.(vS+*vS1+*vS2) |= p by A1,A3;
  hence thesis by VALUAT_1:17;
end;
