theorem Th17:
  not J,v.Val_S(v,S) |= S iff J,v.Val_S(v,S) |= Sub_not S
proof
A1: not J,v.Val_S(v,S) |= S`1 iff J,v.Val_S(v,S) |= 'not' S`1 by VALUAT_1:17;
  J,v.Val_S(v,S) |= 'not' S`1 iff J,v.Val_S(v,S) |= (Sub_not S)`1 by Th16;
  hence thesis by A1;
end;
