theorem Th8:
 for p,q,A,J,v holds (J,v |= p or J,v |= q) iff J,v |= p 'or' q
proof
  let p,q,A,J,v;
  thus (J,v |= p or J,v |= q) implies J,v |= p 'or' q
  proof
    assume J,v |= p or J,v |= q;
    then not J,v |= 'not' p or not J,v |= 'not' q by VALUAT_1:17;
    then not J,v |= 'not' p '&' 'not' q by VALUAT_1:18;
    then J,v |= 'not' ('not' p '&' 'not' q) by VALUAT_1:17;
    hence thesis by QC_LANG2:def 3;
 end;
 thus J,v |= p 'or' q implies (J,v |= p or J,v |= q)
 proof
   assume J,v |= p 'or' q;
   then J,v |= 'not' ('not' p '&' 'not' q) by QC_LANG2:def 3;
   then not J,v |= 'not' p or not J,v |= 'not' q by VALUAT_1:17,18;
   hence J,v |= p or J,v |= q by VALUAT_1:17;
 end;
end;
