theorem
  M,v |= 'not' p '&' 'not' q => 'not'(p 'or' q) & M |= 'not' p '&' 'not'
  q => 'not'(p 'or' q)
proof
  now
    let v;
    now
      assume
A1:   M,v |= 'not' p '&' 'not' q;
      then M,v |= 'not' q by ZF_MODEL:15;
      then
A2:   not M,v |= q by ZF_MODEL:14;
      M,v |= 'not' p by A1,ZF_MODEL:15;
      then not M,v |= p by ZF_MODEL:14;
      then not M,v |= p 'or' q by A2,ZF_MODEL:17;
      hence M,v |= 'not'(p 'or' q) by ZF_MODEL:14;
    end;
    hence M,v |= 'not' p '&' 'not' q => 'not'(p 'or' q) by ZF_MODEL:18;
  end;
  hence thesis;
end;
