theorem Th59:
  i <= len q implies len(q|i) = i
proof
  assume i <= len q;
  then Seg i c= Seg(len q) by Th5;
  then Seg i c= dom q by Def3;
  then i in NAT & Seg i = dom(q|i) by ORDINAL1:def 12,RELAT_1:62;
  hence thesis by Def3;
end;
