reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

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;
