reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;

theorem Th10:
  k <= len p implies dom(p|k) = k
 proof assume k <= len p;
   then Segm k c= Segm len p by NAT_1:39;
  hence dom(p|k) = k by RELAT_1:62;
 end;
