reserve m,j,p,q,n,l for Element of NAT;
reserve e1,e2 for ExtReal;
reserve i for Nat,
        k,k1,k2,j1 for Element of NAT,
        x,x1,x2,y for set;
reserve p1,p2 for FinSequence;
reserve q,q1,q2,q3,q4 for FinSubsequence,
        p1,p2 for FinSequence;
reserve l1 for Nat,
        j2 for Element of NAT;

theorem
  for F, G being non empty NAT-defined finite Function st dom F c= dom G
   holds LastLoc F <= LastLoc G by XXREAL_2:59;
