theorem Th26:
 for k being Nat holds
   k < LastLoc I iff k in dom CutLastLoc I
proof let k be Nat;
   card I > 0;
   then
A1:  card I >= 0+1 by NAT_1:13;
  card CutLastLoc I = card I - 1 by VALUED_1:38
     .= card I -' 1 by A1,XREAL_1:233
     .= LastLoc I by AFINSQ_1:70;
 hence thesis by AFINSQ_1:86;
end;
