reserve S for with_non_trivial_Instructions COM-Struct;
reserve i,j,k for No-StopCode Instruction of S,
        I,J,K for MacroInstruction of S;
reserve i1,i2,i3,i4,i5,i6 for No-StopCode Instruction of S;
reserve I,J for non empty NAT-defined finite Function;
reserve I,J for MacroInstruction of S;

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;
