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
 for K be set st I <= J & J <= K
  holds I <= K
 proof let K be set such that
A1: CutLastLoc I c= J and
A2: CutLastLoc J c= K;
   CutLastLoc I c= CutLastLoc J by A1,Th18;
  hence CutLastLoc I c= K by A2;
 end;
