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;

theorem Th18:
 for I being unique-halt Program of S,
     J being halt-ending Program of S
  st CutLastLoc I c= J
 holds CutLastLoc I c= CutLastLoc J
proof
 let I be unique-halt Program of S,
     J be halt-ending Program of S such that
A1: CutLastLoc I c= J;
A2: not halt S in rng CutLastLoc I by COMPOS_1:def 11;
  J.LastLoc J = halt S by COMPOS_1:def 14;
 hence CutLastLoc I c= CutLastLoc J by A2,A1,Lm1;
end;
