theorem
 for I being MacroInstruction of SCM+FSA, k being Nat
 holds  UsedILoc(I ';' goto  k) = UsedILoc I
proof let I be MacroInstruction of SCM+FSA, k be Nat;
    not LastLoc I in dom CutLastLoc I by COMPOS_2:17;
    then {LastLoc I} misses dom CutLastLoc I by ZFMISC_1:50;
    then
A2: dom CutLastLoc I misses dom (LastLoc I .--> halt SCM+FSA);
A3: dom CutLastLoc I misses dom Reloc(Macro goto k, card I -' 1)
      by COMPOS_1:18;
 thus UsedILoc(I ';' goto  k) =  UsedILoc(I ';' Macro goto  k)
   .= UsedILoc(CutLastLoc I +* Reloc(Macro goto k,card I -' 1))
   .= UsedILoc CutLastLoc I \/ UsedILoc Reloc(Macro goto k,card I -' 1)
          by A3,Th21
   .= UsedILoc CutLastLoc I \/ UsedILoc Macro goto k by Th25
   .= UsedILoc CutLastLoc I \/ UsedIntLoc goto k by Th28
   .= UsedILoc CutLastLoc I \/ {} by Th15
   .= UsedILoc CutLastLoc I \/ UsedIntLoc halt SCM+FSA by Th13
   .= UsedILoc CutLastLoc I \/ UsedILoc (LastLoc I .--> halt SCM+FSA) by Lm7
   .= UsedILoc(CutLastLoc I +* (LastLoc I .--> halt SCM+FSA)) by A2,Th21
   .= UsedILoc I by COMPOS_2:20;
end;
