reserve l, m, n for Nat,
  i,j,k for Instruction of SCM+FSA,
  I,J,K for Program of SCM+FSA;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;

theorem
 n in dom Reloc(J,card I)
  implies (I ";" J).n = Reloc(J,card I).n
 proof assume
A1: n in dom Reloc(J,card I);
   I ";" J
    = CutLastLoc stop Directed I +* Reloc(J,card stop I -' 1) by Th27
   .= Directed I +* Reloc(J,card I) by COMPOS_1:71;
  hence (I ";" J).n = Reloc(J,card I).n by A1,FUNCT_4:13;
 end;
