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
  dom(I ";" J) = dom I \/ dom Reloc(J, card I)
proof
   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 dom(I ";" J) = dom Directed I \/ dom Reloc(J, card I) by FUNCT_4:def 1
       .= dom I \/ dom Reloc(J, card I) by FUNCT_4:99;
end;
