
theorem Th22:
 for I being really-closed MacroInstruction of SCM+FSA,
     n,k being Nat st n < card I & k < card I
  holds I +* (n,goto k) is really-closed
proof let I being really-closed MacroInstruction of SCM+FSA,
     n,k being Nat such that
A1: n < card I and
A2: k < card I;
  set F = I +* (n,goto k);
A3: n in dom I by A1,AFINSQ_1:66;
A4: k in dom I by A2,AFINSQ_1:66;
A5: dom F = dom I by FUNCT_7:30;
 let l be Nat such that
A6: l in dom F;
A7:  F/.l = F.l by A6,PARTFUN1:def 6;
 per cases;
 suppose n = l;
   then F.l = goto k by A3,FUNCT_7:31;
   then NIC (F/.l, l) = {k} by A7,SCMFSA10:33;
  hence NIC (F/.l, l) c= dom F by A5,ZFMISC_1:31,A4;
 end;
 suppose n <> l;
   then F.l = I.l by FUNCT_7:32;
   then F/.l = I.l by A6,PARTFUN1:def 6
     .= I/.l by A6,A5,PARTFUN1:def 6;
  hence NIC (F/.l, l) c= dom F by A5,A6,AMISTD_1:def 9;
 end;
end;
