reserve a, b, d1, d2, d3, d4 for Int-Location,
  A, B for Data-Location,
  f, f1, f2, f3 for FinSeq-Location,
  il, i1, i2 for Nat,
  L for Nat,
  I for Instruction of SCM+FSA,
  s,s1,s2 for State of SCM+FSA,
  T for InsType of the InstructionsF of SCM+FSA,
  k for Nat;
reserve J,K for Element of Segm 13,
  b,b1,c,c1 for Element of SCM-Data-Loc,
  f,f1 for Element of SCM+FSA-Data*-Loc;
reserve a, b, d1, d2, d3, d4 for Int-Location,
  A, B for Data-Location,
  f, f1,
  f2, f3 for FinSeq-Location;

theorem Th33:
  NIC(goto i1, il) = {i1}
proof
  now
    let x be object;
A1: now
    il in NAT by ORDINAL1:def 12;
    then
      reconsider il1 = il as Element of Values IC SCM+FSA by MEMSTR_0:def 6;
      reconsider n = il1 as Nat;
      set I = goto i1;
      set t = the State of SCM+FSA,
      Q = the Instruction-Sequence of SCM+FSA;
      assume
A2:   x = i1;
      reconsider u = t+*(IC SCM+FSA,il1)
       as Element of product the_Values_of SCM+FSA by CARD_3:107;
      reconsider P = Q +* (il,I)
       as Instruction-Sequence of SCM+FSA;
    IC SCM+FSA in dom t by MEMSTR_0:2;
    then
A3: IC u = n by FUNCT_7:31;
    il in NAT by ORDINAL1:def 12;
    then
A4:   P/.il = P.il by PBOOLE:143;
    il in NAT by ORDINAL1:def 12;
    then il in dom Q by PARTFUN1:def 2;
    then
A5: P.n = I by FUNCT_7:31;
    then IC Following(P,u) = i1 by A3,A4,SCMFSA_2:69;
      hence x in {IC Exec(goto i1,s)
       where s is Element of product the_Values_of SCM+FSA
       : IC s = il} by A2,A3,A5,A4;
    end;
    now
      assume x in {IC Exec(goto i1,s)
       where s is Element of product the_Values_of SCM+FSA
       : IC s = il};
      then ex s being Element of product the_Values_of SCM+FSA
       st x = IC Exec(goto i1,s) & IC s = il;
      hence x = i1 by SCMFSA_2:69;
    end;
    hence
    x in {i1} iff x in {IC Exec(goto i1,s)
       where s is Element of product the_Values_of SCM+FSA
     : IC s = il} by A1,TARSKI:def 1;
  end;
  hence thesis by TARSKI:2;
end;
