reserve R for Ring,
  r for Element of R,
  a, b, d1, d2 for Data-Location of R,
  il, i1, i2 for Nat,
  I for Instruction of SCM R,
  s,s1, s2 for State of SCM R,
  T for InsType of the InstructionsF of SCM R,
  k for Nat;

theorem Th29:
  NIC(goto(i1,R), il) = {i1}
proof
  now
    let x be object;
A1: il in NAT by ORDINAL1:def 12;
A2: now
      reconsider il1 = il as Element of Values IC SCM R by MEMSTR_0:def 6,A1;
  set I = goto(i1,R);
  set t = the State of SCM R,
      Q = the Instruction-Sequence of SCM R;
      assume
A3:   x = i1;
  reconsider u = t+*(IC SCM R,il1)
   as Element of product the_Values_of SCM R by CARD_3:107;
  reconsider P = Q +* (il,I)
   as Instruction-Sequence of SCM R;
A4:   P/.il = P.il by PBOOLE:143,A1;
    IC SCM R in dom t by MEMSTR_0:2;
    then
A5: IC u = il by FUNCT_7:31;
    il in NAT by ORDINAL1:def 12;
    then il in dom Q by PARTFUN1:def 2;
    then
A6: P.il = I by FUNCT_7:31;
      then IC Following(P,u) = i1 by A5,A4,SCMRING2:15;
      hence x in {IC Exec(goto(i1,R),s)
       where s is Element of product the_Values_of SCM R
       : IC s = il} by A3,A4,A5,A6;
    end;
    now
      assume x in {IC Exec(goto(i1,R),s)
       where s is Element of product the_Values_of SCM R
       : IC s = il};
      then
      ex s being Element of product the_Values_of SCM R
       st x = IC Exec(goto(i1,R),s) & IC s = il;
      hence x = i1 by SCMRING2:15;
    end;
    hence
    x in {i1} iff x in {IC Exec(goto(i1,R),s)
       where s is Element of product the_Values_of SCM R
     : IC s = il } by A2,TARSKI:def 1;
  end;
  hence thesis by TARSKI:2;
end;
