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 Th30:
  JUMP goto(i1,R) = {i1}
proof
  set X = the set of all  NIC(goto(i1,R), il) ;
  now
    let x be object;
    hereby
      reconsider il1 = 1 as Element of NAT;
A1:   NIC(goto(i1,R), il1) in X;
      assume x in meet X;
      then x in NIC(goto(i1,R), il1) by A1,SETFAM_1:def 1;
      hence x in {i1} by Th29;
    end;
    assume x in {i1};
    then
A2: x = i1 by TARSKI:def 1;
A3: now
      let Y be set;
      assume Y in X;
      then consider il being Nat such that
A4:   Y = NIC(goto(i1,R), il);
      NIC(goto(i1,R), il) = {i1} by Th29;
      hence i1 in Y by A4,TARSKI:def 1;
    end;
    NIC(goto(i1,R), i1) in X;
    hence x in meet X by A2,A3,SETFAM_1:def 1;
  end;
  hence thesis by TARSKI:2;
end;
