reserve a, b, d1, d2 for Data-Location,
  il, i1, i2 for Nat,
  I for Instruction of SCM,
  s, s1, s2 for State of SCM,
  T for InsType of the InstructionsF of SCM,
  k,k1 for Nat;

theorem Th16:
  JUMP SCM-goto k = {k}
proof
  set X = the set of all  NIC(SCM-goto k, il) ;
  now
    let x be object;
    hereby
      set il1 = 1;
A1:   NIC(SCM-goto k, il1) in X;
      assume x in meet X;
      then x in NIC(SCM-goto k, il1) by A1,SETFAM_1:def 1;
      hence x in {k} by Th15;
    end;
    assume x in {k};
    then
A2: x = k by TARSKI:def 1;
A3: now
      let Y be set;
      assume Y in X;
      then consider il being Nat such that
A4:   Y = NIC(SCM-goto k, il);
      NIC(SCM-goto k, il) = {k} by Th15;
      hence k in Y by A4,TARSKI:def 1;
    end;
    reconsider k as Element of NAT by ORDINAL1:def 12;
    NIC(SCM-goto k, k) in X;
    hence x in meet X by A2,A3,SETFAM_1:def 1;
  end;
  hence thesis by TARSKI:2;
end;
