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 Th20:
  JUMP (a>0_goto k) = {k}
proof
  set X = the set of all  NIC(a>0_goto k, il) ;
  now
    let x be object;
A1: now
      let Y be set;
      assume Y in X;
      then consider il being Nat such that
A2:   Y = NIC(a>0_goto k, il);
      NIC(a>0_goto k, il) = {k, il+1} by Th19;
      hence k in Y by A2,TARSKI:def 2;
    end;
    hereby
      set il1 = 1, il2 = 2;
      assume
A3:   x in meet X;
A4:   NIC(a>0_goto k, il2) = {k, il2+1} by Th19;
      NIC(a>0_goto k, il2) in X;
      then x in NIC(a>0_goto k, il2) by A3,SETFAM_1:def 1;
      then
A5:   x = k or x = il2+1 by A4,TARSKI:def 2;
A6:   NIC(a>0_goto k, il1) = {k, il1+1} by Th19;
      NIC(a>0_goto k, il1) in X;
      then x in NIC(a>0_goto k, il1) by A3,SETFAM_1:def 1;
      then x = k or x = il1+1 by A6,TARSKI:def 2;
      hence x in {k} by A5,TARSKI:def 1;
    end;
    assume x in {k};
    then
A7: x = k by TARSKI:def 1;
    reconsider k as Element of NAT by ORDINAL1:def 12;
    NIC(a>0_goto k, k) in X;
    hence x in meet X by A7,A1,SETFAM_1:def 1;
  end;
  hence thesis by TARSKI:2;
end;
