reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set,
  N for with_zero set;

theorem
  for T being InsType of the InstructionsF of STC N holds JumpParts T = {0}
proof
  let T be InsType of the InstructionsF of STC N;
  set A = { JumpPart I where I is Instruction of STC N: InsCode I = T };
  {0} = A
  proof
    hereby
      let a be object;
      assume a in {0};
      then
A1:   a = 0 by TARSKI:def 1;
A2:   the InstructionsF of STC N = {[0,0,0],[1,0,0]} by AMISTD_1:def 7;
      then
A3:   InsCodes the InstructionsF of STC N = {0,1} by MCART_1:91;
      per cases by A3,TARSKI:def 2;
      suppose
A4:     T = 0;
        reconsider I = [0,0,0] as Instruction of STC N by A2,TARSKI:def 2;
A5:     JumpPart I = 0;
        InsCode I = 0;
        hence a in A by A1,A4,A5;
      end;
      suppose
A6:     T = 1;
        reconsider I = [1,0,0] as Instruction of STC N by A2,TARSKI:def 2;
A7:     JumpPart I = 0;
        InsCode I = 1;
        hence a in A by A1,A6,A7;
      end;
    end;
    let a be object;
    assume a in A;
    then ex I being Instruction of STC N st a = JumpPart I & InsCode I = T;
    then a = 0;
    hence thesis by TARSKI:def 1;
  end;
  hence thesis;
end;
