reserve x,A for set, i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set, z for Nat;
reserve S for COM-Struct;
reserve ins for Element of the InstructionsF of S;
reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set;

theorem
  for T being InsType of the InstructionsF of Trivial-COM
   holds JumpParts T = {0}
proof
  let T be InsType of the InstructionsF of Trivial-COM;
  set A = { JumpPart I where I is Instruction of Trivial-COM:
   InsCode I = T };
  {0} = A
  proof
    hereby
      let a be object;
      assume a in {0};
      then
A1:   a = 0 by TARSKI:def 1;
   the InstructionsF of Trivial-COM = {[0,0,0]} by Def1;
      then
A2:   InsCodes the InstructionsF of Trivial-COM = {0} by MCART_1:92;
A3:     T = 0 by A2,TARSKI:def 1;
        [0,0,0] = halt Trivial-COM;
        then reconsider I = [0,0,0] as Instruction of Trivial-COM;
A4:     JumpPart I = 0;
        InsCode I = 0;
        hence a in A by A1,A3,A4;
    end;
    let a be object;
    assume a in A;
    then ex I being Instruction of Trivial-COM st a = JumpPart I &
     InsCode I = T;
    then a = 0 by Th4;
    hence thesis by TARSKI:def 1;
  end;
  hence thesis;
end;
