reserve N for with_zero set;
reserve N for with_zero set;

theorem
  for s being State of Trivial-AMI N, i being Instruction of
  Trivial-AMI N holds Exec(i,s) = s
proof
  set T = Trivial-AMI N;
  let s be State of Trivial-AMI N, i be Instruction of Trivial-AMI N;
  set f = (N --> NAT)*(0 .--> 0);
A1: the Object-Kind of T = 0 .--> 0 &
  the ValuesF of T = N --> NAT by Def1;
   reconsider ss=s as Element of product the_Values_of T by CARD_3:107;
  the InstructionsF of T = {[0,{},{}]} by Def1;
  then (i .--> id product f).i = id product f & i = [0,{},{}] by FUNCOP_1:72
,TARSKI:def 1;
  hence Exec(i,s) = (id product f).ss by Def1
    .= s by A1;
end;
