reserve F for total
  NAT-defined (the InstructionsF of SCM)-valued Function;

theorem
  for i1, i2, i3, i4 being Integer,
  s being State of SCM st s.dl.0 = i1 & s.dl.1 = i2 & s.dl.2 = i3 & s.dl.3 = i4
   holds s is State-consisting of <%i1,i2,i3,i4%>
proof
  let i1, i2, i3, i4 be Integer, s be State of SCM such that
A1: s.dl.0 = i1 & s.dl.1 = i2 & s.dl.2 = i3 & s.dl.3 = i4;
  set D = <%i1,i2,i3,i4%>;
  now
    let k be Element of NAT;
A2: len D=4 & 4=3+1 by AFINSQ_1:84;
    assume k < len D;
    then k <= 3 by A2,NAT_1:13;
    then k=0 or ... or k=3;
    hence s.dl.k=D.k by A1;
  end;
  hence thesis by Def1;
end;
