reserve n,i,j,k for Nat;
reserve T for TuringStr,
  s for All-State of T;

theorem
  n >=1 implies ZeroTuring computes n const 0
proof
  assume
A1: n>=1;
  now
    set cs=n const 0;
    let s be All-State of ZeroTuring,t be Tape of ZeroTuring, h be Element of
    NAT, x be FinSequence of NAT;
    assume that
A2: x in dom cs and
A3: s=[the InitS of ZeroTuring,h,t] and
A4: t storeData <*h*>^x;
    x in n-tuples_on NAT by A2;
    then x in { f where f is Element of NAT*: len f = n } by FINSEQ_2:def 4;
    then
A6: ex f be Element of NAT* st x = f & len f = n;
A7: s = [0,h,t] by A3,Def19;
    hence s is Accept-Halt by A1,A4,A6,Th34;
    take h2=h;
    take y=0;
    thus (Result s)`2_3=h2 by A1,A4,A6,A7,Th34;
    thus y=cs.x by A2,FUNCOP_1:7;
    (Result s)`3_3 storeData <*h2,0*> by A1,A4,A6,A7,Th34;
    hence (Result s)`3_3 storeData <*h2*>^<*y*>;
  end;
  hence thesis;
end;
