let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting AMI-Struct of N
for F being NAT -defined the Instructions of b₁ -valued total Function
for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let S be non empty stored-program IC-Ins-separated definite halting AMI-Struct of N; :: thesis: for F being NAT -defined the Instructions of S -valued total Function
for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let F be NAT -defined the Instructions of S -valued total Function; :: thesis: for s being State of S
for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let s be State of S; :: thesis: for k being Element of NAT st F . (IC (Comput (F,s,k))) = halt S holds
Result (F,s) = Comput (F,s,k)
let k be Element of NAT ; :: thesis: ( F . (IC (Comput (F,s,k))) = halt S implies Result (F,s) = Comput (F,s,k) )
assume Z: F . (IC (Comput (F,s,k))) = halt S ; :: thesis: Result (F,s) = Comput (F,s,k)
then X: F halts_on s by Th31;
dom F = NAT by PARTFUN1:def 4;
then IC (Comput (F,s,k)) in dom F ;
then CurInstr (F,(Comput (F,s,k))) = halt S by Z, PARTFUN1:def 8;
hence Result (F,s) = Comput (F,s,k) by X, Def22; :: thesis: verum