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 P being NAT -defined the Instructions of b₁ -valued Function
for s being State of S
for k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
Result (P,s) = Comput (P,s,k)
let S be non empty stored-program IC-Ins-separated definite halting AMI-Struct of N; :: thesis: for P being NAT -defined the Instructions of S -valued Function
for s being State of S
for k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
Result (P,s) = Comput (P,s,k)
let P be NAT -defined the Instructions of S -valued Function; :: thesis: for s being State of S
for k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
Result (P,s) = Comput (P,s,k)
let s be State of S; :: thesis: for k being Element of NAT st P halts_at IC (Comput (P,s,k)) holds
Result (P,s) = Comput (P,s,k)
let k be Element of NAT ; :: thesis: ( P halts_at IC (Comput (P,s,k)) implies Result (P,s) = Comput (P,s,k) )
assume A1: P halts_at IC (Comput (P,s,k)) ; :: thesis: Result (P,s) = Comput (P,s,k)
then P halts_on s by Th83;
hence Result (P,s) = Comput (P,s,k) by A1, Th85; :: thesis: verum