let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated steady-programmed definite AMI-Struct of N
for P being the Instructions of b₁ -valued ManySortedSet of NAT
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 halting IC-Ins-separated steady-programmed definite AMI-Struct of N; :: thesis: for P being the Instructions of S -valued ManySortedSet of NAT
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 the Instructions of S -valued ManySortedSet of NAT ; :: 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