let N be non empty with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N

for P being NAT -defined the InstructionsF of b_{1} -valued Function

for s being State of S

for k being Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being NAT -defined the InstructionsF of S -valued Function

for s being State of S

for k being Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let P be NAT -defined the InstructionsF of S -valued Function; :: thesis: for s being State of S

for k being 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 Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let k be 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 Th16;

hence Result (P,s) = Comput (P,s,k) by A1, Th17; :: thesis: verum

for P being NAT -defined the InstructionsF of b

for s being State of S

for k being Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being NAT -defined the InstructionsF of S -valued Function

for s being State of S

for k being Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let P be NAT -defined the InstructionsF of S -valued Function; :: thesis: for s being State of S

for k being 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 Nat st P halts_at IC (Comput (P,s,k)) holds

Result (P,s) = Comput (P,s,k)

let k be 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 Th16;

hence Result (P,s) = Comput (P,s,k) by A1, Th17; :: thesis: verum