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

for P being Instruction-Sequence of S

for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let P be Instruction-Sequence of S; :: thesis: for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let s be State of S; :: thesis: ( s = Following (P,s) implies for n being Nat holds Comput (P,s,n) = s )

defpred S_{1}[ Nat] means Comput (P,s,$1) = s;

assume A1: s = Following (P,s) ; :: thesis: for n being Nat holds Comput (P,s,n) = s

A2: for n being Nat st S_{1}[n] holds

S_{1}[n + 1]
by A1, EXTPRO_1:3;

A3: S_{1}[ 0 ]
;

thus for n being Nat holds S_{1}[n]
from NAT_1:sch 2(A3, A2); :: thesis: verum

for P being Instruction-Sequence of S

for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; :: thesis: for P being Instruction-Sequence of S

for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let P be Instruction-Sequence of S; :: thesis: for s being State of S st s = Following (P,s) holds

for n being Nat holds Comput (P,s,n) = s

let s be State of S; :: thesis: ( s = Following (P,s) implies for n being Nat holds Comput (P,s,n) = s )

defpred S

assume A1: s = Following (P,s) ; :: thesis: for n being Nat holds Comput (P,s,n) = s

A2: for n being Nat st S

S

A3: S

thus for n being Nat holds S