let i, j be Element of NAT ; :: thesis: for N being non empty with_non-empty_elements set st i <= j holds
for S being non empty stored-program IC-Ins-separated definite halting AMI-Struct of N
for P being NAT -defined the Instructions of b₂ -valued Function
for s being State of S st P halts_at IC (Comput P,s,i) holds
Comput P,s,j = Comput P,s,i
let N be non empty with_non-empty_elements set ; :: thesis: ( i <= j implies 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 st P halts_at IC (Comput P,s,i) holds
Comput P,s,j = Comput P,s,i )
assume A1: i <= j ; :: 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 st P halts_at IC (Comput P,s,i) holds
Comput P,s,j = Comput P,s,i
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 st P halts_at IC (Comput P,s,i) holds
Comput P,s,j = Comput P,s,i
let P be NAT -defined the Instructions of S -valued Function; :: thesis: for s being State of S st P halts_at IC (Comput P,s,i) holds
Comput P,s,j = Comput P,s,i
let s be State of S; :: thesis: ( P halts_at IC (Comput P,s,i) implies Comput P,s,j = Comput P,s,i )
assume A2: P halts_at IC (Comput P,s,i) ; :: thesis: Comput P,s,j = Comput P,s,i
then P halts_at IC (Comput P,s,j) by A1, Th88;
hence Comput P,s,j = Result P,s by Th87
.= Comput P,s,i by A2, Th87 ;
:: thesis: verum