let i be Nat; :: thesis: for j being Element of NAT st i <= j holds
for N being non empty with_non-empty_elements set
for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₃ -valued finite 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 j be Element of NAT ; :: thesis: ( i <= j implies for N being non empty with_non-empty_elements set
for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₂ -valued finite 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 N being non empty with_non-empty_elements set
for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₂ -valued finite 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: for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₁ -valued finite 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 halting IC-Ins-separated definite AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued finite 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 finite 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