let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite halting AMI-Struct of N
for F being NAT -defined the Instructions of b₁ -valued total Function
for s being State of S
for k being Element of NAT st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let S be non empty stored-program IC-Ins-separated definite halting AMI-Struct of N; :: thesis: for F being NAT -defined the Instructions of S -valued total Function
for s being State of S
for k being Element of NAT st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let F be NAT -defined the Instructions of S -valued total Function; :: thesis: for s being State of S
for k being Element of NAT st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let s be State of S; :: thesis: for k being Element of NAT st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let k be Element of NAT ; :: thesis: ( F halts_on Comput (F,s,k) implies Result (F,(Comput (F,s,k))) = Result (F,s) )
set s2 = Comput (F,s,k);
assume A2: F halts_on Comput (F,s,k) ; :: thesis: Result (F,(Comput (F,s,k))) = Result (F,s)
then consider l being Element of NAT such that
A4: ( Result (F,(Comput (F,s,k))) = Comput (F,(Comput (F,s,k)),l) & CurInstr (F,(Result (F,(Comput (F,s,k))))) = halt S ) by Def22;
A3: F halts_on s by A2, Th22;
Comput (F,(Comput (F,s,k)),l) = Comput (F,s,(k + l)) by Th5;
hence Result (F,(Comput (F,s,k))) = Result (F,s) by A3, A4, Def22; :: thesis: verum