let N be non empty with_zero set ; for S being non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N
for F being Instruction-Sequence of S
for s being State of S
for k being Nat st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let S be non empty with_non-empty_values IC-Ins-separated halting AMI-Struct over N; for F being Instruction-Sequence of S
for s being State of S
for k being Nat st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let F be Instruction-Sequence of S; for s being State of S
for k being 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; for k being Nat st F halts_on Comput (F,s,k) holds
Result (F,(Comput (F,s,k))) = Result (F,s)
let k be Nat; ( F halts_on Comput (F,s,k) implies Result (F,(Comput (F,s,k))) = Result (F,s) )
set s2 = Comput (F,s,k);
assume A1:
F halts_on Comput (F,s,k)
; Result (F,(Comput (F,s,k))) = Result (F,s)
then consider l being Nat such that
A2:
( Result (F,(Comput (F,s,k))) = Comput (F,(Comput (F,s,k)),l) & CurInstr (F,(Result (F,(Comput (F,s,k))))) = halt S )
by Def9;
A3:
F halts_on s
by A1, Th22;
Comput (F,(Comput (F,s,k)),l) = Comput (F,s,(k + l))
by Th4;
hence
Result (F,(Comput (F,s,k))) = Result (F,s)
by A3, A2, Def9; verum