let N be non empty with_zero set ; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: 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 A1: F halts_on Comput (F,s,k) ; :: thesis: 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; :: thesis: verum