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

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