let s be State of SCM+FSA ; :: thesis: for I being parahalting Program of SCM+FSA
for a being Int-Location
for k being Element of NAT st I does_not_destroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let I be parahalting Program of SCM+FSA ; :: thesis: for a being Int-Location
for k being Element of NAT st I does_not_destroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let a be Int-Location ; :: thesis: for k being Element of NAT st I does_not_destroy a holds
(IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
let k be Element of NAT ; :: thesis: ( I does_not_destroy a implies (IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a )
set s0 = Initialize s;
set s1 = (Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ));
A1: I is_closed_on Initialize s by SCMFSA7B:24;
ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))) halts_on (Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )) by FUNCT_4:26, SCMFSA6B:18;
then A2: I is_halting_on Initialize s by SCMFSA7B:def 8;
assume I does_not_destroy a ; :: thesis: (IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a
hence (IExec I,s) . a = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),k) . a by A1, A2, Th89; :: thesis: verum