let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for I being parahalting Program of SCM+FSA
for a being Int-Location
for k being Element of NAT st not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
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 not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let I be parahalting Program of SCM+FSA; :: thesis: for a being Int-Location
for k being Element of NAT st not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let a be Int-Location ; :: thesis: for k being Element of NAT st not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let k be Element of NAT ; :: thesis: ( not I destroys a implies (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a )
set s0 = Initialized s;
set s1 = Initialize (Initialized s);
set P1 = P +* I;
A1: I c= P +* I by FUNCT_4:26;
A2: Start-At (0,SCM+FSA) c= Initialize (Initialized s) by FUNCT_4:26;
P +* I halts_on Initialize (Initialized s) by A1, A2, SCMFSA6B:18;
then I is_halting_on Initialized s,P by SCMFSA7B:def 8;
hence ( not I destroys a implies (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a ) by Th89, SCMFSA7B:24; :: thesis: verum