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),((Initialized s) +* (Initialize I)),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),((Initialized s) +* (Initialize I)),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),((Initialized s) +* (Initialize I)),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),((Initialized s) +* (Initialize I)),k)) . a
let k be Element of NAT ; :: thesis: ( not I destroys a implies (IExec (I,P,s)) . a = (Comput ((P +* I),((Initialized s) +* (Initialize I)),k)) . a )
set s0 = Initialized s;
set s1 = (Initialized s) +* (Initialize I);
set P1 = P +* I;
A1: I c= P +* I by FUNCT_4:26;
A2: Initialize I c= (Initialized s) +* (Initialize I) by FUNCT_4:26;
A3: I is_closed_on Initialized s,P by SCMFSA7B:24;
A4: ProgramPart I = I by RELAT_1:209;
P +* I halts_on (Initialized s) +* (Initialize I) by SCMFSA6B:18, A1, A2;
then A5: I is_halting_on Initialized s,P by SCMFSA7B:def 8, A4;
assume not I destroys a ; :: thesis: (IExec (I,P,s)) . a = (Comput ((P +* I),((Initialized s) +* (Initialize I)),k)) . a
hence (IExec (I,P,s)) . a = (Comput ((P +* I),((Initialized s) +* (Initialize I)),k)) . a by A3, A5, Th89; :: thesis: verum