let s be State of SCM+FSA; :: thesis: for aa being Int-Location
for I being Program of {INT,(INT *)}
for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not I destroys aa holds
(IExec (I,p,s)) . aa = (Initialized s) . aa
let aa be Int-Location ; :: thesis: for I being Program of {INT,(INT *)}
for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not I destroys aa holds
(IExec (I,p,s)) . aa = (Initialized s) . aa
let I be Program of {INT,(INT *)}; :: thesis: for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not I destroys aa holds
(IExec (I,p,s)) . aa = (Initialized s) . aa
let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not I destroys aa implies (IExec (I,p,s)) . aa = (Initialized s) . aa )
set a = aa;
A1: DataPart (Initialized s) = DataPart ((Initialized s) +* (Initialize I)) by SCMFSA8A:11;
assume ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not I destroys aa ) ; :: thesis: (IExec (I,p,s)) . aa = (Initialized s) . aa
hence (IExec (I,p,s)) . aa = (Comput ((p +* I),((Initialized s) +* (Initialize I)),0)) . aa by SCMFSA8C:89
.= ((Initialized s) +* (Initialize I)) . aa by EXTPRO_1:3
.= (Initialized s) . aa by A1, SCMFSA6A:38 ;
:: thesis: verum