let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for I being good InitHalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p
let s be State of SCM+FSA; :: thesis: for I being good InitHalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p
let I be good InitHalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st not I destroys a & s . a > 0 holds
Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p
let a be read-write Int-Location ; :: thesis: ( not I destroys a & s . a > 0 implies Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p )
assume A1: not I destroys a ; :: thesis: ( not s . a > 0 or Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p )
A2: ( (Initialized s) . a = s . a & (Initialized s) . (intloc 0) = 1 ) by SCMFSA6C:3;
assume s . a > 0 ; :: thesis: Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p
then loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,p by A1, A2, Th73;
hence Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s,p by SCMFSA8C:47; :: thesis: verum