let s be State of SCM+FSA; :: thesis: for I being parahalting good 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
let I be parahalting good 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
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 )
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 )
A2: (Initialized s) . a = s . a by SCMFSA6C:3;
A3: (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
then loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s by A1, A2, A3, Th117;
hence Initialized (loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0))))))) is_pseudo-closed_on s by Lm1; :: thesis: verum