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 I does_not_destroy a & s . a > 0 holds
Initialized (loop (if=0 a,(Goto (insloc 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 I does_not_destroy a & s . a > 0 holds
Initialized (loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 ))))) is_pseudo-closed_on s
let a be read-write Int-Location ; :: thesis: ( I does_not_destroy a & s . a > 0 implies Initialized (loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 ))))) is_pseudo-closed_on s )
assume A1: I does_not_destroy a ; :: thesis: ( not s . a > 0 or Initialized (loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 ))))) is_pseudo-closed_on s )
assume A2: s . a > 0 ; :: thesis: Initialized (loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 ))))) is_pseudo-closed_on s
( (Initialize s) . a = s . a & (Initialize s) . (intloc 0 ) = 1 ) by SCMFSA6C:3;
then loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 )))) is_pseudo-closed_on Initialize s by A1, A2, Th117;
hence Initialized (loop (if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 ))))) is_pseudo-closed_on s by Lm1; :: thesis: verum