let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being good parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P
let s be State of SCM+FSA; :: thesis: for I being good parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a & s . a > 0 holds
loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P
let I be good parahalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st not I destroys a & s . a > 0 holds
loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P
let a be read-write Int-Location ; :: thesis: ( not I destroys a & s . a > 0 implies loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P )
assume A1: not I destroys a ; :: thesis: ( not s . a > 0 or loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P )
A2: (Initialized s) . a = s . a by SCMFSA6C:3;
A3: (Initialized s) . (intloc 0) = 1 by SCMFSA6A:38;
assume s . a > 0 ; :: thesis: loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P
hence loop (if=0 (a,(Goto 2),(I ';' (SubFrom (a,(intloc 0)))))) is_pseudo-closed_on Initialized s,P by A1, A2, A3, Th117; :: thesis: verum