let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being good really-closed parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a holds
(IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (s . a) - 1
let s be State of SCM+FSA; :: thesis: for I being good really-closed parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a holds
(IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (s . a) - 1
let I be good really-closed parahalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st not I destroys a holds
(IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (s . a) - 1
let a be read-write Int-Location; :: thesis: ( not I destroys a implies (IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (s . a) - 1 )
set I1 = I ";" (SubFrom (a,(intloc 0)));
set ss = IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s);
set s0 = Initialized s;
A1: I is_halting_on Initialized s,P by SCMFSA7B:19;
assume A2: not I destroys a ; :: thesis: (IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (s . a) - 1
thus (IExec ((I ";" (SubFrom (a,(intloc 0)))),P,s)) . a = (Exec ((SubFrom (a,(intloc 0))),(IExec (I,P,s)))) . a by SCMFSA6C:6
.= ((IExec (I,P,s)) . a) - ((IExec (I,P,s)) . (intloc 0)) by SCMFSA_2:65
.= ((IExec (I,P,s)) . a) - 1 by A1, Th54
.= ((Initialized s) . a) - 1 by A2, Th53
.= (s . a) - 1 by SCMFSA_M:37 ; :: thesis: verum