let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being keeping_0 really-closed parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a holds
(Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = (s . a) - 1
let s be State of SCM+FSA; :: thesis: for I being keeping_0 really-closed parahalting Program of SCM+FSA
for a being read-write Int-Location st not I destroys a holds
(Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = (s . a) - 1
let I be keeping_0 really-closed parahalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st not I destroys a holds
(Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = (s . a) - 1
let a be read-write Int-Location; :: thesis: ( not I destroys a implies (Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = (s . a) - 1 )
assume A1: not I destroys a ; :: thesis: (Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = (s . a) - 1
set s0 = Initialized s;
set s1 = Initialize (Initialized s);
set P1 = P +* (I ";" (SubFrom (a,(intloc 0))));
A2: not a in dom (Start-At (0,SCM+FSA)) by SCMFSA_2:102;
(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 SCMFSA6B:11
.= ((Comput ((P +* I),(Initialize (Initialized s)),0)) . a) - 1 by A1, Th52
.= ((Initialize (Initialized s)) . a) - 1
.= ((Initialized s) . a) - 1 by A2, FUNCT_4:11 ;
hence (Comput ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)),(LifeSpan ((P +* (I ";" (SubFrom (a,(intloc 0))))),(Initialize (Initialized s)))))) . a = ((Initialized s) . a) - 1 by Th50
.= (s . a) - 1 by SCMFSA_M:37 ;
:: thesis: verum