set D = Int-Locations \/ FinSeq-Locations ;
let s be State of SCM+FSA ; :: thesis: for I being good InitHalting Program of SCM+FSA
for f being FinSeq-Location
for a being read-write Int-Location st I does_not_destroy a & s . a > 0 holds
(IExec (Times a,I),s) . f = (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f
let I be good InitHalting Program of SCM+FSA ; :: thesis: for f being FinSeq-Location
for a being read-write Int-Location st I does_not_destroy a & s . a > 0 holds
(IExec (Times a,I),s) . f = (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f
let f be FinSeq-Location ; :: thesis: for a being read-write Int-Location st I does_not_destroy a & s . a > 0 holds
(IExec (Times a,I),s) . f = (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f
let a be read-write Int-Location ; :: thesis: ( I does_not_destroy a & s . a > 0 implies (IExec (Times a,I),s) . f = (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f )
assume A1: ( I does_not_destroy a & s . a > 0 ) ; :: thesis: (IExec (Times a,I),s) . f = (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f
set IT = IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s);
f in FinSeq-Locations by SCMFSA_2:10;
then A2: f in Int-Locations \/ FinSeq-Locations by XBOOLE_0:def 3;
hence (IExec (Times a,I),s) . f = (DataPart (IExec (Times a,I),s)) . f by FUNCT_1:72, SCMFSA_2:127
.= (DataPart (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s))) . f by A1, Th79
.= (IExec (Times a,I),(IExec (I ';' (SubFrom a,(intloc 0 ))),s)) . f by A2, FUNCT_1:72, SCMFSA_2:127 ;
:: thesis: verum