set D = Int-Locations \/ FinSeq-Locations ;
let s be State of SCM+FSA ; :: thesis: for I being Program of SCM+FSA
for f being FinSeq-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec (while>0 a,I),s) . f = s . f
let I be Program of SCM+FSA ; :: thesis: for f being FinSeq-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec (while>0 a,I),s) . f = s . f
let f be FinSeq-Location ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds
(IExec (while>0 a,I),s) . f = s . f
let a be read-write Int-Location ; :: thesis: ( s . a <= 0 implies (IExec (while>0 a,I),s) . f = s . f )
assume A1: s . a <= 0 ; :: thesis: (IExec (while>0 a,I),s) . f = s . f
f in FinSeq-Locations by SCMFSA_2:10;
then A2: f in Int-Locations \/ FinSeq-Locations by XBOOLE_0:def 3;
hence (IExec (while>0 a,I),s) . f = (DataPart (IExec (while>0 a,I),s)) . f by FUNCT_1:72, SCMFSA_2:127
.= (DataPart (Initialize s)) . f by A1, Th32
.= (Initialize s) . f by A2, FUNCT_1:72, SCMFSA_2:127
.= s . f by SCMFSA6C:3 ;
:: thesis: verum