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 s . a <= 0 holds
(IExec (Times a,I),s) . f = 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 s . a <= 0 holds
(IExec (Times 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 (Times a,I),s) . f = s . f
let a be read-write Int-Location ; :: thesis: ( s . a <= 0 implies (IExec (Times a,I),s) . f = s . f )
assume A1: s . a <= 0 ; :: thesis: (IExec (Times a,I),s) . f = s . f
set s0 = Initialize s;
A2: ( (Initialize s) . a = s . a & (Initialize s) . (intloc 0 ) = 1 ) by SCMFSA6C:3;
f in FinSeq-Locations by SCMFSA_2:10;
then A3: f in Int-Locations \/ FinSeq-Locations by XBOOLE_0:def 3;
DataPart (IExec (Times a,I),s) = DataPart (IExec (Times a,I),(Initialize s)) by SCMFSA8C:17
.= DataPart (Initialize s) by A1, A2, Th78 ;
hence (IExec (Times a,I),s) . f = (DataPart (Initialize s)) . f by A3, FUNCT_1:72, SCMFSA_2:127
.= (Initialize s) . f by A3, FUNCT_1:72, SCMFSA_2:127
.= s . f by SCMFSA6C:3 ;
:: thesis: verum