set D = Int-Locations \/ FinSeq-Locations ;
let s be State of SCM+FSA ; :: thesis: for I being good InitHalting Program of SCM+FSA
for b being Int-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec (Times a,I),s) . b = (Initialize s) . b
let I be good InitHalting Program of SCM+FSA ; :: thesis: for b being Int-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec (Times a,I),s) . b = (Initialize s) . b
let b be Int-Location ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds
(IExec (Times a,I),s) . b = (Initialize s) . b
let a be read-write Int-Location ; :: thesis: ( s . a <= 0 implies (IExec (Times a,I),s) . b = (Initialize s) . b )
assume A1: s . a <= 0 ; :: thesis: (IExec (Times a,I),s) . b = (Initialize s) . b
set s0 = Initialize s;
A2: ( (Initialize s) . a = s . a & (Initialize s) . (intloc 0 ) = 1 ) by SCMFSA6C:3;
b in Int-Locations by SCMFSA_2:9;
then A3: b 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) . b = (DataPart (Initialize s)) . b by A3, FUNCT_1:72, SCMFSA_2:127
.= (Initialize s) . b by A3, FUNCT_1:72, SCMFSA_2:127 ;
:: thesis: verum