let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
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)),p,s)) . b = (Initialized s) . b
set D = Data-Locations SCM+FSA;
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)),p,s)) . b = (Initialized 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)),p,s)) . b = (Initialized s) . b
let b be Int-Location ; :: thesis: for a being read-write Int-Location st s . a <= 0 holds
(IExec ((Times (a,I)),p,s)) . b = (Initialized s) . b
let a be read-write Int-Location ; :: thesis: ( s . a <= 0 implies (IExec ((Times (a,I)),p,s)) . b = (Initialized s) . b )
assume A1: s . a <= 0 ; :: thesis: (IExec ((Times (a,I)),p,s)) . b = (Initialized s) . b
set s0 = Initialized s;
set p0 = p;
A2: ( (Initialized s) . a = s . a & (Initialized s) . (intloc 0) = 1 ) by SCMFSA6C:3;
b in Int-Locations by SCMFSA_2:9;
then A3: b in Data-Locations SCM+FSA by SCMFSA_2:127, XBOOLE_0:def 3;
DataPart (IExec ((Times (a,I)),p,s)) = DataPart (IExec ((Times (a,I)),p,(Initialized s))) by SCMFSA8C:17
.= DataPart (Initialized s) by A1, A2, Th78 ;
hence (IExec ((Times (a,I)),p,s)) . b = (DataPart (Initialized s)) . b by A3, FUNCT_1:72
.= (Initialized s) . b by A3, FUNCT_1:72 ;
:: thesis: verum