let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for s being State of SCM+FSA
for I being Program of SCM+FSA
for b being Int-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b
let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA
for b being Int-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b
let I be Program of SCM+FSA; :: thesis: for b being Int-Location
for a being read-write Int-Location st s . a <= 0 holds
(IExec ((while>0 (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 ((while>0 (a,I)),P,s)) . b = (Initialized s) . b
let a be read-write Int-Location ; :: thesis: ( s . a <= 0 implies (IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b )
set D = Data-Locations SCM+FSA;
assume A1: s . a <= 0 ; :: thesis: (IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b
b in Int-Locations by SCMFSA_2:9;
then A2: b in Data-Locations SCM+FSA by SCMFSA_2:127, XBOOLE_0:def 3;
hence (IExec ((while>0 (a,I)),P,s)) . b = (DataPart (IExec ((while>0 (a,I)),P,s))) . b by FUNCT_1:72
.= (DataPart (Initialized s)) . b by A1, Th32
.= (Initialized s) . b by A2, FUNCT_1:72 ;
:: thesis: verum