let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA

for I being MacroInstruction 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 MacroInstruction 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 MacroInstruction 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 ;

assume A1: s . a <= 0 ; :: thesis: (IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b

b in Int-Locations by AMI_2:def 16;

then A2: b in Data-Locations by SCMFSA_2:100, XBOOLE_0:def 3;

hence (IExec ((while>0 (a,I)),P,s)) . b = (DataPart (IExec ((while>0 (a,I)),P,s))) . b by FUNCT_1:49

.= (DataPart (Initialized s)) . b by A1, Th13

.= (Initialized s) . b by A2, FUNCT_1:49 ;

:: thesis: verum

for I being MacroInstruction 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 MacroInstruction 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 MacroInstruction 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 ;

assume A1: s . a <= 0 ; :: thesis: (IExec ((while>0 (a,I)),P,s)) . b = (Initialized s) . b

b in Int-Locations by AMI_2:def 16;

then A2: b in Data-Locations by SCMFSA_2:100, XBOOLE_0:def 3;

hence (IExec ((while>0 (a,I)),P,s)) . b = (DataPart (IExec ((while>0 (a,I)),P,s))) . b by FUNCT_1:49

.= (DataPart (Initialized s)) . b by A1, Th13

.= (Initialized s) . b by A2, FUNCT_1:49 ;

:: thesis: verum