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

for a being Int-Location

for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let p be Instruction-Sequence of SCM+FSA; :: thesis: for a being Int-Location

for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let a be Int-Location; :: thesis: for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let I be really-closed Program of ; :: thesis: ( ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I implies (IExec (I,p,s)) . a = s . a )

assume that

A1: ( I is_halting_on Initialized s,p or I is parahalting ) and

A2: ( s . (intloc 0) = 1 or a is read-write ) and

A3: not a in UsedILoc I ; :: thesis: (IExec (I,p,s)) . a = s . a

A4: ( a = intloc 0 or a is read-write ) by SCMFSA_M:def 2;

I is_halting_on Initialized s,p by A1, SCMFSA7B:19;

hence (IExec (I,p,s)) . a = (Initialized s) . a by A3, Th1

.= s . a by A2, A4, SCMFSA_M:9, SCMFSA_M:37 ;

:: thesis: verum

for a being Int-Location

for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let p be Instruction-Sequence of SCM+FSA; :: thesis: for a being Int-Location

for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let a be Int-Location; :: thesis: for I being really-closed Program of st ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I holds

(IExec (I,p,s)) . a = s . a

let I be really-closed Program of ; :: thesis: ( ( I is_halting_on Initialized s,p or I is parahalting ) & ( s . (intloc 0) = 1 or a is read-write ) & not a in UsedILoc I implies (IExec (I,p,s)) . a = s . a )

assume that

A1: ( I is_halting_on Initialized s,p or I is parahalting ) and

A2: ( s . (intloc 0) = 1 or a is read-write ) and

A3: not a in UsedILoc I ; :: thesis: (IExec (I,p,s)) . a = s . a

A4: ( a = intloc 0 or a is read-write ) by SCMFSA_M:def 2;

I is_halting_on Initialized s,p by A1, SCMFSA7B:19;

hence (IExec (I,p,s)) . a = (Initialized s) . a by A3, Th1

.= s . a by A2, A4, SCMFSA_M:9, SCMFSA_M:37 ;

:: thesis: verum