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

for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds

for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds

for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

let I be Program of SCM+FSA; :: thesis: ( I is_halting_on Initialized s,P implies for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a )

set s0 = Initialized s;

set s1 = Initialize (Initialized s);

set A = NAT ;

set P1 = P +* I;

assume I is_halting_on Initialized s,P ; :: thesis: for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

then A1: P +* I halts_on Initialize (Initialized s) by SCMFSA7B:def 7;

for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds

for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds

for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

let I be Program of SCM+FSA; :: thesis: ( I is_halting_on Initialized s,P implies for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a )

set s0 = Initialized s;

set s1 = Initialize (Initialized s);

set A = NAT ;

set P1 = P +* I;

assume I is_halting_on Initialized s,P ; :: thesis: for a being Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

then A1: P +* I halts_on Initialize (Initialized s) by SCMFSA7B:def 7;

hereby :: thesis: verum

let a be Int-Location; :: thesis: (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a

Initialized s = Initialize (Initialized s) by MEMSTR_0:44;

hence (IExec (I,P,s)) . a = (Result ((P +* I),(Initialize (Initialized s)))) . a by SCMFSA6B:def 1

.= (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a by A1, EXTPRO_1:23 ;

:: thesis: verum

end;Initialized s = Initialize (Initialized s) by MEMSTR_0:44;

hence (IExec (I,P,s)) . a = (Result ((P +* I),(Initialize (Initialized s)))) . a by SCMFSA6B:def 1

.= (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a by A1, EXTPRO_1:23 ;

:: thesis: verum