let s be State of SCM+FSA; :: thesis: for Ig being good Program of SCM+FSA
for j being parahalting Instruction of SCM+FSA
for f being FinSeq-Location st ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) holds
(IExec ((Ig ';' j),s)) . f = (Exec (j,(IExec (Ig,s)))) . f
let Ig be good Program of SCM+FSA; :: thesis: for j being parahalting Instruction of SCM+FSA
for f being FinSeq-Location st ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) holds
(IExec ((Ig ';' j),s)) . f = (Exec (j,(IExec (Ig,s)))) . f
let j be parahalting Instruction of SCM+FSA; :: thesis: for f being FinSeq-Location st ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) holds
(IExec ((Ig ';' j),s)) . f = (Exec (j,(IExec (Ig,s)))) . f
let f be FinSeq-Location ; :: thesis: ( ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) implies (IExec ((Ig ';' j),s)) . f = (Exec (j,(IExec (Ig,s)))) . f )
set I = Ig;
set Mj = Macro j;
f in FinSeq-Locations by SCMFSA_2:10;
then A1: f in Int-Locations \/ FinSeq-Locations by XBOOLE_0:def 3;
assume A2: ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) ; :: thesis: (IExec ((Ig ';' j),s)) . f = (Exec (j,(IExec (Ig,s)))) . f
A3: DataPart (Initialized (IExec (Ig,s))) = DataPart (IExec (Ig,s)) by A2, Th11;
thus (IExec ((Ig ';' j),s)) . f = (IExec ((Macro j),(IExec (Ig,s)))) . f by A2, Th9
.= (Exec (j,(Initialized (IExec (Ig,s))))) . f by SCMFSA6C:6
.= (DataPart (Exec (j,(Initialized (IExec (Ig,s)))))) . f by A1, FUNCT_1:72, SCMFSA_2:127
.= (DataPart (Exec (j,(IExec (Ig,s))))) . f by A3, SCMFSA6C:5
.= (Exec (j,(IExec (Ig,s)))) . f by A1, FUNCT_1:72, SCMFSA_2:127 ; :: thesis: verum