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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize s ) ) implies (IExec (Ig ';' j),s) . f = (Exec j,(IExec Ig,s)) . f )
set I = Ig;
assume A1: ( Ig is parahalting or ( Ig is_halting_on Initialize s & Ig is_closed_on Initialize s ) ) ; :: thesis: (IExec (Ig ';' j),s) . f = (Exec j,(IExec Ig,s)) . f
set Mj = Macro j;
A2: DataPart (Initialize (IExec Ig,s)) = DataPart (IExec Ig,s) by A1, Th11;
f in FinSeq-Locations by SCMFSA_2:10;
then A3: f in Int-Locations \/ FinSeq-Locations by XBOOLE_0:def 3;
thus (IExec (Ig ';' j),s) . f = (IExec (Macro j),(IExec Ig,s)) . f by A1, Th9
.= (Exec j,(Initialize (IExec Ig,s))) . f by SCMFSA6C:6
.= (DataPart (Exec j,(Initialize (IExec Ig,s)))) . f by A3, FUNCT_1:72, SCMFSA_2:127
.= (DataPart (Exec j,(IExec Ig,s))) . f by A2, SCMFSA6C:5
.= (Exec j,(IExec Ig,s)) . f by A3, FUNCT_1:72, SCMFSA_2:127 ; :: thesis: verum