let s be State of SCM+FSA; :: thesis: for J being Program of SCM+FSA
for Ig being good Program of SCM+FSA st ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) & ( J is parahalting or ( J is_halting_on IExec (Ig,s) & J is_closed_on IExec (Ig,s) ) ) holds
DataPart (IExec ((Ig ';' J),s)) = DataPart (IExec (J,(IExec (Ig,s))))
let J be Program of SCM+FSA; :: thesis: for Ig being good Program of SCM+FSA st ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) & ( J is parahalting or ( J is_halting_on IExec (Ig,s) & J is_closed_on IExec (Ig,s) ) ) holds
DataPart (IExec ((Ig ';' J),s)) = DataPart (IExec (J,(IExec (Ig,s))))
let Ig be good Program of SCM+FSA; :: thesis: ( ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) & ( J is parahalting or ( J is_halting_on IExec (Ig,s) & J is_closed_on IExec (Ig,s) ) ) implies DataPart (IExec ((Ig ';' J),s)) = DataPart (IExec (J,(IExec (Ig,s)))) )
set I = Ig;
assume that
A1: ( Ig is parahalting or ( Ig is_halting_on Initialized s & Ig is_closed_on Initialized s ) ) and
A2: ( J is parahalting or ( J is_halting_on IExec (Ig,s) & J is_closed_on IExec (Ig,s) ) ) ; :: thesis: DataPart (IExec ((Ig ';' J),s)) = DataPart (IExec (J,(IExec (Ig,s))))
A3: for f being FinSeq-Location holds (IExec ((Ig ';' J),s)) . f = (IExec (J,(IExec (Ig,s)))) . f by A1, A2, Th9;
for a being Int-Location holds (IExec ((Ig ';' J),s)) . a = (IExec (J,(IExec (Ig,s)))) . a by A1, A2, Th8;
hence DataPart (IExec ((Ig ';' J),s)) = DataPart (IExec (J,(IExec (Ig,s)))) by A3, SCMFSA6A:38; :: thesis: verum