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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize 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 Initialize s & Ig is_closed_on Initialize 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