let s be State of SCM+FSA ; :: thesis: for J being Program of SCM+FSA
for i being parahalting good Instruction of SCM+FSA
for a being Int-Location st ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . a = (IExec J,(Exec i,(Initialize s))) . a
let J be Program of SCM+FSA ; :: thesis: for i being parahalting good Instruction of SCM+FSA
for a being Int-Location st ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . a = (IExec J,(Exec i,(Initialize s))) . a
let i be parahalting good Instruction of SCM+FSA ; :: thesis: for a being Int-Location st ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) holds
(IExec (i ';' J),s) . a = (IExec J,(Exec i,(Initialize s))) . a
let a be Int-Location ; :: thesis: ( ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) implies (IExec (i ';' J),s) . a = (IExec J,(Exec i,(Initialize s))) . a )
set Mi = Macro i;
assume A1: ( J is parahalting or ( J is_halting_on Exec i,(Initialize s) & J is_closed_on Exec i,(Initialize s) ) ) ; :: thesis: (IExec (i ';' J),s) . a = (IExec J,(Exec i,(Initialize s))) . a
A2: J is_closed_on IExec (Macro i),s by A1, SCMFSA6C:6, SCMFSA7B:24;
J is_halting_on IExec (Macro i),s by A1, SCMFSA6C:6, SCMFSA7B:25;
hence (IExec (i ';' J),s) . a = (IExec J,(IExec (Macro i),s)) . a by A2, Th8
.= (IExec J,(Exec i,(Initialize s))) . a by SCMFSA6C:6 ;
:: thesis: verum