let s be State of SCM+FSA ; :: thesis: for aa being Int-Location
for I being Program of SCM+FSA st I is_closed_on Initialize s & I is_halting_on Initialize s & I does_not_destroy aa holds
(IExec I,s) . aa = (Initialize s) . aa
let aa be Int-Location ; :: thesis: for I being Program of SCM+FSA st I is_closed_on Initialize s & I is_halting_on Initialize s & I does_not_destroy aa holds
(IExec I,s) . aa = (Initialize s) . aa
let I be Program of SCM+FSA ; :: thesis: ( I is_closed_on Initialize s & I is_halting_on Initialize s & I does_not_destroy aa implies (IExec I,s) . aa = (Initialize s) . aa )
set D = Int-Locations \/ FinSeq-Locations ;
set a = aa;
A1: DataPart (Initialize s) = DataPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))) by SCMFSA8A:11;
assume ( I is_closed_on Initialize s & I is_halting_on Initialize s & I does_not_destroy aa ) ; :: thesis: (IExec I,s) . aa = (Initialize s) . aa
hence (IExec I,s) . aa = (Comput (ProgramPart ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA )))),((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))),0 ) . aa by SCMFSA8C:89
.= ((Initialize s) +* (I +* (Start-At 0 ,SCM+FSA ))) . aa by AMI_1:13
.= (Initialize s) . aa by A1, SCMFSA6A:38 ;
:: thesis: verum