let I be Program of SCM+FSA ; :: thesis: for a being Int-Location holds card (while<0 a,I) = (card I) + 11
let a be Int-Location ; :: thesis: card (while<0 a,I) = (card I) + 11
set i = ((card I) + 4) .--> (goto 0 );
set C = if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )));
set P = (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) +* (((card I) + 4) .--> (goto 0 ));
A1: card (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) = (card I) + 11 by Th3;
(card I) + 4 < (card I) + 11 by XREAL_1:8;
then (card I) + 4 in dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) by A1, SCMFSA6A:15;
then A2: {((card I) + 4)} c= dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) by ZFMISC_1:37;
dom ((if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) +* (((card I) + 4) .--> (goto 0 ))) = (dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 ))))) \/ (dom (((card I) + 4) .--> (goto 0 ))) by FUNCT_4:def 1
.= (dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 ))))) \/ {((card I) + 4)} by FUNCOP_1:19
.= dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 )))) by A2, XBOOLE_1:12 ;
hence card (while<0 a,I) = card (dom (if=0 a,(Stop SCM+FSA ),(if>0 a,(Stop SCM+FSA ),(I ';' (Goto 0 ))))) by CARD_1:104
.= (card I) + 11 by A1, CARD_1:104 ;
:: thesis: verum