let I be Program of SCM+FSA ; :: thesis: for a being Int-Location holds card (while>0 a,I) = (card I) + 6
let a be Int-Location ; :: thesis: card (while>0 a,I) = (card I) + 6
set i = ((card I) + 4) .--> (goto 0 );
set C = if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA );
set P = (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ));
A1: card (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) = (card I) + 6 by Th2;
(card I) + 4 < (card I) + 6 by XREAL_1:8;
then (card I) + 4 in dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by A1, SCMFSA6A:15;
then A2: {((card I) + 4)} c= dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by ZFMISC_1:37;
dom ((if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ))) = (dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA ))) \/ (dom (((card I) + 4) .--> (goto 0 ))) by FUNCT_4:def 1
.= (dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA ))) \/ {((card I) + 4)} by FUNCOP_1:19
.= dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by A2, XBOOLE_1:12 ;
hence card (while>0 a,I) = card (dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA ))) by CARD_1:104
.= (card I) + 6 by A1, CARD_1:104 ;
:: thesis: verum