set C = if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA );
set i = ((card I) + 4) .--> (goto 0 );
set P = (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ));
( card (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) = (card I) + 6 & (card I) + 4 < (card I) + 6 ) by Th2, XREAL_1:8;
then (card I) + 4 in dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by AFINSQ_1:70;
then A3: {((card I) + 4)} c= dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by ZFMISC_1:37;
A4: 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 A3, XBOOLE_1:12 ;
(if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 )) is initial

proof

let m, n be Nat; :: according to AFINSQ_1:def 13 :: thesis: ( not n in proj1 ((if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ))) or n <= m or m in proj1 ((if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ))) )
thus ( not n in proj1 ((if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ))) or n <= m or m in proj1 ((if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 ))) ) by A4, AFINSQ_1:def 13; :: thesis: verum

end;

hence (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) +* (((card I) + 4) .--> (goto 0 )) is Program of SCM+FSA ; :: thesis: verum