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 Th1, XREAL_1:6;
then (card I) + 4 in dom (if=0 (a,(I ';' (Goto 0)),(Stop SCM+FSA))) by AFINSQ_1:66;
then A1: {((card I) + 4)} c= dom (if=0 (a,(I ';' (Goto 0)),(Stop SCM+FSA))) by ZFMISC_1:31;
A2: 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_1:13
.= dom (if=0 (a,(I ';' (Goto 0)),(Stop SCM+FSA))) by A1, 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 12 :: 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 A2, AFINSQ_1:def 12; :: thesis: verum

end;

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