theorem ::#Th44
p^p1^p2 is X-valued implies (p2 is X-valued & p1 is X-valued & p is X-valued)
proof
set q=p^p1^p2; assume q is X-valued; then rng q c= X & rng (p^p1) c= rng q
& rng p2 c= rng q by  FINSEQ_1:29,30; then rng p2 c= X
& rng p c= rng (p^p1) & rng p1 c= rng (p^p1) & rng (p^p1) c= X by
FINSEQ_1:29, 30;
hence thesis by  XBOOLE_1:1;
end;
