theorem Th24: :: PCS_0:24

for P being pcs-Str
for a being set
for p being Element of P
for p1, q1 being Element of (pcs-extension (P,a)) st p = p1 & p <> a & p1 <= q1 & not a in the carrier of P holds
( q1 in the carrier of P & q1 <> a )