theorem Th9: :: ABCMIZ_0:9

for T1, T2 being non empty TA-structure st TA-structure(# the carrier of T1, the adjectives of T1, the InternalRel of T1, the non-op of T1, the adj-map of T1 #) = TA-structure(# the carrier of T2, the adjectives of T2, the InternalRel of T2, the non-op of T2, the adj-map of T2 #) & T1 is adj-structured holds
T2 is adj-structured