for T being non empty reflexive transitive non void TAS-structure
for t being type of T
for A being Subset of the adjectives of T st A is_properly_applicable_to t holds
ex B being Subset of the adjectives of T st
( B c= A & B is_properly_applicable_to t & A ast t = B ast t & ( for C being Subset of the adjectives of T st C c= B & C is_properly_applicable_to t & A ast t = C ast t holds
C = B ) )