let T be reflexive transitive antisymmetric with_suprema adj-structured TA-structure ; :: thesis: for A being Subset of the adjectives of T
for t being type of T st A is_applicable_to t holds
(types A) /\ (downarrow t) is Ideal of T
let A be Subset of the adjectives of T; :: thesis: for t being type of T st A is_applicable_to t holds
(types A) /\ (downarrow t) is Ideal of T
let t be type of T; :: thesis: ( A is_applicable_to t implies (types A) /\ (downarrow t) is Ideal of T )
given t' being type of T such that A1: ( A c= adjs t' & t' <= t ) ; :: according to ABCMIZ_0:def 16 :: thesis: (types A) /\ (downarrow t) is Ideal of T
( t' in downarrow t & t' in types A ) by A1, Th14, WAYBEL_0:17;
hence (types A) /\ (downarrow t) is Ideal of T by WAYBEL_0:27, WAYBEL_0:44, XBOOLE_0:def 4; :: thesis: verum