
theorem
  for T being consistent TA-structure for a being adjective of T holds
  types a misses types non-a
proof
  let T be consistent TA-structure;
  let a be adjective of T;
  assume types a meets types non-a;
  then consider x being object such that
A1: x in types a and
A2: x in types non-a by XBOOLE_0:3;
A3: ex t2 being type of T st x = t2 & non-a in adjs t2 by A2,Def12;
  ex t1 being type of T st x = t1 & a in adjs t1 by A1,Def12;
  hence thesis by A3,Def9;
end;
