
theorem Th36:
  for T being non empty non void reflexive transitive TA-structure
for t being type of T for v1,v2 being FinSequence of the adjectives of T holds
  apply(v1^v2, t).(len v1+1) = v1 ast t
proof
  let T be non empty non void reflexive transitive TA-structure;
  let t be type of T;
  let v1,v2 be FinSequence of the adjectives of T;
  set v = v1^v2;
A1: len apply(v2, v1 ast t) = len v2+1 by Def19;
A2: apply(v,t) = apply(v1,t) $^ apply(v2, v1 ast t) by Th34;
  len apply(v1,t) = len v1+1 by Def19;
  then apply(v,t).(len v1+1+0) = apply(v2, v1 ast t).(0+1) by A1,A2,Th33;
  hence thesis by Def19;
end;
