let T1, T2 be DTree-set of D; :: thesis: ( ( for T being DecoratedTree of holds T in T1 ) & ( for T being DecoratedTree of holds T in T2 ) implies T1 = T2 )
assume that
A5: for T being DecoratedTree of holds T in T1 and
A6: for T being DecoratedTree of holds T in T2 ; :: thesis: T1 = T2
thus T1 c= T2 :: according to XBOOLE_0:def 10 :: thesis: T2 c= T1

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in T1 or x in T2 )
assume x in T1 ; :: thesis: x in T2
then x is DecoratedTree of by Def6;
hence x in T2 by A6; :: thesis: verum

end;

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in T2 or x in T1 )
assume x in T2 ; :: thesis: x in T1
then x is DecoratedTree of by Def6;
hence x in T1 by A5; :: thesis: verum