let X, Y be set ; :: thesis: ( X is constituted-Trees & Y is constituted-Trees implies X \+\ Y is constituted-Trees )
assume that
A1: for x being object st x in X holds
x is Tree and
A2: for x being object st x in Y holds
x is Tree ; :: according to TREES_3:def 3 :: thesis: X \+\ Y is constituted-Trees
let x be object ; :: according to TREES_3:def 3 :: thesis: ( x in X \+\ Y implies x is Tree )
assume x in X \+\ Y ; :: thesis: x is Tree
then ( not x in X iff x in Y ) by XBOOLE_0:1;
hence x is Tree by A1, A2; :: thesis: verum