let X, Y be set ; :: thesis: ( X is constituted-FinTrees & Y is constituted-FinTrees implies X \+\ Y is constituted-FinTrees )
assume that
A1: for x being object st x in X holds
x is finite Tree and
A2: for x being object st x in Y holds
x is finite Tree ; :: according to TREES_3:def 4 :: thesis: X \+\ Y is constituted-FinTrees
let x be object ; :: according to TREES_3:def 4 :: thesis: ( x in X \+\ Y implies x is finite Tree )
assume x in X \+\ Y ; :: thesis: x is finite Tree
then ( not x in X iff x in Y ) by XBOOLE_0:1;
hence x is finite Tree by A1, A2; :: thesis: verum