let X, Y be set ; :: thesis: (proj1_4 X) \+\ (proj1_4 Y) c= proj1_4 (X \+\ Y)
( (proj1_4 X) \ (proj1_4 Y) c= proj1_4 (X \ Y) & (proj1_4 Y) \ (proj1_4 X) c= proj1_4 (Y \ X) ) by Th41;
then (proj1_4 X) \+\ (proj1_4 Y) c= (proj1_4 (X \ Y)) \/ (proj1_4 (Y \ X)) by XBOOLE_1:13;
hence (proj1_4 X) \+\ (proj1_4 Y) c= proj1_4 (X \+\ Y) by Th39; :: thesis: verum