let i be object ; :: according to FINSET_1:def 5 :: thesis: ( not i in I or (A (\/) B) . i is finite )
assume A1: i in I ; :: thesis: (A (\/) B) . i is finite
(A . i) \/ (B . i) is finite ;
hence (A (\/) B) . i is finite by A1, PBOOLE:def 4; :: thesis: verum