let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a '&' b '<' a
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a '&' b '<' a
let x be Element of Y; :: according to BVFUNC_1:def 12 :: thesis: ( not (a '&' b) . x = TRUE or a . x = TRUE )
assume (a '&' b) . x = TRUE ; :: thesis: a . x = TRUE
then (a . x) '&' (b . x) = TRUE by MARGREL1:def 20;
hence a . x = TRUE by MARGREL1:12; :: thesis: verum