let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a = (a '&' b) 'or' (a '&' ('not' b))
let a, b be Function of Y,BOOLEAN; :: thesis: a = (a '&' b) 'or' (a '&' ('not' b))
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11(a,x) = K11(((a '&' b) 'or' (a '&' ('not' b))),x)
((a '&' b) 'or' (a '&' ('not' b))) . x = (a '&' (b 'or' ('not' b))) . x by BVFUNC_1:12
.= (a '&' (I_el Y)) . x by BVFUNC_4:6
.= a . x by BVFUNC_1:6 ;
hence K11(a,x) = K11(((a '&' b) 'or' (a '&' ('not' b))),x) ; :: thesis: verum