let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a = (a 'or' b) '&' (a 'or' ('not' b))
let a, b be Function of Y,BOOLEAN; :: thesis: a = (a 'or' b) '&' (a 'or' ('not' b))
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11(a,x) = K11(((a 'or' b) '&' (a 'or' ('not' b))),x)
((a 'or' b) '&' (a 'or' ('not' b))) . x = (a 'or' (b '&' ('not' b))) . x by BVFUNC_1:11
.= (a 'or' (O_el Y)) . x by BVFUNC_4:5
.= a . x by BVFUNC_1:9 ;
hence K11(a,x) = K11(((a 'or' b) '&' (a 'or' ('not' b))),x) ; :: thesis: verum