let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'or' b = a 'or' (('not' a) '&' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'or' b = a 'or' (('not' a) '&' b)
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11((a 'or' b),x) = K11((a 'or' (('not' a) '&' b)),x)
(a 'or' (('not' a) '&' b)) . x = (a . x) 'or' ((('not' a) '&' b) . x) by BVFUNC_1:def 4
.= (a . x) 'or' ((('not' a) . x) '&' (b . x)) by MARGREL1:def 20
.= ((a . x) 'or' (('not' a) . x)) '&' ((a . x) 'or' (b . x)) by XBOOLEAN:9
.= ((a . x) 'or' ('not' (a . x))) '&' ((a . x) 'or' (b . x)) by MARGREL1:def 19
.= TRUE '&' ((a . x) 'or' (b . x)) by XBOOLEAN:102
.= (a . x) 'or' (b . x)
.= (a 'or' b) . x by BVFUNC_1:def 4 ;
hence K11((a 'or' b),x) = K11((a 'or' (('not' a) '&' b)),x) ; :: thesis: verum