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