let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a = ((((a 'or' b) 'or' c) '&' ((a 'or' b) 'or' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))
let a, b, c be Function of Y,BOOLEAN; :: thesis: a = ((((a 'or' b) 'or' c) '&' ((a 'or' b) 'or' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11(a,x) = K11((((((a 'or' b) 'or' c) '&' ((a 'or' b) 'or' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))),x)
(((((a 'or' b) 'or' c) '&' ((a 'or' b) 'or' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))) . x = ((((a 'or' b) 'or' (c '&' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))) . x by BVFUNC_1:11
.= ((((a 'or' b) 'or' (O_el Y)) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))) . x by BVFUNC_4:5
.= (((a 'or' b) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))) . x by BVFUNC_1:9
.= ((a 'or' b) '&' (((a 'or' ('not' b)) 'or' c) '&' ((a 'or' ('not' b)) 'or' ('not' c)))) . x by BVFUNC_1:4
.= ((a 'or' b) '&' ((a 'or' ('not' b)) 'or' (c '&' ('not' c)))) . x by BVFUNC_1:11
.= ((a 'or' b) '&' ((a 'or' ('not' b)) 'or' (O_el Y))) . x by BVFUNC_4:5
.= ((a 'or' b) '&' (a 'or' ('not' b))) . x by BVFUNC_1:9
.= (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) 'or' c) '&' ((a 'or' b) 'or' ('not' c))) '&' ((a 'or' ('not' b)) 'or' c)) '&' ((a 'or' ('not' b)) 'or' ('not' c))),x) ; :: thesis: verum