let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'or' (a '&' b) = a

let a, b be Function of Y,BOOLEAN; :: thesis: a 'or' (a '&' b) = a

let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'or' (a '&' b)) . x = a . x

thus (a 'or' (a '&' b)) . x = (a . x) 'or' ((a '&' b) . x) by BVFUNC_1:def 4

.= (a . x) 'or' ((a . x) '&' (b . x)) by MARGREL1:def 20

.= a . x by XBOOLEAN:5 ; :: thesis: verum

let a, b be Function of Y,BOOLEAN; :: thesis: a 'or' (a '&' b) = a

let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: (a 'or' (a '&' b)) . x = a . x

thus (a 'or' (a '&' b)) . x = (a . x) 'or' ((a '&' b) . x) by BVFUNC_1:def 4

.= (a . x) 'or' ((a . x) '&' (b . x)) by MARGREL1:def 20

.= a . x by XBOOLEAN:5 ; :: thesis: verum