let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN st a '&' b = I_el Y holds
a 'or' b = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: ( a '&' b = I_el Y implies a 'or' b = I_el Y )
assume A1: a '&' b = I_el Y ; :: thesis: a 'or' b = I_el Y
for x being Element of Y holds (a 'or' b) . x = TRUE

proof

let x be Element of Y; :: thesis: (a 'or' b) . x = TRUE
(a '&' b) . x = TRUE by A1, BVFUNC_1:def 11;
then A2: (a . x) '&' (b . x) = TRUE by MARGREL1:def 20;
then a . x = TRUE by MARGREL1:12;
then (a 'or' b) . x = TRUE 'or' TRUE by A2, BVFUNC_1:def 4
.= TRUE ;
hence (a 'or' b) . x = TRUE ; :: thesis: verum

end;

hence a 'or' b = I_el Y by BVFUNC_1:def 11; :: thesis: verum