let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN st a = I_el Y holds
a 'or' b = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: ( a = I_el Y implies a 'or' b = I_el Y )
assume A1: a = 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 . x = TRUE by A1, BVFUNC_1:def 11;
then (a 'or' b) . x = TRUE 'or' (b . x) by BVFUNC_1:def 4
.= TRUE by BINARITH:10 ;
hence (a 'or' b) . x = TRUE ; :: thesis: verum

end;

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