let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN st a 'or' b = I_el Y & 'not' a = I_el Y holds
b = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: ( a 'or' b = I_el Y & 'not' a = I_el Y implies b = I_el Y )
assume that
A1: a 'or' b = I_el Y and
A2: 'not' a = I_el Y ; :: thesis: b = I_el Y
for x being Element of Y holds b . x = TRUE

proof

let x be Element of Y; :: thesis: b . x = TRUE
('not' a) . x = TRUE by A2, BVFUNC_1:def 11;
then A3: 'not' (a . x) = TRUE by MARGREL1:def 19;
(a 'or' b) . x = TRUE by A1, BVFUNC_1:def 11;
then (a . x) 'or' (b . x) = TRUE by BVFUNC_1:def 4;
hence b . x = TRUE by A3; :: thesis: verum

end;

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