set A = {{} };
A1: {{} } is compatible

proof

let f, g be Function; :: according to COMPUT_1:def 1 :: thesis: ( f in {{} } & g in {{} } implies f tolerates g )
assume ( f in {{} } & g in {{} } ) ; :: thesis: f tolerates g
then f = {} by TARSKI:def 1;
hence f tolerates g by PARTFUN1:135, XBOOLE_1:2; :: thesis: verum

end;

take {{} } ; :: thesis: ( not {{} } is empty & {{} } is functional & {{} } is compatible )
thus ( not {{} } is empty & {{} } is functional & {{} } is compatible ) by A1; :: thesis: verum