set A = {{}};
take {{}} ; :: thesis: ( not {{}} is empty & {{}} is functional & {{}} is compatible )
{{}} is compatible

proof

let f, g be Function; :: according to COMPUT_1:def 1 :: thesis: ( f in {{}} & g in {{}} implies f tolerates g )
assume that
A1: f in {{}} and
g in {{}} ; :: thesis: f tolerates g
f = {} by A1, TARSKI:def 1;
hence f tolerates g ; :: thesis: verum

end;

hence ( not {{}} is empty & {{}} is functional & {{}} is compatible ) ; :: thesis: verum