How can I define general properties of symbolic functions?

I'm trying to work with undefined symbolic functions, but I want to take advantage of some of its properties. For instance, I know that my functions fulfill:

As such I tried the following:

syms x y xx yy f(x) 
assume(f(x)*f(y)==f(x+y))
Z=f(x)*f(y);
K=f(yy)*f(xx);
simplify(Z)
simplify(K)

While Z returns f(x+y) (the set identity as expected), it doesn't work on K as I don't know how to set the assumption on generic variables. I would very much like to avoid setting the assumption on every pair of arguments of my model, any clue on how to do this?

Answer 1

[Ananya Tewari]

I understand that you want to set assumptions on generic variables. Currently it is not supported by MATLAB. A workaround if you do not wish to set assumption on every pair of argument, you can try using function handle to create a generic assume statement.

% creating function handle for assume statement
funAssume = @(a,b) assumeAlso(f(a)*f(b)==f(a+b))    % using assumeAlso to keep multiple assumptions

% calling funAssume() with any symbolic variable
funAssume(xx,yy)

K=f(yy)*f(xx);
simplify(K)

[Jaime Abad Arredondo]

In the end I created a new class with objects that operated as I wanted. Much more laborious, but worked as intended. I accept the answer as it's a nice work-around. Still have to loop through every single variable combination calling the funAssume though...