Proof of Thevenin's and Norton's Theorem?
Let there be some linear circuit in a black box with two terminals exposed.

We measure the open circuit voltage \$V_{OC}\$ and the short circuit current \$I_{SC}\$ at the two terminals.

Now, according to Thevenin's theorem, the voltage across the terminals is given by

$$V_O = V_{OC} - I_O \frac{V_{OC}}{I_{SC}} = V_{TH} - I_OR_{TH}$$

Remember, this result is derived without an assumption as to the functional IV relationship for the load.

The above equation for \$V_O\$ is a load line and, whether the load is linear or not, the solution is the intersection of the load line and the IV curve of the load.

For example:



In equation form, let the load be some not necessarily linear circuit element where

$$V_L = V_O = f(I_L) $$

Then, it follows that

$$f(I_L) = V_{TH} - I_L R_{TH}$$