Definition differentiable_pt (f : R -> R -> R) (x y : R) :=
exists lx, exists ly, differentiable_pt_lim f x y lx ly.

Lemma differentiable_pt_lim_unique (f : R -> R -> R) (x y : R) (lx ly : R) :
differentiable_pt_lim f x y lx ly
-> Derive (fun x => f x y) x = lx /\ Derive (fun y => f x y) y = ly.