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_proj1_0 (f : R -> R) (x y l : R) : derivable_pt_lim f x l -> differentiable_pt_lim (fun u v => f u) x y l 0.