intro; assert (H := Dyi t).
unfold yi in H; assert (H0 := cond_y intr t).
cut
(derive_pt (y intr) t (yi_derivable intr t) =
derive_pt (y intr) t (cond_diff (y intr) t)); [ intro | apply pr_nu ].
rewrite H1 in H.
rewrite H0 in H.
unfold vi, thetat in |- *; symmetry  in |- *; assumption.
Qed.

(**********)
Lemma eq_plus_eq_is_eq :
forall x y z t : R, x = y -> z = t -> (x + z)%R = (y + t)%R.