Section equatesLemma.
Variables (A0 A1 : Type).
Variables (A2 : forall (x1 : A1), Type).
Variables (A3 : forall (x1 : A1) (x2 : A2 x1), Type).
Variables (A4 : forall (x1 : A1) (x2 : A2 x1) (x3 : A3 x2), Type).
Variables (A5 : forall (x1 : A1) (x2 : A2 x1) (x3 : A3 x2) (x4 : A4 x3), Type).
Variables (A6 : forall (x1 : A1) (x2 : A2 x1) (x3 : A3 x2) (x4 : A4 x3) (x5 : A5 x4), Type).
Proof using. intros. subst. auto. Qed.
Proof using. intros. subst. auto. Qed.
Proof using. intros. subst. auto. Qed.
Proof using. intros. subst. auto. Qed.
Proof using. intros. subst. auto. Qed.
Proof using. intros. subst. auto. Qed.

Lemma equates_6 :
forall y1 (P:A0->forall(x1:A1)(x2:A2 x1)(x3:A3 x2)(x4:A4 x3)(x5:A5 x4),Prop)
x1 x2 x3 x4 x5 x6,
P y1 x2 x3 x4 x5 x6 -> x1 = y1 -> P x1 x2 x3 x4 x5 x6.