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Inductive sigT3 {A: Type} {P: A -> Type} (Q: forall a: A, P a -> Type) :=
existT3: forall a: A, forall b: P a, Q a b -> sigT3 Q
.
Definition projT3_1 {A: Type} {P: A -> Type} {Q: forall a: A, P a -> Type} (a: sigT3 Q) :=
let 'existT3 _ x0 _ _ := a in x0.
Definition projT3_2 {A: Type} {P: A -> Type} {Q: forall a: A, P a -> Type} (a: sigT3 Q) : P (projT3_1 a) :=
let 'existT3 _ x0 x1 _ := a in x1.
Lemma projT3_3_eq' (A B: Type) (Q: B -> Type) (a b: sigT3 (fun (_: A) b => Q b)) (H: a = b) :
unit.
Proof.
destruct a as [x0 x1 x2], b as [y0 y1 y2].
assert (H' := f_equal projT3_1 H).
cbn in H'.
subst x0.
assert (H' := f_equal (projT3_2 (P := fun _ => B)) H).
cbn in H'.
subst x1.
injection H as H'.
exact tt.
Qed.
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