lemma eq_rect_Type0_r:
∀A.∀a.∀P: ∀x:A. eq ? x a → Type[0]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
- #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+ #A #a #P #H #x #p (generalize {match H}) (generalize {match P})
cases p; //; qed.
lemma eq_rect_Type1_r:
∀A.∀a.∀P: ∀x:A. eq ? x a → Type[1]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
- #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+ #A #a #P #H #x #p (generalize {match H}) (generalize {match P})
cases p; //; qed.
lemma eq_rect_Type2_r:
∀A.∀a.∀P: ∀x:A. eq ? x a → Type[2]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
- #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+ #A #a #P #H #x #p (generalize {match H}) (generalize {match P})
cases p; //; qed.
lemma eq_rect_Type3_r:
∀A.∀a.∀P: ∀x:A. eq ? x a → Type[3]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
- #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+ #A #a #P #H #x #p (generalize {match H}) (generalize {match P})
cases p; //; qed.
theorem rewrite_l: ∀A:Type[2].∀x.∀P:A → Type[2]. P x → ∀y. x = y → P y.