lean2/tests/lean/run/nested_begin.lean

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import logic data.nat.basic
open nat
inductive vector (A : Type) : nat → Type :=
| vnil : vector A zero
| vcons : Π {n : nat}, A → vector A n → vector A (succ n)
namespace vector
definition no_confusion2 {A : Type} {n : nat} {P : Type} {v₁ v₂ : vector A n} : v₁ = v₂ → vector.no_confusion_type P v₁ v₂ :=
assume H₁₂ : v₁ = v₂,
begin
show vector.no_confusion_type P v₁ v₂, from
have aux : v₁ = v₁ → vector.no_confusion_type P v₁ v₁, from
take H₁₁,
begin
apply (vector.cases_on v₁),
exact (assume h : P, h),
intros (n, a, v, h),
apply (h rfl),
repeat (apply rfl),
repeat (apply heq.refl)
end,
eq.rec_on H₁₂ aux H₁₂
end
theorem vcons.inj₁ {A : Type} {n : nat} (a₁ a₂ : A) (v₁ v₂ : vector A n) : vcons a₁ v₁ = vcons a₂ v₂ → a₁ = a₂ :=
begin
intro h, apply (vector.no_confusion h), intros, assumption
end
theorem vcons.inj₂ {A : Type} {n : nat} (a₁ a₂ : A) (v₁ v₂ : vector A n) : vcons a₁ v₁ = vcons a₂ v₂ → v₁ == v₂ :=
begin
intro h, apply (vector.no_confusion h), intros, eassumption
end
end vector