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