46 lines
1.1 KiB
Text
46 lines
1.1 KiB
Text
universes u v
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inductive Vec2 (α : Type u) (β : Type v) : Nat → Type (max u v)
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| nil : Vec2 0
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| cons : α → β → forall {n}, Vec2 n → Vec2 (n+1)
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inductive Fin2 : Nat → Type
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| zero (n : Nat) : Fin2 (n+1)
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| succ {n : Nat} (s : Fin2 n) : Fin2 (n+1)
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new_frontend
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theorem test1 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : a₁ = a₂ :=
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begin
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injection h;
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assumption
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end
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theorem test2 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : v = w :=
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begin
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injection h with h1 h2 h3 h4;
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assumption
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end
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theorem test3 {α β} {n} (a₁ a₂ : α) (b₁ b₂ : β) (v w : Vec2 α β n) (h : Vec2.cons a₁ b₁ v = Vec2.cons a₂ b₂ w) : v = w :=
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begin
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injection h with _ _ _ h4;
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exact h4
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end
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theorem test4 {α} (v : Fin2 0) : α :=
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begin
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cases v
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end
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def test5 {α β} {n} (v : Vec2 α β (n+1)) : α :=
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begin
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cases v with
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| cons h1 h2 n tail => exact h1
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end
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def test6 {α β} {n} (v : Vec2 α β (n+2)) : α :=
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begin
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cases v with
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| cons h1 h2 n tail => exact h1
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end
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