17 lines
841 B
Text
17 lines
841 B
Text
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import data.nat
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open nat
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constant tuple.{l} : Type.{l} → nat → Type.{l}
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constant nil {A : Type} : tuple A 0
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constant cons {A : Type} {n : nat} : A → tuple A n → tuple A (succ n)
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constant append {A : Type} {n m : nat} : tuple A n → tuple A m → tuple A (n + m)
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infix ` ++ ` := append
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axiom append_nil {A : Type} {n : nat} (v : tuple A n) : v ++ nil = v
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axiom nil_append {A : Type} {n : nat} (v : tuple A n) : nil ++ v == v
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axiom append_assoc {A : Type} {n₁ n₂ n₃ : nat} (v₁ : tuple A n₁) (v₂ : tuple A n₂) (v₃ : tuple A n₃) : (v₁ ++ v₂) ++ v₃ == v₁ ++ (v₂ ++ v₃)
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attribute append_nil nil_append append_assoc [simp]
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example (A : Type) (n m : nat) (v₁ v₂ : tuple A n) (w₁ w₂ : tuple A m) :
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v₁ ++ nil ++ (v₂ ++ w₁) ++ (nil ++ w₂) == v₁ ++ v₂ ++ w₁ ++ w₂ :=
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by inst_simp
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