25 lines
762 B
Text
25 lines
762 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 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_assoc {A : Type} {n₁ n₂ n₃ : nat} (v₁ : tuple A n₁) (v₂ : tuple A n₂) (v₃ : tuple A n₃) :
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(v₁ ++ v₂) ++ v₃ == v₁ ++ (v₂ ++ v₃)
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attribute append_assoc [simp]
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variables {A : Type}
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variables {p m n q : nat}
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variables {xs : tuple A m}
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variables {ys : tuple A n}
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variables {zs : tuple A p}
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variables {ws : tuple A q}
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example : p = m + n → zs == xs ++ ys → zs ++ ws == xs ++ (ys ++ ws) :=
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by inst_simp
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example : p = n + m → zs == xs ++ ys → zs ++ ws == xs ++ (ys ++ ws) :=
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by inst_simp
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