35 lines
995 B
Text
35 lines
995 B
Text
set_option new_elaborator true
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inductive tree_core (A : Type) : bool → Type
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| leaf' : A → tree_core ff
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| node' : tree_core tt → tree_core ff
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| nil' {} : tree_core tt
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| cons' : tree_core ff → tree_core tt → tree_core tt
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attribute [reducible]
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definition tree (A : Type) := tree_core A ff
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attribute [reducible]
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definition tree_list (A : Type) := tree_core A tt
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open tree_core
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definition pack {A : Type} : list (tree A) → tree_core A tt
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| [] := nil'
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| (a::l) := cons' a (pack l)
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definition unpack {A : Type} : ∀ {b}, tree_core A b → list (tree A)
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| .tt nil' := []
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| .tt (cons' a t) := a :: unpack t
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| .ff (leaf' a) := []
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| .ff (node' l) := []
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attribute [injectivity]
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lemma unpack_pack {A : Type} : ∀ (l : list (tree A)), unpack (pack l) = l
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| [] := rfl
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| (a::l) :=
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show a :: unpack (pack l) = a :: l, from
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congr_arg (λ x, a :: x) (unpack_pack l)
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definition tree.node {A : Type} (l : list (tree A)) : tree A :=
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tree_core.node' (pack l)
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