23 lines
752 B
Text
23 lines
752 B
Text
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import logic data.nat.basic
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open nat
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inductive inftree (A : Type) : Type :=
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leaf : A → inftree A,
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node : (nat → inftree A) → inftree A → inftree A
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namespace inftree
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inductive dsub {A : Type} : inftree A → inftree A → Prop :=
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intro₁ : Π (f : nat → inftree A) (a : nat) (t : inftree A), dsub (f a) (node f t),
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intro₂ : Π (f : nat → inftree A) (t : inftree A), dsub t (node f t)
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definition dsub.node.acc {A : Type} (f : nat → inftree A) (hf : ∀a, acc dsub (f a))
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(t : inftree A) (ht : acc dsub t) : acc dsub (node f t) :=
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acc.intro (node f t) (λ (y : inftree A) (hlt : dsub y (node f t)),
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begin
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inversion hlt,
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apply (hf a),
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apply ht
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end)
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end inftree
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