8 lines
471 B
Text
8 lines
471 B
Text
open list
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lemma induction₂ {α₁ α₂ : Type*} (p : list α₁ → list α₂ → Prop)
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(h_base : p [] [])
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(h_step : ∀ {xs₁ xs₂}, p xs₁ xs₂ → (∀ x₁ x₂, p (x₁::xs₁) (x₂::xs₂))) :
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Π (xs₁ : list α₁) (xs₂ : list α₂) (H_same_len : length xs₁ = length xs₂), p xs₁ xs₂
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| [] [] h := h_base
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| (x₁::xs₁) (x₂::xs₂) h := h_step (induction₂ xs₁ xs₂ sorry) x₁ x₂
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