The Coq mailing list

[Nils Anders Danielsson <nad AT Cs.Nott.AC.UK>]

On 2009-08-28 18:35, Edsko de Vries wrote:
> would Agda accept it?

Yes, the following relation is trivial:

 data _∼_ : PCoℕ → PCoℕ → Set where
   zero   :                                 zero  ∼ zero
   suc    : ∀ {m n} (m∼n : ∞ (♭ m ∼ ♭ n)) → suc m ∼ suc n
   τ      : ∀ {m n} (m∼n : ∞ (♭ m ∼ ♭ n)) → τ   m ∼ τ   n
   τˡ     : ∀ {m n} (m∼n :    ♭ m ∼   n ) → τ   m ∼     n
   τʳ     : ∀ {m n} (m∼n :      m ∼ ♭ n ) →     m ∼ τ   n

   -- Transitivity.
   _∼⟨_⟩_ : ∀ n₁ {n₂ n₃}
            (n₁∼n₂ : n₁ ∼ n₂) (n₂∼n₃ : n₂ ∼ n₃) → n₁ ∼ n₃

   -- Reflexivity.
   _∎     : ∀ n → n ∼ n

 trivial : ∀ m n → m ∼ n
 trivial m n =
   m       ∼⟨ τʳ (m ∎) ⟩
   τ (♯ m) ∼⟨ τ (♯ trivial m n) ⟩
   τ (♯ n) ∼⟨ τˡ (n ∎) ⟩
   n       ∎

--
/NAD



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