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author ryokka
date Wed, 12 Feb 2020 17:55:00 +0900
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open import Relation.Binary.PropositionalEquality
open import nat
open import nat_add
open @$\equiv$@-Reasoning

module nat_add_sym where

addSym : (n m : Nat) @$\rightarrow$@ n + m @$\equiv$@ m + n
addSym O       O   = refl
addSym O    (S m)  = cong S (addSym O m)
addSym (S n)   O   = cong S (addSym n O) 
addSym (S n) (S m) = {!!} -- 後述