Mercurial > hg > Papers > 2022 > soto-sigos

diff Paper/src/NatAddSym.agda @ 0:14a0e409d574

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author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 24 Apr 2022 23:13:44 +0900
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/src/NatAddSym.agda	Sun Apr 24 23:13:44 2022 +0900
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+open import Relation.Binary.PropositionalEquality
+open import nat
+open import nat_add
+open ≡-Reasoning
+
+module nat_add_sym where
+
+addSym : (n m : Nat) -> n + m ≡ 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