Mercurial > hg > Papers > 2020 > soto-midterm

annotate src/NatAddSym.agda @ 1:73127e0ab57c

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author soto@cr.ie.u-ryukyu.ac.jp
date Tue, 08 Sep 2020 18:38:08 +0900
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soto@cr.ie.u-ryukyu.ac.jp
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1 open import Relation.Binary.PropositionalEquality
soto@cr.ie.u-ryukyu.ac.jp
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2 open import nat
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3 open import nat_add
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4 open ≡-Reasoning
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5
soto@cr.ie.u-ryukyu.ac.jp
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6 module nat_add_sym where
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7
soto@cr.ie.u-ryukyu.ac.jp
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8 addSym : (n m : Nat) -> n + m ≡ m + n
soto@cr.ie.u-ryukyu.ac.jp
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9 addSym O O = refl
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10 addSym O (S m) = cong S (addSym O m)
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11 addSym (S n) O = cong S (addSym n O)
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12 addSym (S n) (S m) = {!!} -- 後述