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