Mercurial > hg > Papers > 2022 > soto-sigos

annotate Paper/src/agda-term2.agda @ 0:14a0e409d574

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ADD fast commit
author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 24 Apr 2022 23:13:44 +0900
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Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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14a0e409d574 ADD fast commit
soto <soto@cr.ie.u-ryukyu.ac.jp>
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1 +-comm : (x y : ℕ) → x + y ≡ y + x
14a0e409d574 ADD fast commit
soto <soto@cr.ie.u-ryukyu.ac.jp>
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2 +-comm zero y rewrite (+zero {y}) = refl
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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3 +-comm (suc x) y = let open ≡-Reasoning in
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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4 begin
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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5 (suc x) + y ≡⟨⟩
14a0e409d574 ADD fast commit
soto <soto@cr.ie.u-ryukyu.ac.jp>
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6 suc (x + y) ≡⟨ cong suc (+-comm x y) ⟩
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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7 suc (y + x) ≡⟨ ?0 ⟩
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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8 ?1 ∎
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soto <soto@cr.ie.u-ryukyu.ac.jp>
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9
14a0e409d574 ADD fast commit
soto <soto@cr.ie.u-ryukyu.ac.jp>
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10 -- ?0 : suc (y + x) ≡ y + suc x
14a0e409d574 ADD fast commit
soto <soto@cr.ie.u-ryukyu.ac.jp>
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11 -- ?1 : y + suc x