Mercurial > hg > Papers > 2020 > soto-midterm

annotate src/agda-term1.agda.replaced @ 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 +-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x
soto@cr.ie.u-ryukyu.ac.jp
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2 +-comm zero y rewrite (+zero {y}) = refl
soto@cr.ie.u-ryukyu.ac.jp
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3 +-comm (suc x) y = let open @$\equiv$@-Reasoning in
soto@cr.ie.u-ryukyu.ac.jp
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4 begin
soto@cr.ie.u-ryukyu.ac.jp
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5 ?0 @$\equiv$@@$\langle$@ ?1 @$\rangle$@
soto@cr.ie.u-ryukyu.ac.jp
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6 ?2 @$\blacksquare$@
soto@cr.ie.u-ryukyu.ac.jp
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7
soto@cr.ie.u-ryukyu.ac.jp
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8 -- ?0 : @$\mathbb{N}$@ {(suc x) + y}
soto@cr.ie.u-ryukyu.ac.jp
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9 -- ?1 : suc x + y @$\equiv$@ y + suc x
soto@cr.ie.u-ryukyu.ac.jp
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10 -- ?2 : @$\mathbb{N}$@