Mercurial > hg > Papers > 2021 > soto-prosym

annotate Paper/src/agda-term2.agda.replaced @ 0:c59202657321

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author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Tue, 02 Nov 2021 06:55:58 +0900
parents
children 339fb67b4375
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soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
1 +-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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2 +-comm zero y rewrite (+zero {y}) = refl
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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3 +-comm (suc x) y = let open @$\equiv$@-Reasoning in
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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4 begin
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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5 (suc x) + y @$\equiv$@@$\langle$@@$\rangle$@
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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6 suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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7 suc (y + x) @$\equiv$@@$\langle$@ ?0 @$\rangle$@
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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8 ?1 @$\blacksquare$@
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
diff changeset
9
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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10 -- ?0 : suc (y + x) @$\equiv$@ y + suc x
soto <soto@cr.ie.u-ryukyu.ac.jp>
parents:
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11 -- ?1 : y + suc x