Mercurial > hg > Papers > 2020 > soto-midterm
comparison src/agda-term2.agda.replaced @ 1:73127e0ab57c
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author | soto@cr.ie.u-ryukyu.ac.jp |
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date | Tue, 08 Sep 2020 18:38:08 +0900 |
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0:b919985837a3 | 1:73127e0ab57c |
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1 +-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x | |
2 +-comm zero y rewrite (+zero {y}) = refl | |
3 +-comm (suc x) y = let open @$\equiv$@-Reasoning in | |
4 begin | |
5 (suc x) + y @$\equiv$@@$\langle$@@$\rangle$@ | |
6 suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@ | |
7 suc (y + x) @$\equiv$@@$\langle$@ ?0 @$\rangle$@ | |
8 ?1 @$\blacksquare$@ | |
9 | |
10 -- ?0 : suc (y + x) @$\equiv$@ y + suc x | |
11 -- ?1 : y + suc x |