Mercurial > hg > Papers > 2020 > soto-midterm
annotate src/agda-term3.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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rev | line source |
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1 | 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) @$\equiv$@@$\langle$@ sym (+-suc {y} {x}) @$\rangle$@ | |
8 y + suc x @$\blacksquare$@ | |
9 | |
10 -- +-suc : {x y : @$\mathbb{N}$@} @$\rightarrow$@ x + suc y @$\equiv$@ suc (x + y) | |
11 -- +-suc {zero} {y} = refl | |
12 -- +-suc {suc x} {y} = cong suc (+-suc {x} {y}) |