Mercurial > hg > Papers > 2022 > soto-sigos

comparison Paper/src/agda-term1.agda.replaced @ 0:14a0e409d574

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author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 24 Apr 2022 23:13:44 +0900
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-1:000000000000 0:14a0e409d574
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 ?0 !$\equiv$!!$\langle$! ?1 !$\rangle$!
6 ?2 !$\blacksquare$!
7
8 -- ?0 : !$\mathbb{N}$! {(suc x) + y}
9 -- ?1 : suc x + y !$\equiv$! y + suc x
10 -- ?2 : !$\mathbb{N}$!