Mercurial > hg > Papers > 2021 > soto-prosym
diff Paper/src/agda-term2.agda.replaced @ 5:339fb67b4375
INIT rbt.agda
author | soto <soto@cr.ie.u-ryukyu.ac.jp> |
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date | Sun, 07 Nov 2021 00:51:16 +0900 |
parents | c59202657321 |
children |
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--- a/Paper/src/agda-term2.agda.replaced Sat Nov 06 20:06:24 2021 +0900 +++ b/Paper/src/agda-term2.agda.replaced Sun Nov 07 00:51:16 2021 +0900 @@ -1,11 +1,11 @@ -+-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x ++-comm : (x y : !$\mathbb{N}$!) !$\rightarrow$! x + y !$\equiv$! y + x +-comm zero y rewrite (+zero {y}) = refl -+-comm (suc x) y = let open @$\equiv$@-Reasoning in ++-comm (suc x) y = let open !$\equiv$!-Reasoning in begin - (suc x) + y @$\equiv$@@$\langle$@@$\rangle$@ - suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@ - suc (y + x) @$\equiv$@@$\langle$@ ?0 @$\rangle$@ - ?1 @$\blacksquare$@ + (suc x) + y !$\equiv$!!$\langle$!!$\rangle$! + suc (x + y) !$\equiv$!!$\langle$! cong suc (+-comm x y) !$\rangle$! + suc (y + x) !$\equiv$!!$\langle$! ?0 !$\rangle$! + ?1 !$\blacksquare$! --- ?0 : suc (y + x) @$\equiv$@ y + suc x +-- ?0 : suc (y + x) !$\equiv$! y + suc x -- ?1 : y + suc x