Mercurial > hg > Papers > 2021 > soto-thesis
view paper/src/agda-term3.agda.replaced @ 4:bf1f62556b81
add while_test_init_imple
author | soto |
---|---|
date | Thu, 11 Feb 2021 17:03:31 +0900 |
parents | 959f4b34d6f4 |
children |
line wrap: on
line source
+-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 begin suc (x + y) @$\equiv$@@$\langle$@@$\rangle$@ suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@ suc (y + x) @$\equiv$@@$\langle$@ sym (+-suc {y} {x}) @$\rangle$@ y + suc x @$\blacksquare$@ -- +-suc : {x y : @$\mathbb{N}$@} @$\rightarrow$@ x + suc y @$\equiv$@ suc (x + y) -- +-suc {zero} {y} = refl -- +-suc {suc x} {y} = cong suc (+-suc {x} {y})