Mercurial > hg > Papers > 2021 > soto-thesis

annotate prepaper/src/agda-term3.agda.replaced @ 14:a63df15c9afc default tip

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DONE
author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Mon, 15 Feb 2021 23:36:39 +0900
parents 3dba680da508
children
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1 +-comm : (x y : @$\mathbb{N}$@) @$\rightarrow$@ x + y @$\equiv$@ y + x
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2 +-comm zero y rewrite (+zero {y}) = refl
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3 +-comm (suc x) y = let open @$\equiv$@-Reasoning in
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4 begin
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5 suc (x + y) @$\equiv$@@$\langle$@@$\rangle$@
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6 suc (x + y) @$\equiv$@@$\langle$@ cong suc (+-comm x y) @$\rangle$@
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7 suc (y + x) @$\equiv$@@$\langle$@ sym (+-suc {y} {x}) @$\rangle$@
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8 y + suc x @$\blacksquare$@
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9
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10 -- +-suc : {x y : @$\mathbb{N}$@} @$\rightarrow$@ x + suc y @$\equiv$@ suc (x + y)
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11 -- +-suc {zero} {y} = refl
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12 -- +-suc {suc x} {y} = cong suc (+-suc {x} {y})