Mercurial > hg > Papers > 2021 > soto-prosym
view Paper/src/while_loop_verif/conversion.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 | 9176dff8f38a |
children |
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conversion1 : {l : Level} {t : Set l } !$\rightarrow$! (env : Env) !$\rightarrow$! {c10 : !$\mathbb{N}$! } !$\rightarrow$! ((vari env) !$\equiv$! 0) !$\wedge$! ((varn env) !$\equiv$! c10) !$\rightarrow$! (Code : (env1 : Env) !$\rightarrow$! (varn env1 + vari env1 !$\equiv$! c10) !$\rightarrow$! t) !$\rightarrow$! t conversion1 env {c10} p1 next = next env proof4 where proof4 : varn env + vari env !$\equiv$! c10 proof4 = let open !$\equiv$!-Reasoning in begin varn env + vari env !$\equiv$!!$\langle$! cong ( !$\lambda$! n !$\rightarrow$! n + vari env ) (pi2 p1 ) !$\rangle$! c10 + vari env !$\equiv$!!$\langle$! cong ( !$\lambda$! n !$\rightarrow$! c10 + n ) (pi1 p1 ) !$\rangle$! c10 + 0 !$\equiv$!!$\langle$! +-sym {c10} {0} !$\rangle$! c10 !$\blacksquare$!