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view Paper/src/while_loop_verif/conversion.agda.replaced @ 1:a72446879486
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author | soto <soto@cr.ie.u-ryukyu.ac.jp> |
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date | Thu, 12 Jan 2023 20:28:50 +0900 |
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conversion1 : {l : Level} {t : Set l } !$\rightarrow$! (env : Env) !$\rightarrow$! {c10 : !$\mathbb{N}$! } !$\rightarrow$! ((vari env) !$\equiv$! 0) /\ ((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 !$\blacksquare$!