--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/src/while_loop_verif/conversion.agda.replaced	Thu Jan 12 20:28:50 2023 +0900
@@ -0,0 +1,10 @@
+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
+          !$\blacksquare$!
\ No newline at end of file