--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/src/agda-hoare-write.agda.replaced	Tue Nov 02 06:55:58 2021 +0900
@@ -0,0 +1,15 @@
+-- Nomal CodeGear
+whileLoop' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc)
+  @$\rightarrow$@ (n @$\equiv$@ varn env)
+  @$\rightarrow$@ (next : Envc @$\rightarrow$@ t)
+  @$\rightarrow$@ (exit : Envc @$\rightarrow$@ t) @$\rightarrow$@ t
+whileLoop' zero env refl _ exit = exit env
+whileLoop' (suc n) env refl next _ = next (record env {varn = pred (varn env) ; vari = suc (vari env) })
+
+-- Hoare Logic base CodeGear
+whileLoopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
+  @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ (pre : varn env + vari env @$\equiv$@ c10 env)
+  @$\rightarrow$@ (next : (env : Envc ) @$\rightarrow$@ (pred n @$\equiv$@ varn env) @$\rightarrow$@ (post : varn env + vari env @$\equiv$@ c10 env) @$\rightarrow$@ t)
+  @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ (fin : vari env @$\equiv$@ c10 env)  @$\rightarrow$@ t) @$\rightarrow$@ t
+whileLoopPwP' zero env refl refl next exit = exit env refl
+whileLoopPwP' (suc n) env refl refl next exit = next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env))