--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/cbc-hoare-loop.agda.replaced	Tue Sep 08 18:38:08 2020 +0900
@@ -0,0 +1,15 @@
+whileLoopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
+    @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env
+    @$\rightarrow$@ (next : (env : Envc ) @$\rightarrow$@ (pred n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env  @$\rightarrow$@ t)
+    @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ whileTestStateP sf env  @$\rightarrow$@ t) @$\rightarrow$@ t
+whileLoopPwP' zero env refl refl _ exit = exit env refl
+whileLoopPwP' (suc n) env refl refl next _ =
+    next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env))
+
+
+loopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc )
+    @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ whileTestStateP s2 env
+    @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ whileTestStateP sf env @$\rightarrow$@ t) @$\rightarrow$@ t
+loopPwP' zero env refl refl exit = exit env refl
+loopPwP' (suc n) env refl refl exit
+    = whileLoopPwP' (suc n) env refl refl (@$\lambda$@ env x y @$\rightarrow$@ loopPwP' n env x y exit) exit