# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1600562915 -32400
# Node ID 28a985c263dc87a96e3cd882f601b16901fbf82b
# Parent  8951ed37c1abb781d7a594edf1f42205fff5733f
...

diff -r 8951ed37c1ab -r 28a985c263dc FLutil.agda
--- a/FLutil.agda	Fri Sep 18 11:19:16 2020 +0900
+++ b/FLutil.agda	Sun Sep 20 09:48:35 2020 +0900
@@ -240,14 +240,20 @@
     af3 : (w : Fin (suc n)) (x y : FL n) → Level.Lift Level.zero (True (x f<? y )) → (w :: x ) f< (w :: y )
     af3 w x y (Level.lift z) with x f<? y
     ... | yes x<y = f<t x<y
-    af4 : ( y : FList n ) → ( z : FList (suc n)) →  fresh (FL n) ⌊ _f<?_ ⌋ {!!} y → FList (suc n)
-    af4r : fresh (FL (suc n)) ⌊ _f<?_ ⌋ (? :: ?) (af4 ? ? ?)
-    af4 [] z _ = z
-    af4 (cons a y x) z _ = cons ( {!!} :: a ) (af4 y z {!!} )  {!!} 
-    af4r = ?
+    af4 : (i : ℕ) → (i<n : i < suc n) →  ( y : FList n ) → ( z : FList (suc n)) →  FList (suc n)
+    af4r : (i : ℕ) → (i<n : i < suc n) → (a : FL n) → ( y : FList n ) → ( z : FList (suc n))
+       → fresh (FL (suc n)) ⌊ _f<?_ ⌋ (fromℕ< i<n :: a) (af4 i i<n y z ) 
+    af4 i i<n [] z = z
+    af4 zero (s≤s i<n) (cons a y x) z  = cons (fromℕ< (s≤s i<n) :: a) (af4 zero 0<s y z ) (af4r zero  0<s a y z)
+    af4 (suc i) (s≤s i<n) (cons a y x) z  = cons (fromℕ< (s≤s i<n) :: a) (af4 i (≤-trans i<n a≤sa) y z ) af5 where
+        af6 : fromℕ< (≤-trans i<n a≤sa) ≡ fromℕ< (s≤s i<n)
+        af6 = {!!}
+        af5 : fresh (FL (suc n)) ⌊ _f<?_ ⌋ (fromℕ< (s≤s i<n) :: a) (af4 i (≤-trans i<n a≤sa) y z)
+        af5 = subst (λ k → fresh (FL (suc n)) ⌊ _f<?_ ⌋ (k :: a) (af4 i (≤-trans i<n a≤sa) y z)) af6 (af4r i (≤-trans i<n a≤sa) a y z)
+    af4r = {!!}
     af1 : (i : ℕ ) → i ≤ suc n  → FList (suc n)
     af1 zero i<n  = Data.List.Fresh.map (zero ::_ ) (λ {x} {x₁} xr → Level.lift (fromWitness (af3 zero x x₁ xr ) )) (∀FListP.∀list af0 )
-    af1 (suc i) (s≤s i<n) = af4 (∀FListP.∀list af0 ) ( af1 i (≤-trans i<n a≤sa)) {!!}
+    af1 (suc i) (s≤s i<n) = af4 i (s≤s i<n) (∀FListP.∀list af0 ) ( af1 i (≤-trans i<n a≤sa)) 
     af2 : (x : FL (suc n)) → (y : FList (suc n)) → Any (_≡_ x) y
     af2 = {!!}