# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1637223367 -32400
# Node ID fbd2adb6d9c5b4ee2db9edc14bd8f878dfc69e59
# Parent  6e319e44271b49d3eaace2a7341bb4b0ded1cc6b
...

diff -r 6e319e44271b -r fbd2adb6d9c5 hoareBinaryTree.agda
--- a/hoareBinaryTree.agda	Thu Nov 18 16:24:51 2021 +0900
+++ b/hoareBinaryTree.agda	Thu Nov 18 17:16:07 2021 +0900
@@ -241,8 +241,6 @@
 replaceP key value tree repl (node key₁ value₁ left right ∷ st) Pre next exit with <-cmp key key₁
 ... | tri< a ¬b ¬c = next key value (node key₁ value₁ tree right ) (node key₁ value₁ repl right ) st {!!}  ≤-refl
 ... | tri≈ ¬a b ¬c = exit (node key₁ value₁  left right ) (node key₁ value  left right )  ⟪ repl1 , repl3 ⟫ where
-    Pre1 :  treeInvariant tree ∧ stackInvariant repl tree (node key₁ value₁ left right ∷ st) ∧ replacedTree key value tree repl
-    Pre1 = Pre
     repleq : repl ≡ node key₁ value₁ left right
     repleq with si-property1 _ _ _ (proj1 (proj2 Pre))
     ... | refl = refl
@@ -251,8 +249,20 @@
         (subst (λ k → stackInvariant k tree (node key₁ value₁ left right ∷ st)) repleq (proj1 (proj2 Pre)))
     repl3 : replacedTree key value (node key₁ value₁ left right) (node key₁ value left right)
     repl3 = subst (λ k → replacedTree k value (node key₁ value₁ left right) (node key₁ value left right) ) (sym b) r-node
-... | tri> ¬a ¬b c = next key value (node key₁ value₁ left tree ) (node key₁ value₁ left repl )st {!!}  ≤-refl
-
+... | tri> ¬a ¬b c = next key value (node key₁ value₁ left tree ) (node key₁ value₁ left repl ) st ⟪ repl2 , ⟪ repl4 , repl5 ⟫ ⟫ ≤-refl  where
+    Pre1 :  treeInvariant tree ∧ stackInvariant repl tree (node key₁ value₁ left right ∷ st) ∧ replacedTree key value tree repl
+    Pre1 = Pre
+    repleq : repl ≡ node key₁ value₁ left right
+    repleq with si-property1 _ _ _ (proj1 (proj2 Pre))
+    ... | refl = refl
+    repl2 :  treeInvariant (node key₁ value₁ left tree)
+    repl2 = stackTreeInvariant _ _ (node key₁ value₁ left right ∷ st) (proj1 Pre)
+        (subst (λ k → stackInvariant k tree (node key₁ value₁ left right ∷ st)) {!!} (proj1 (proj2 Pre)))
+    repl4 : stackInvariant (node key₁ value₁ left repl) (node key₁ value₁ left tree) st
+    repl4 = ?
+    repl5 : replacedTree key value (node key₁ value₁ left tree) (node key₁ value₁ left repl)
+    repl5 with r-left c (proj2 (proj2 Pre))
+    ... | t = {!!}
 open import Relation.Binary.Definitions
 
 nat-≤> : { x y : ℕ } → x ≤ y → y < x → ⊥