# HG changeset patch
# User Shinji KONO <kono@ie.u-ryukyu.ac.jp>
# Date 1711004968 -32400
# Node ID d873ae970fc67b0a11e232c4d33c593340ea4525
# Parent  ee2dd920e41432f39fae816383b6523b2f66fb3f
...

diff -r ee2dd920e414 -r d873ae970fc6 hoareBinaryTree1.agda
--- a/hoareBinaryTree1.agda	Thu Mar 21 15:25:37 2024 +0900
+++ b/hoareBinaryTree1.agda	Thu Mar 21 16:09:28 2024 +0900
@@ -1024,10 +1024,22 @@
       (t-node key₁ _ key₂ x₁ x₂ x₃ x₄ x₅ x₆ ti ti₁) (rbr-black-right x x₇ trb) = t-node _ _ _ x₁ (proj1 rr00) x₃ x₄ (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) ti (RB-repl→ti _ _ _ _ ti₁ trb) where
         rr00 : (key₃ < key₄) ∧ tr> key₃ t₂ ∧ tr> key₃ t₃
         rr00 = RB-repl→ti> _ _ _ _ _ trb x₇ ⟪ x₂ , ⟪ x₅ , x₆ ⟫ ⟫
-RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ leaf leaf) (node key₂ ⟪ Black , _ ⟫ t .leaf) key value (t-single .key₂ .(⟪ Black , _ ⟫)) (rbr-black-left x x₇ trb) = ?
-RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ leaf (node key₁ _ _ _)) (node key₂ ⟪ Black , _ ⟫ t .(node key₁ _ _ _)) key value (t-right .key₂ key₁ x₁ x₂ x₃ ti) (rbr-black-left x x₇ trb) = ?
-RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ (node key₁ _ _ _) leaf) (node key₂ ⟪ Black , _ ⟫ t .leaf) key value (t-left key₁ .key₂ x₁ x₂ x₃ ti) (rbr-black-left x x₇ trb) = ?
-RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ (node key₁ _ _ _) (node key₃ _ _ _)) (node key₂ ⟪ Black , _ ⟫ t .(node key₃ _ _ _)) key value (t-node key₁ .key₂ key₃ x₁ x₂ x₃ x₄ x₅ x₆ ti ti₁) (rbr-black-left x x₇ trb) = ?
+RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ leaf leaf) (node key₂ ⟪ Black , _ ⟫ (node key₁ value₁ t t₁) .leaf) key value 
+       (t-single .key₂ .(⟪ Black , _ ⟫)) (rbr-black-left x x₇ trb) = t-left _ _ (proj1 rr00) (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) (RB-repl→ti _ _ _ _ t-leaf trb) where
+        rr00 : (key₁ < key₂) ∧ tr< key₂ t ∧ tr< key₂ t₁
+        rr00 = RB-repl→ti< _ _ _ _ _ trb x₇ tt
+RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ leaf (node key₁ _ _ _)) (node key₂ ⟪ Black , _ ⟫ (node key₃ value₁ t t₁) .(node key₁ _ _ _)) key value 
+       (t-right .key₂ key₁ x₁ x₂ x₃ ti) (rbr-black-left x x₇ trb) = t-node _ _ _ (proj1 rr00) x₁ (proj1 (proj2 rr00)) (proj2 (proj2 rr00))  x₂ x₃ (RB-repl→ti _ _ _ _ t-leaf trb) ti where
+        rr00 : (key₃ < key₂) ∧ tr< key₂ t ∧ tr< key₂ t₁
+        rr00 = RB-repl→ti< _ _ _ _ _ trb x₇ tt
+RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ (node key₁ _ _ _) leaf) (node key₂ ⟪ Black , _ ⟫ (node key₃ value₁ t t₁) .leaf) key value 
+       (t-left key₁ .key₂ x₁ x₂ x₃ ti) (rbr-black-left x x₇ trb) = t-left _ _ (proj1 rr00) (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) (RB-repl→ti _ _ _ _ ti trb) where
+        rr00 : (key₃ < key₂) ∧ tr< key₂ t ∧ tr< key₂ t₁
+        rr00 = RB-repl→ti< _ _ _ _ _ trb x₇ ⟪ x₁ , ⟪ x₂ , x₃ ⟫ ⟫
+RB-repl→ti .(node key₂ ⟪ Black , _ ⟫ (node key₁ _ _ _) (node key₃ _ _ _)) (node key₂ ⟪ Black , _ ⟫ (node key₄ value₁ t t₁) .(node key₃ _ _ _)) key value 
+     (t-node key₁ .key₂ key₃ x₁ x₂ x₃ x₄ x₅ x₆ ti ti₁) (rbr-black-left x x₇ trb) = t-node _ _ _ (proj1 rr00) x₂ (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) x₅ x₆ (RB-repl→ti _ _ _ _ ti trb) ti₁ where
+        rr00 : (key₄ < key₂) ∧ tr< key₂ t ∧ tr< key₂ t₁
+        rr00 = RB-repl→ti< _ _ _ _ _ trb x₇ ⟪ x₁ , ⟪ x₃ , x₄ ⟫ ⟫
 RB-repl→ti .(node _ ⟪ Black , _ ⟫ (node _ ⟪ Red , _ ⟫ _ _) _) .(node _ ⟪ Red , _ ⟫ (node _ ⟪ Black , _ ⟫ _ _) (to-black _)) key value ti (rbr-flip-ll x trb) = ?
 RB-repl→ti .(node _ ⟪ Black , _ ⟫ (node _ ⟪ Red , _ ⟫ _ _) _) .(node _ ⟪ Red , _ ⟫ (node _ ⟪ Black , _ ⟫ _ _) (to-black _)) key value ti (rbr-flip-lr x trb) = ?
 RB-repl→ti .(node _ ⟪ Black , _ ⟫ _ (node _ ⟪ Red , _ ⟫ _ _)) .(node _ ⟪ Red , _ ⟫ (to-black _) (node _ ⟪ Black , _ ⟫ _ _)) key value ti (rbr-flip-rl x trb) = ?