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changeset 877:100e9fd87d83

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Fri, 03 May 2024 14:33:41 +0900
parents f772362dde8d
children feeb6982fd46
files hoareBinaryTree1.agda
diffstat 1 files changed, 18 insertions(+), 8 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree1.agda	Thu May 02 19:29:15 2024 +0900
+++ b/hoareBinaryTree1.agda	Fri May 03 14:33:41 2024 +0900
@@ -1234,17 +1234,27 @@
         rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₄ , ⟪ x₇ , x₈ ⟫ ⟫
         rr01 : (kn < kg) ∧ ⊤ ∧ ⊤
         rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂
-... | t-right .kn key₃ {v1} {v3} {t₇} {t₈} x₉ x₁₀ x₁₁ t = t-node _ _ _ (proj1 rr00) ? ? ? ? ? (t-left _ _ ? ? ? ti) (t-left _ _ ? ? ? (treeRightDown _ _ (RB-repl→ti _ _ _ _ ti₁ trb))) where
-        rr00 : (kp < kn) ∧ ⊤ ∧ tr> kp (node key₃ v3 t₇ t₈)
+... | t-right .kn key₃ {v1} {v3} {t₇} {t₈} x₉ x₁₀ x₁₁ t = t-node _ _ _ (proj1 rr00) (proj1 rr01) ⟪ <-trans x₃ (proj1 rr00) , ⟪ >-tr< x₅ (proj1 rr00) , >-tr< x₆ (proj1 rr00) ⟫ ⟫  tt ⟪ x₉ , ⟪ x₁₀ , x₁₁ ⟫ ⟫ tt (t-left _ _ x₃ x₅ x₆ ti) (t-left _ _ (proj1 rr03) (proj1 (proj2 rr03)) (proj2 (proj2 rr03)) (treeRightDown _ _ (RB-repl→ti _ _ _ _ ti₁ trb))) where
+        rr00 : (kp < kn) ∧ ⊤ ∧ ((kp < key₃) ∧ tr> kp t₇ ∧ tr> kp t₈) -- tr> kp (node key₃ v3 t₇ t₈)
+        rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₄ , ⟪ x₇ , x₈ ⟫ ⟫
+        rr02 = proj1 (proj2 rr00)
+        rr01 : (kn < kg) ∧ ⊤ ∧ ((key₃ < kg) ∧ tr< kg t₇ ∧ tr< kg t₈) -- tr< kg (node key₃ v3 t₇ t₈)
+        rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂
+        rr03 = proj2 (proj2 rr01)
+... | t-left key₃ .kn {v1} {v3} {t₇} {t₈} x₉ x₁₀ x₁₁ t = t-node _ _ _ (proj1 rr00) (proj1 rr01) ⟪ <-trans x₃ (proj1 rr00) , ⟪ >-tr< x₅ (proj1 rr00) , >-tr< x₆ (proj1 rr00) ⟫ ⟫  ⟪ x₉ , ⟪ x₁₀ , x₁₁ ⟫ ⟫ tt tt (t-node key₂ kp key₃ x₃ (proj1 rr02) x₅ x₆ (proj1 (proj2 rr02))  (proj2 (proj2 rr02)) ti (treeLeftDown _ _ (RB-repl→ti _ _ _ _ ti₁ trb))) (t-single _ _) where
+        rr00 : (kp < kn) ∧ ((kp < key₃) ∧ tr> kp t₇ ∧ tr> kp t₈) ∧ ⊤
         rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₄ , ⟪ x₇ , x₈ ⟫ ⟫
         rr02 = proj1 (proj2 rr00)
-        rr01 : (kn < kg) ∧ ⊤ ∧ tr< kg (node key₃ v3 t₇ t₈)
+        rr01 : (kn < kg) ∧ ((key₃ < kg) ∧ tr< kg t₇ ∧ tr< kg t₈) ∧ ⊤
         rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂
-        rr03 : ?
-        rr03 with RB-repl→ti _ _ _ _ ti₁ trb
-        ... | t-right .kn .key₃ x x₁ x₂ t = ?
-... | t-left key₃ .kn x₉ x₁₀ x₁₁ t = ?
-... | t-node key₃ .kn key₄ x₉ x₁₀ x₁₁ x₁₂ x₁₃ x₁₄ t t₃ = ?
+... | t-node key₃ .kn key₄ {v0} {v1} {v2} {t₇} {t₈} {t₉}  {t₁₀} x₉ x₁₀ x₁₁ x₁₂ x₁₃ x₁₄ t t₃ = t-node _ _ _ (proj1 rr00) (proj1 rr01) ⟪ <-trans x₃ (proj1 rr00)  , ⟪ >-tr< x₅ (proj1 rr00) , >-tr< x₆ (proj1 rr00) ⟫ ⟫  ⟪ x₉ , ⟪ x₁₁ , x₁₂ ⟫ ⟫  ⟪ x₁₀ , ⟪ x₁₃ , x₁₄ ⟫ ⟫  tt (t-node _ _ _ x₃ (proj1 rr02) x₅ x₆ (proj1 (proj2 rr02)) (proj2 (proj2 rr02)) ti (treeLeftDown _ _ (RB-repl→ti _ _ _ _ ti₁ trb))) (t-left _ _ (proj1 rr03) (proj1 (proj2 rr03)) (proj2 (proj2 rr03)) t₃) where
+        rr00 : (kp < kn) ∧ ((kp < key₃) ∧ tr> kp t₇ ∧ tr> kp t₈) ∧ ((kp < key₄) ∧ tr> kp t₉ ∧ tr> kp t₁₀)
+        rr00 = RB-repl→ti> _ _ _ _ _ trb lt1 ⟪ x₄ , ⟪ x₇ , x₈ ⟫ ⟫
+        rr02 = proj1 (proj2 rr00)
+        rr01 : (kn < kg) ∧ ((key₃ < kg) ∧ tr< kg t₇ ∧ tr< kg t₈) ∧ ((key₄ < kg) ∧ tr< kg t₉ ∧ tr< kg t₁₀)
+        rr01 = RB-repl→ti< _ _ _ _ _ trb lt2 x₂
+        rr03 = proj2 (proj2 rr01)
+   
 RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ t leaf) .(node key₂ _ _ _)) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₃) (node kg ⟪ Red , _ ⟫ t₄ _)) key value (t-node .kp .kg key₂ x x₁ x₂ x₃ x₄ x₅ ti ti₁) (rbr-rotate-lr t₃ t₄ kg kp kn lt1 lt2 trb) = ?
 RB-repl→ti (node kg ⟪ Black , v1 ⟫ (node kp ⟪ Red , v2 ⟫ t (node key₁ value₁ t₁ t₂)) .(node key₂ _ _ _)) (node kn ⟪ Black , _ ⟫ (node kp ⟪ Red , _ ⟫ _ t₃) (node kg ⟪ Red , _ ⟫ t₄ _)) key value (t-node .kp .kg key₂ x x₁ x₂ x₃ x₄ x₅ ti ti₁) (rbr-rotate-lr t₃ t₄ kg kp kn lt1 lt2 trb) = ?
 RB-repl→ti .(node kg ⟪ Black , _ ⟫ _ (node kp ⟪ Red , _ ⟫ _ _)) .(node kn ⟪ Black , _ ⟫ (node kg ⟪ Red , _ ⟫ _ t₂) (node kp ⟪ Red , _ ⟫ leaf _)) key value ti (rbr-rotate-rl t₂ leaf kg kp kn lt1 lt2 trb) = ?