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changeset 864:d181dd606877

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author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Tue, 02 Apr 2024 20:42:52 +0900
parents 5a34330bc850
children 35c09d99840c
files hoareBinaryTree1.agda
diffstat 1 files changed, 26 insertions(+), 3 deletions(-) [+]
line wrap: on
line diff
--- a/hoareBinaryTree1.agda	Tue Apr 02 12:29:30 2024 +0900
+++ b/hoareBinaryTree1.agda	Tue Apr 02 20:42:52 2024 +0900
@@ -1120,9 +1120,32 @@
         rr04 = RTtoTI0 _ _ _ _ (t-left _ _ (proj1 x₃) (proj1 (proj2 x₃)) (proj2 (proj2 x₃)) ti₁ ) (r-left (proj1 x₃) r-node) 
         rr05 : treeInvariant (node key₁ value₁ t₂ t₃)
         rr05 = RB-repl→ti _ _ _ _ ti trb
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-single .key₂ .(⟪ Red , c2 ⟫)) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .(node key₅ _ _ _)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₅ _ _ _) (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-right .key₂ key₅ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
-RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-left key₅ .key₂ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ ? x₁ ? ? ? ? ? ?
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .leaf .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value 
+   (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-single .key₂ .(⟪ Red , c2 ⟫)) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ (proj1 rr00) x₁ (proj1 (proj2 rr00))  (proj2 (proj2 rr00))  tt ⟪ <-trans x₁ x₂ , ⟪ <-tr> x₅ x₁ , <-tr> x₆ x₁  ⟫ ⟫  rr02 rr03 where
+       rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
+       rr00 = RB-repl→ti< _ _ _ _ _ trb lt tt
+       rr02 : treeInvariant (node key₄ value₁ t₄ t₅) 
+       rr02 = RB-repl→ti _ _ _ _ t-leaf trb
+       rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ leaf (node key₃ v3 t₂ t₃))
+       rr03 = RTtoTI0 _ _ _ _ (t-right _ _ {v3} {_} x₂ x₅ x₆ ti₁) r-node
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ leaf (node key₅ _ _ _)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ (node key₅ value₂ t₁ t₆) (node key₃ _ _ _))) key value 
+    (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-right .key₂ key₅ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ (proj1 rr00) x₁ (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) ⟪ x₇ , ⟪ x₈ , x₉ ⟫ ⟫  ⟪ <-trans x₁ x₂  , ⟪ <-tr> x₅ x₁ , <-tr> x₆ x₁ ⟫ ⟫ rr02 rr03 where
+       rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
+       rr00 = RB-repl→ti< _ _ _ _ _ trb lt tt
+       rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
+       rr02 = RB-repl→ti _ _ _ _ t-leaf trb
+       rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ (node key₅ value₂ t₁ t₆) (node key₃ v3 t₂ t₃))
+       rr03 = RTtoTI0 _ _ _ _ (t-node _ _ _ {_} {v3} {_} {_} {_} {_} {_} (proj1 x₄) x₂ (proj1 (proj2 x₄)) (proj2 (proj2 x₄)) x₅ x₆ ti ti₁ ) r-node
+RB-repl→ti (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) .leaf) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .leaf (node key₃ _ _ _))) key value (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ 
+    (t-left key₅ .key₂ x₇ x₈ x₉ ti) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ (proj1 rr00) x₁ (proj1 (proj2 rr00)) (proj2 (proj2 rr00))  tt ⟪ <-trans x₁ x₂  , ⟪ <-tr> x₅ x₁  , <-tr> x₆ x₁ ⟫ ⟫  rr02 rr04 where
+        rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅
+        rr00 = RB-repl→ti< _ _ _ _ _ trb lt ⟪ x₇ , ⟪ x₈ , x₉ ⟫ ⟫
+        rr02 : treeInvariant (node key₄ value₁ t₄ t₅)
+        rr02 = RB-repl→ti _ _ _ _ ti trb
+        rr03 : treeInvariant (node key₁ ⟪ Red , c1 ⟫ (node key₅ _ _ _) (node key₃ v3 t₂ t₃))
+        rr03 = RTtoTI0 _ _ _ _ (t-node _ _ _ {_} {v3} {_} {_} {_} {_} {_} (proj1 x₃) x₂ (proj1 (proj2 x₃)) (proj2 (proj2 x₃)) x₅ x₆ ti ti₁) r-node
+        rr04 :  treeInvariant (node key₁ ⟪ Red , c1 ⟫ leaf (node key₃ v3 t₂ t₃))
+        rr04 = RTtoTI0 _ _ _ _ (t-right _ _ {v3} {_} x₂ x₅ x₆ ti₁) r-node
 RB-repl→ti {_} {A} (node key₁ ⟪ Black , c1 ⟫ (node key₂ ⟪ Red , c2 ⟫ .(node key₅ _ _ _) (node key₆ value₆ t₆ t₇)) (node key₃ v3 t₂ t₃)) (node _ ⟪ Black , _ ⟫ (node key₄ value₁ t₄ t₅) (node _ ⟪ Red , _ ⟫ .(node key₆ _ _ _) (node key₃ _ _ _))) key value 
   (t-node _ _ key₃ x₁ x₂ x₃ x₄ x₅ x₆ (t-node key₅ .key₂ key₆ x₇ x₈ x₉ x₁₀ x₁₁ x₁₂ ti ti₂) ti₁) (rbr-rotate-ll x lt trb) = t-node _ _ _ (proj1 rr00) x₁ (proj1 (proj2 rr00)) (proj2 (proj2 rr00)) ⟪ x₈ , ⟪ x₁₁ , x₁₂ ⟫ ⟫  ⟪ <-trans x₁ x₂ , ⟪ rr05 , <-tr> x₆ x₁ ⟫ ⟫ rr02 rr03 where
         rr00 : (key₄ < key₂) ∧ tr< key₂ t₄ ∧ tr< key₂ t₅