diff options
| -rw-r--r-- | AvlVerification/Insert.lean | 51 |
1 files changed, 26 insertions, 25 deletions
diff --git a/AvlVerification/Insert.lean b/AvlVerification/Insert.lean index 870e9c2..92691b2 100644 --- a/AvlVerification/Insert.lean +++ b/AvlVerification/Insert.lean @@ -11,49 +11,50 @@ open Tree (AVLTree) variable {T: Type} @[pspec] -theorem AVLTreeSet.insert_loop_spec {H: avl_verification.Ord T} - (a: T) (t: Option (AVLNode T)) - [LT T] - (Hbs_search: BST.BST t) - (Hcmp_spec: ∀ a b, ∃ o, H.cmp a b = Result.ret o): +theorem AVLTreeSet.insert_loop_spec_local (p: T -> Prop) + (Hcmp_spec: ∀ a b, ∃ o, H.cmp a b = Result.ret o) + (a: T) (t: Option (AVLNode T)): ∃ added t_new, AVLTreeSet.insert_loop T H a t = Result.ret ⟨ added, t_new ⟩ -- ∧ AVLTree.set t'.2 = insert a (AVLTree.set t) - ∧ BST.BST t_new + ∧ (BST.ForallNode p t -> p a -> BST.ForallNode p t_new) := by match t with | none => - simp [AVLTreeSet.insert_loop, AVLTree.set, setOf, BST.BST] + simp [AVLTreeSet.insert_loop, AVLTree.set, setOf] + intros _ Hpa + constructor; all_goals try simp [BST.ForallNode.none] + exact Hpa | some (AVLNode.mk b left right) => rw [AVLTreeSet.insert_loop] simp only [] progress keep Hordering as ⟨ ordering ⟩ cases ordering all_goals simp only [] - have Hbs_search_right: BST.BST right := BST.right Hbs_search - have Hbs_search_left: BST.BST left := BST.left Hbs_search { - progress keep Htree as ⟨ added₁, right₁, Hbst ⟩ + progress keep Htree as ⟨ added₁, right₁, Hnode ⟩ refine' ⟨ added₁, ⟨ some (AVLNode.mk b left right₁), _ ⟩ ⟩ simp only [true_and] - refine' (BST.BST.some b left right₁ _ _ Hbs_search_left Hbst) - cases' Hbs_search; assumption - induction right with - | none => - simp [AVLTreeSet.insert_loop] at Htree - rw [← Htree.2] - refine' (BST.ForallNode.some _ _ _ BST.ForallNode.none _ BST.ForallNode.none) - sorry - | some node => - -- clef: ∀ x ∈ node.right, b < x - -- de plus: b < a - -- or, right₁ = insert a node.right moralement - -- donc, il suffit de prouver que: ∀ x ∈ insert a node.right, b < x <-> b < a /\ ∀ x ∈ node.right, b < x - sorry + intros Hptree Hpa + constructor + exact Hptree.left + exact Hptree.label + exact Hnode Hptree.right Hpa } { - simp [Hbs_search] + simp; tauto } { + -- TODO: investigate wlog. -- Symmetric case of left. + progress keep Htree as ⟨ added₁, left₁, Hnode ⟩ + refine' ⟨ added₁, ⟨ some (AVLNode.mk b left₁ right), _ ⟩ ⟩ + simp only [true_and] + intros Hptree Hpa + constructor + exact Hnode Hptree.left Hpa + exact Hptree.label + exact Hptree.right + } + sorry } |