feat: close `find` / `insert` proofs

After a complete 180 with the Order theory, we close the goals of find
and insert and we give an example of U32 order that we will upstream to
Aeneas directly.

Signed-off-by: Raito Bezarius <masterancpp@gmail.com>

1 files changed, 0 insertions, 54 deletions

diff --git a/AvlVerification/BinarySearchTree.lean b/AvlVerification/BinarySearchTree.lean
deleted file mode 100644
index 2b17d52..0000000
--- a/AvlVerification/BinarySearchTree.lean
+++ /dev/null
@@ -1,54 +0,0 @@
-import AvlVerification.Tree
-
-namespace BST
-
-open Primitives (Result)
-open avl_verification (AVLNode Ordering)
-open Tree (AVLTree AVLNode.left AVLNode.right AVLNode.val)
-
-inductive ForallNode (p: T -> Prop): AVLTree T -> Prop
-| none : ForallNode p none
-| some (a: T) (left: AVLTree T) (right: AVLTree T) : ForallNode p left -> p a -> ForallNode p right -> ForallNode p (some (AVLNode.mk a left right))
-
-theorem ForallNode.left {p: T -> Prop} {t: AVLTree T}: ForallNode p t -> ForallNode p t.left := by
-  intro Hpt
-  cases Hpt with 
-  | none => simp [AVLTree.left, ForallNode.none]
-  | some a left right f_pleft f_pa f_pright => simp [AVLTree.left, f_pleft]
-
-theorem ForallNode.right {p: T -> Prop} {t: AVLTree T}: ForallNode p t -> ForallNode p t.right := by
-  intro Hpt
-  cases Hpt with 
-  | none => simp [AVLTree.right, ForallNode.none]
-  | some a left right f_pleft f_pa f_pright => simp [AVLTree.right, f_pright]
-
-theorem ForallNode.label {a: T} {p: T -> Prop} {left right: AVLTree T}: ForallNode p (AVLNode.mk a left right) -> p a := by
-  intro Hpt
-  cases Hpt with 
-  | some a left right f_pleft f_pa f_pright => exact f_pa
-
--- This is the binary search invariant.
-inductive Invariant [LT T]: AVLTree T -> Prop
-| none : Invariant none
-| some (a: T) (left: AVLTree T) (right: AVLTree T) : 
-  ForallNode (fun v => v < a) left -> ForallNode (fun v => a < v) right
-  -> Invariant left -> Invariant right -> Invariant (some (AVLNode.mk a left right))
-
-@[simp]
-theorem singleton_bst [LT T] {a: T}: Invariant (some (AVLNode.mk a none none)) := by
-  apply Invariant.some
-  all_goals simp [ForallNode.none, Invariant.none] 
-
-theorem left [LT T] {t: AVLTree T}: Invariant t -> Invariant t.left := by
-  intro H
-  induction H with 
-  | none => exact Invariant.none
-  | some _ _ _ _ _ _ _ _ _ => simp [AVLTree.left]; assumption
-
-theorem right [LT T] {t: AVLTree T}: Invariant t -> Invariant t.right := by
-  intro H
-  induction H with 
-  | none => exact Invariant.none
-  | some _ _ _ _ _ _ _ _ _ => simp [AVLTree.right]; assumption
-
-end BST