Move AStar into a separte library and use it for Day17-1

1 files changed, 0 insertions, 123 deletions

diff --git a/Common/HashSet.lean b/Common/HashSet.lean
deleted file mode 100644
index 3271121..0000000
--- a/Common/HashSet.lean
+++ /dev/null
@@ -1,123 +0,0 @@
-import Std.Data.HashSet
-import Common.Finite
-
-
-open Std.HashSet
-namespace Std.HashSet
-
-theorem erase_not_mem {α : Type u} [BEq α] [Hashable α] [LawfulBEq α] (set : HashSet α) (a : α) : a ∉ (set.erase a) := by
-  simp only [HashSet.mem_iff_contains, HashSet.contains_erase, beq_self_eq_true, Bool.not_true, Bool.false_and, Bool.false_eq_true, not_false_eq_true]
-
-theorem erase_not_mem_of_not_mem {α : Type u} [BEq α] [Hashable α] [LawfulBEq α] (set : HashSet α) {a : α} (b : α) (h₁ : a ∉ set) : a ∉ (set.erase b) := by
-  intro h₂
-  rw[HashSet.mem_erase] at h₂
-  exact absurd h₂.right h₁
-
-protected theorem size_le_finite_worker_size (α : Type u) [Finite α] [BEq α] [Hashable α] [LawfulBEq α] : ∀ (set : Std.HashSet α) (n : Fin (Finite.cardinality α)) (_h₁ : ∀(o : Fin (Finite.cardinality α)) (_h : o > n), Finite.nth o ∉ set), set.size ≤ (Finite.set.set_worker α HashSet.empty  n).size := by
-  intros set n h₁
-  cases n
-  case mk n h₂ =>
-  cases n
-  case zero =>
-    have h₃ : (Finite.set.set_worker α empty ⟨0,h₂⟩).size = 1 := by simp[Finite.set.set_worker, HashSet.size_insert]
-    rw[h₃]
-    cases h₄ : set.contains (Finite.nth ⟨0,h₂⟩)
-    case false =>
-      have h₅ : ∀(o : Fin (Finite.cardinality α)), Finite.nth o ∉ set := by
-        simp[←Bool.not_eq_true, ←HashSet.mem_iff_contains] at h₄
-        intro o
-        cases o
-        case mk o ho =>
-        cases o
-        case zero => exact h₄
-        case succ oo => exact h₁ ⟨oo+1, ho⟩ (Nat.succ_pos oo)
-      have h₆ : ∀(a : α), a∉set := Finite.forall_nth (λx ↦ x∉set) h₅
-      have h₇ : set.isEmpty = true := HashSet.isEmpty_iff_forall_not_mem.mpr h₆
-      have h₈ : true = (set.size == 0) := HashSet.isEmpty_eq_size_eq_zero.subst h₇.symm
-      have h₈ : set.size = 0 := beq_iff_eq.mp h₈.symm
-      rw[h₈]
-      exact Nat.zero_le _
-    case true =>
-      --show that the set from which we erase (nth 0) has size 0, just like in case false.
-      --then show that, since we removed one element, set.size equals 1.
-      let rset := set.erase $ Finite.nth ⟨0,h₂⟩
-      have h₅ : (Finite.nth ⟨0,h₂⟩) ∉ rset := erase_not_mem set (Finite.nth ⟨0,h₂⟩)
-      have h₆ : ∀(o : Fin (Finite.cardinality α)), Finite.nth o ∉ rset := by
-        intro o
-        cases o
-        case mk o ho =>
-        cases o
-        case zero => exact h₅
-        case succ oo => exact erase_not_mem_of_not_mem set _ $ h₁ ⟨oo+1, ho⟩ (Nat.succ_pos oo)
-      have h₇ : ∀(a : α), a∉rset := Finite.forall_nth (λx ↦ x∉rset) h₆
-      have h₈ : rset.isEmpty = true := HashSet.isEmpty_iff_forall_not_mem.mpr h₇
-      have h₉ : true = (rset.size == 0) := HashSet.isEmpty_eq_size_eq_zero.subst h₈.symm
-      have h₉ : rset.size = 0 := beq_iff_eq.mp h₉.symm
-      have h₁₀ : set.size ≤ rset.size + 1 := HashSet.size_le_size_erase
-      rw[h₉, Nat.zero_add] at h₁₀
-      assumption
-  case succ m =>
-    --erase (nth m) from the set and recurse.
-    --then show that the current set can only be larger by 1, and therefore fulfills the goal
-    --HashSet.size_le_size_erase
-    let rset := set.erase $ Finite.nth ⟨m+1,h₂⟩
-    have h₃ : (Finite.nth ⟨m+1,h₂⟩) ∉ rset := erase_not_mem set (Finite.nth ⟨m+1,h₂⟩)
-    have h₄ : ∀(o : Fin (Finite.cardinality α)) (h₄ : o > ⟨m,Nat.lt_of_succ_lt h₂⟩), Finite.nth o ∉ rset := by
-      intros o h₄
-      cases o
-      case mk o h₅ =>
-      cases h₆ : o == (m+1) <;> simp at h₆
-      case true =>
-        simp only[h₆]
-        exact erase_not_mem set $ Finite.nth ⟨m+1, h₂⟩
-      case false =>
-        have h₆ : o > m+1 := by simp at h₄; omega
-        exact erase_not_mem_of_not_mem _ _ (h₁ ⟨o,h₅⟩ h₆)
-    have h₅ := Std.HashSet.size_le_finite_worker_size α rset ⟨m, Nat.lt_of_succ_lt h₂⟩ h₄
-    have h₆ : (Finite.set.set_worker α empty ⟨m, Nat.lt_of_succ_lt h₂⟩).size = empty.size + m + 1 :=
-      Finite.set_worker_size α empty ⟨m, Nat.lt_of_succ_lt h₂⟩ (λa _ ↦Bool.eq_false_iff.mp $ HashSet.contains_empty (a := Finite.nth a))
-    have h₇ : (Finite.set.set_worker α empty ⟨m+1,h₂⟩).size = empty.size + (m + 1) + 1 :=
-      Finite.set_worker_size α empty ⟨m+1,h₂⟩ (λa _ ↦Bool.eq_false_iff.mp $ HashSet.contains_empty (a := Finite.nth a))
-    have h₈ := HashSet.size_le_size_erase (m := set) (k:=Finite.nth ⟨m+1,h₂⟩)
-    simp[h₆] at h₅
-    simp[h₇]
-    exact Nat.le_trans h₈ (Nat.succ_le_succ h₅)
-
-theorem size_le_finite_set_size {α : Type u} [Finite α] [BEq α] [LawfulBEq α] [Hashable α] (set : Std.HashSet α) : set.size ≤ (Finite.set α).size := by
-  unfold Finite.set
-  split
-  case h_1 h₁ =>
-    if h : set.isEmpty then
-      have := HashSet.isEmpty_eq_size_eq_zero (m := set)
-      simp[h] at this
-      simp[this]
-    else
-      have := HashSet.isEmpty_eq_false_iff_exists_mem.mp (Bool.eq_false_iff.mpr h)
-      cases this
-      case intro x hx =>
-        let xx := Finite.enumerate x
-        exact (Fin.cast h₁ xx).elim0
-  case h_2 l h =>
-    exact Std.HashSet.size_le_finite_worker_size α set ⟨l,h.substr $ Nat.lt_succ_self l⟩ (λa hx ↦
-      by
-      have h₁ := a.isLt
-      simp_arith[h] at h₁
-      have h₂ : a > l := Fin.lt_iff_val_lt_val.mp hx
-      exact absurd h₁ (Nat.not_le.mpr h₂)
-    )
-
-theorem size_le_finite_cardinality {α : Type u} [Finite α] [BEq α] [LawfulBEq α] [Hashable α] (set : Std.HashSet α) : set.size ≤ Finite.cardinality α :=
-  (Finite.set_size_eq_cardinality α).subst (size_le_finite_set_size set)
-
-theorem size_lt_finite_cardinality_of_not_mem {α : Type u} [Finite α] [BEq α] [LawfulBEq α] [Hashable α] (set : Std.HashSet α) (h₁ : ∃(a : α), a ∉ set) : set.size < Finite.cardinality α := by
-  have h₂ : set.size ≤ Finite.cardinality α := size_le_finite_cardinality set
-  cases h₁
-  case intro e h₁ =>
-  let iset := set.insert e
-  have h₂ : iset.size = set.size + 1 := by
-    have := HashSet.size_insert (m := set) (k := e)
-    simp[h₁] at this
-    assumption
-  have h₃ : iset.size ≤ Finite.cardinality α := size_le_finite_cardinality iset
-  rw[h₂] at h₃
-  exact Nat.lt_of_succ_le h₃