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data.​list.​bag_inter

data.​list.​bag_inter

source
list.​bag_inter_nil
list.​bag_inter_nil_iff_inter_nil
list.​bag_inter_sublist_left
list.​cons_bag_inter_of_neg
list.​cons_bag_inter_of_pos
list.​count_bag_inter
list.​mem_bag_inter
list.​nil_bag_inter
source
@[simp]
theorem list.​nil_bag_inter {α : Type u} [decidable_eq α] (l : list α) :
list.nil.bag_inter l = list.nil

source
@[simp]
theorem list.​bag_inter_nil {α : Type u} [decidable_eq α] (l : list α) :
l.bag_inter list.nil = list.nil

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@[simp]
theorem list.​cons_bag_inter_of_pos {α : Type u} [decidable_eq α] {a : α} (l₁ : list α) {l₂ : list α} :
a ∈ l₂ → (a :: l₁).bag_inter l₂ = a :: l₁.bag_inter (l₂.erase a)

source
@[simp]
theorem list.​cons_bag_inter_of_neg {α : Type u} [decidable_eq α] {a : α} (l₁ : list α) {l₂ : list α} :
a ∉ l₂ → (a :: l₁).bag_inter l₂ = l₁.bag_inter l₂

source
@[simp]
theorem list.​mem_bag_inter {α : Type u} [decidable_eq α] {a : α} {l₁ l₂ : list α} :
a ∈ l₁.bag_inter l₂ ↔ a ∈ l₁ ∧ a ∈ l₂

source
@[simp]
theorem list.​count_bag_inter {α : Type u} [decidable_eq α] {a : α} {l₁ l₂ : list α} :
list.count a (l₁.bag_inter l₂) = min (list.count a l₁) (list.count a l₂)

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theorem list.​bag_inter_sublist_left {α : Type u} [decidable_eq α] (l₁ l₂ : list α) :
l₁.bag_inter l₂ <+ l₁

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theorem list.​bag_inter_nil_iff_inter_nil {α : Type u} [decidable_eq α] (l₁ l₂ : list α) :
l₁.bag_inter l₂ = list.nil ↔ l₁ ∩ l₂ = list.nil

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