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data.​list.​erase_dup

data.​list.​erase_dup

source
list.​erase_dup_append
list.​erase_dup_cons_of_mem
list.​erase_dup_cons_of_mem'
list.​erase_dup_cons_of_not_mem
list.​erase_dup_cons_of_not_mem'
list.​erase_dup_eq_self
list.​erase_dup_idempotent
list.​erase_dup_nil
list.​erase_dup_sublist
list.​erase_dup_subset
list.​mem_erase_dup
list.​nodup_erase_dup
list.​subset_erase_dup
source
@[simp]
theorem list.​erase_dup_nil {α : Type u} [decidable_eq α] :
list.nil.erase_dup = list.nil

source
theorem list.​erase_dup_cons_of_mem' {α : Type u} [decidable_eq α] {a : α} {l : list α} :
a ∈ l.erase_dup → (a :: l).erase_dup = l.erase_dup

source
theorem list.​erase_dup_cons_of_not_mem' {α : Type u} [decidable_eq α] {a : α} {l : list α} :
a ∉ l.erase_dup → (a :: l).erase_dup = a :: l.erase_dup

source
@[simp]
theorem list.​mem_erase_dup {α : Type u} [decidable_eq α] {a : α} {l : list α} :
a ∈ l.erase_dup ↔ a ∈ l

source
@[simp]
theorem list.​erase_dup_cons_of_mem {α : Type u} [decidable_eq α] {a : α} {l : list α} :
a ∈ l → (a :: l).erase_dup = l.erase_dup

source
@[simp]
theorem list.​erase_dup_cons_of_not_mem {α : Type u} [decidable_eq α] {a : α} {l : list α} :
a ∉ l → (a :: l).erase_dup = a :: l.erase_dup

source
theorem list.​erase_dup_sublist {α : Type u} [decidable_eq α] (l : list α) :
l.erase_dup <+ l

source
theorem list.​erase_dup_subset {α : Type u} [decidable_eq α] (l : list α) :
l.erase_dup ⊆ l

source
theorem list.​subset_erase_dup {α : Type u} [decidable_eq α] (l : list α) :
l ⊆ l.erase_dup

source
theorem list.​nodup_erase_dup {α : Type u} [decidable_eq α] (l : list α) :
l.erase_dup.nodup

source
theorem list.​erase_dup_eq_self {α : Type u} [decidable_eq α] {l : list α} :
l.erase_dup = l ↔ l.nodup

source
@[simp]
theorem list.​erase_dup_idempotent {α : Type u} [decidable_eq α] {l : list α} :
l.erase_dup.erase_dup = l.erase_dup

source
theorem list.​erase_dup_append {α : Type u} [decidable_eq α] (l₁ l₂ : list α) :
(l₁ ++ l₂).erase_dup = l₁ ∪ l₂.erase_dup

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