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feat(library/data/list/basic): add aux theorems

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Leonardo de Moura 2015-03-31 18:38:05 -07:00
parent 4eb270a572
commit e35de54cee
1 changed files with 6 additions and 0 deletions
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6
library/data/list/basic.lean
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@ -219,6 +219,12 @@ list.induction_on l
from H3 ▸ rfl, from H3 ▸ rfl,
!exists.intro (!exists.intro H4))) !exists.intro (!exists.intro H4)))
theorem mem_append_left {a : T} {l₁ : list T} (l₂ : list T) : a ∈ l₁ → a ∈ l₁ ++ l₂ :=
assume ainl₁, mem_append_of_mem_or_mem (or.inl ainl₁)
theorem mem_append_right {a : T} (l₁ : list T) {l₂ : list T} : a ∈ l₂ → a ∈ l₁ ++ l₂ :=
assume ainl₂, mem_append_of_mem_or_mem (or.inr ainl₂)
definition decidable_mem [instance] [H : decidable_eq T] (x : T) (l : list T) : decidable (x ∈ l) := definition decidable_mem [instance] [H : decidable_eq T] (x : T) (l : list T) : decidable (x ∈ l) :=
list.rec_on l list.rec_on l
(decidable.inr (not_of_iff_false !mem_nil)) (decidable.inr (not_of_iff_false !mem_nil))