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This will collect definitions from Std.Logic --------- Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
10 lines
456 B
Text
10 lines
456 B
Text
variable (R : α → α → Prop)
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inductive List.Pairwise : List α → Prop
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| nil : Pairwise []
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| cons : ∀ {a : α} {l : List α}, (∀ {a} (_ : a' ∈ l), R a a') → Pairwise l → Pairwise (a :: l)
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theorem pairwise_append {l₁ l₂ : List α} :
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(l₁ ++ l₂).Pairwise R ↔ l₁.Pairwise R ∧ l₂.Pairwise R ∧ ∀ {a} (_ : a ∈ l₁), ∀ {b} (_ : b ∈ l₂), R a b := by
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induction l₁ <;> simp [*, and_left_comm]
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repeat sorry
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