4575799f8e
This PR cleans up the style of the library in anticipation of a future PR that requires strict indentation for tactic sequences.
25 lines
852 B
Text
25 lines
852 B
Text
variable {α : Type} {r : α → α → Prop} {b : α}
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inductive ReflTransGen (r : α → α → Prop) (a : α) : α → Prop
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| refl : ReflTransGen r a a
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| tail {b c} : ReflTransGen r a b → r b c → ReflTransGen r a c
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namespace ReflTransGen
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theorem head (hab : r a b) (hbc : ReflTransGen r b c) : ReflTransGen r a c := by
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induction hbc
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case refl => exact refl.tail hab
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case tail c d _ hcd hac => exact hac.tail hcd
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@[elab_as_elim]
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theorem head_induction_on {P : ∀ a : α, ReflTransGen r a b → Prop} {a : α} (h : ReflTransGen r a b)
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(refl : P b refl)
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(head : ∀ {a c} (h' : r a c) (h : ReflTransGen r c b), P c h → P a (h.head h')) : P a h := by
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induction h
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case refl => exact refl
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case tail b c _ hbc ih =>
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apply ih
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{ exact head hbc _ refl }
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{ exact fun h1 h2 => head h1 (h2.tail hbc) }
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end ReflTransGen
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