fb135b8cfe
Currently this will fail in two tests, because of changes in #3965. * Sometimes we need to add an additional universe annotation, or we get a `stuck at solving universe constraint max u ?u =?= u`. * Sometimes we need to specify arguments that could previously be found by unification. --------- Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
98 lines
2.3 KiB
Text
98 lines
2.3 KiB
Text
section Mathlib.Init.Order.Defs
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universe u
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variable {α : Type u}
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class PartialOrder (α : Type u) extends LE α, LT α where
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theorem le_antisymm [PartialOrder α] : ∀ {a b : α}, a ≤ b → b ≤ a → a = b := sorry
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end Mathlib.Init.Order.Defs
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section Mathlib.Init.Data.Nat.Lemmas
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namespace Nat
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instance : PartialOrder Nat where
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le := Nat.le
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lt := Nat.lt
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section Find
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variable {p : Nat → Prop}
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private def lbp (m n : Nat) : Prop :=
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m = n + 1 ∧ ∀ k ≤ n, ¬p k
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variable [DecidablePred p] (H : ∃ n, p n)
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private def wf_lbp {p : Nat → Prop} (H : ∃ n, p n) : WellFounded (@lbp p) := sorry
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protected noncomputable def findX : { n // p n ∧ ∀ m < n, ¬p m } :=
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@WellFounded.fix _ (fun k => (∀ n < k, ¬p n) → { n // p n ∧ ∀ m < n, ¬p m }) lbp (wf_lbp H)
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sorry 0 sorry
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protected noncomputable def find {p : Nat → Prop} [DecidablePred p] (H : ∃ n, p n) : Nat :=
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(Nat.findX H).1
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protected theorem find_spec : p (Nat.find H) := sorry
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protected theorem find_min' {m : Nat} (h : p m) : Nat.find H ≤ m := sorry
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end Find
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end Nat
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end Mathlib.Init.Data.Nat.Lemmas
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section Mathlib.Logic.Basic
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theorem Exists.fst {b : Prop} {p : b → Prop} : Exists p → b
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| ⟨h, _⟩ => h
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end Mathlib.Logic.Basic
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section Mathlib.Order.Basic
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open Function
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def PartialOrder.lift {α β} [PartialOrder β] (f : α → β) : PartialOrder α where
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le x y := f x ≤ f y
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lt x y := f x < f y
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end Mathlib.Order.Basic
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section Mathlib.Data.Fin.Basic
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instance {n : Nat} : PartialOrder (Fin n) :=
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PartialOrder.lift Fin.val
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end Mathlib.Data.Fin.Basic
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section Mathlib.Data.Fin.Tuple.Basic
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universe u v
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namespace Fin
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variable {n : Nat}
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def find : ∀ {n : Nat} (p : Fin n → Prop) [DecidablePred p], Option (Fin n)
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| 0, _p, _ => none
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| n + 1, p, _ => by
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exact
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Option.casesOn (@find n (fun i ↦ p (i.castLT sorry)) _)
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(if _ : p (Fin.last n) then some (Fin.last n) else none) fun i ↦
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some (i.castLT sorry)
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theorem nat_find_mem_find {p : Fin n → Prop} [DecidablePred p]
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(h : ∃ i, ∃ hin : i < n, p ⟨i, hin⟩) :
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(⟨Nat.find h, (Nat.find_spec h).fst⟩ : Fin n) ∈ find p := by
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rcases hf : find p with f | f
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· sorry
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· exact Option.some_inj.2 (le_antisymm sorry (Nat.find_min' _ ⟨f.2, sorry⟩))
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end Fin
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end Mathlib.Data.Fin.Tuple.Basic
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