08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
42 lines
1.2 KiB
Text
42 lines
1.2 KiB
Text
class HasMem (α : outParam $ Type u) (β : Type v) where
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mem : α → β → Prop
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class PartialOrder (P : Type u) extends LE P where
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refl (s : P) : s ≤ s
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antisymm (s t : P) : s ≤ t → t ≤ s → s = t
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trans (s t u : P) : s ≤ t → t ≤ u → s ≤ u
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theorem LE.le.trans {P : Type _} [PartialOrder P] {x y z : P} : x ≤ y → y ≤ z → x ≤ z := PartialOrder.trans _ _ _
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infix:50 " ∈ " => HasMem.mem
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def Set (α : Type u) := α → Prop
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namespace Set
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instance : HasMem α (Set α) := ⟨λ a s => s a⟩
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theorem ext {s t : Set α} (h : ∀ x, x ∈ s ↔ x ∈ t) : s = t :=
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funext $ λ x => propext $ h x
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instance : LE (Set α) := ⟨λ s t => ∀ {x : α}, x ∈ s → x ∈ t⟩
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instance : PartialOrder (Set α) where
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refl := λ s x => id
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antisymm := λ s t hst hts => ext $ λ x => ⟨hst, hts⟩
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trans := λ s t u hst htu x hxs => htu $ hst hxs
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variable (x y z : Set α) (hxy : x ≤ y) (hyz : y ≤ z)
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example : x ≤ z := hxy.trans hyz
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example : x ≤ z := by
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refine hxy.trans ?_
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exact hyz
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example : x ≤ z := by
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apply hxy.trans
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assumption
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example : x ≤ y → y ≤ z → x ≤ z :=
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λ h h' => _ -- goal view has the unfolded `x✝ ∈ x → x✝ ∈ z` instead of `x ≤ y`
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