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.
26 lines
848 B
Text
26 lines
848 B
Text
def Set α := α → Prop
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class HasMem (α : outParam $ Type u) (β : Type v) where
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mem : α → β → Prop
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infix:50 " ∈ " => HasMem.mem
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instance {α : Type u} : HasMem α (Set α) := ⟨λ a s => s a⟩
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instance {α : Type u} : LE (Set α) := ⟨λ s t => ∀ {x : α}, x ∈ s → x ∈ t⟩
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class HasInf (P : Type u) where
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inf : P → P → P
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infix:70 " ⊓ " => HasInf.inf
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instance {α : Type u} : HasInf (Set α) := ⟨λ s t x => x ∈ s ∧ x ∈ t⟩
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theorem infLeLeft {s t : Set α} : s ⊓ t ≤ s := And.left
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theorem infLeRight {s t : Set α} : s ⊓ t ≤ t := And.right
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theorem inter_mem_sets_iff {α : Type u} (f : Set (Set α)) (hf : ∀ {s t}, s ∈ f → s ≤ t → t ∈ f) {x y : Set α}
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: x ⊓ y ∈ f → x ∈ f ∧ y ∈ f := by
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intro h
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refine ⟨hf h infLeLeft, hf h ?_⟩
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apply infLeRight
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