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.
27 lines
1 KiB
Text
27 lines
1 KiB
Text
/-- `OrientedCmp cmp` asserts that `cmp` is determined by the relation `cmp x y = .lt`. -/
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class OrientedCmp (cmp : α → α → Ordering) : Prop where
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/-- The comparator operation is symmetric, in the sense that if `cmp x y` equals `.lt` then
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`cmp y x = .gt` and vice versa. -/
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symm (x y) : (cmp x y).swap = cmp y x
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namespace OrientedCmp
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theorem cmp_eq_gt [OrientedCmp cmp] : cmp x y = .gt ↔ cmp y x = .lt := by
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rw [← Ordering.swap_inj, symm]; exact .rfl
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end OrientedCmp
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/-- `TransCmp cmp` asserts that `cmp` induces a transitive relation. -/
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class TransCmp (cmp : α → α → Ordering) : Prop extends OrientedCmp cmp where
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/-- The comparator operation is transitive. -/
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le_trans : cmp x y ≠ .gt → cmp y z ≠ .gt → cmp x z ≠ .gt
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namespace TransCmp
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variable [TransCmp cmp]
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open OrientedCmp
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theorem ge_trans (h₁ : cmp x y ≠ .lt) (h₂ : cmp y z ≠ .lt) : cmp x z ≠ .lt := by
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have := @TransCmp.le_trans _ cmp _ z y x
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simp [cmp_eq_gt] at *
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-- `simp` did not fire at `this`
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exact this h₂ h₁
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