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.
37 lines
1.1 KiB
Text
37 lines
1.1 KiB
Text
class CommAddSemigroup (α : Type u) extends Add α where
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addComm : {a b : α} → a + b = b + a
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addAssoc : {a b c : α} → a + b + c = a + (b + c)
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open CommAddSemigroup
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theorem addComm3 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
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have h : b + c = c + b := addComm;
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have h' := congrArg (a + ·) h;
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simp at h';
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rw [←addAssoc] at h';
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rw [←addAssoc (a := a)] at h';
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exact h';
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}
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theorem addComm4 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
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rw [addAssoc, addAssoc];
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rw [addComm (a := b)];
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}
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theorem addComm5 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
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have h : b + c = c + b := addComm;
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have h' := congrArg (a + ·) h;
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simp at h';
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rw [←addAssoc] at h';
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rw [←addAssoc (a := a)] at h';
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exact h';
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}
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theorem addComm6 [CommAddSemigroup α] {a b c : α} : a + b + c = a + c + b := by {
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have h : b + c = c + b := addComm;
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have h' := congrArg (a + ·) h;
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simp at h';
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rw [←addAssoc] at h';
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rw [←addAssoc] at h';
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exact h';
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}
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