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.
62 lines
1.6 KiB
Text
62 lines
1.6 KiB
Text
set_option autoImplicit true
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section Mathlib.Algebra.Group.Defs
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class MulOneClass (M : Type) extends One M, Mul M where
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one_mul : ∀ a : M, 1 * a = a
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export MulOneClass (one_mul)
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end Mathlib.Algebra.Group.Defs
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section Mathlib.Algebra.Ring.Defs
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class Distrib (R : Type) extends Mul R, Add R where
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right_distrib : ∀ a b c : R, (a + b) * c = a * c + b * c
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class RightDistribClass (R : Type) [Mul R] [Add R] : Prop where
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right_distrib : ∀ a b c : R, (a + b) * c = a * c + b * c
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instance Distrib.rightDistribClass (R : Type) [Distrib R] : RightDistribClass R :=
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⟨Distrib.right_distrib⟩
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theorem add_mul [Mul R] [Add R] [RightDistribClass R] (a b c : R) :
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(a + b) * c = a * c + b * c :=
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RightDistribClass.right_distrib a b c
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theorem add_one_mul [Add α] [MulOneClass α] [RightDistribClass α] (a b : α) :
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(a + 1) * b = a * b + b := by
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rw [add_mul, one_mul]
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class Semiring (R : Type) extends Distrib R, MulOneClass R
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end Mathlib.Algebra.Ring.Defs
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section Mathlib.Data.Nat.Basic
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instance : Semiring Nat where
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add := Nat.add
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mul := Nat.mul
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one := Nat.succ Nat.zero
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one_mul := sorry
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right_distrib := sorry
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end Mathlib.Data.Nat.Basic
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#synth MulOneClass Nat -- works
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#synth RightDistribClass Nat -- works
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theorem ex1 [Add α] [MulOneClass α] [RightDistribClass α] (a b : α) :
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(a + 1) * b = a * b + b := by
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sorry
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#check (ex1) -- should work
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#check (add_one_mul) -- should work
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#check @add_one_mul
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example {a b : Nat} : (a + 1) * b = a * b + b := by
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have := add_one_mul a b -- works
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rw [add_one_mul] -- should work
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example {a b : Nat} : (a + 1) * b = a * b + b := by
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rw [add_one_mul] -- should work
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