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.
46 lines
1.4 KiB
Text
46 lines
1.4 KiB
Text
structure PreInt where
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minuend : Nat
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subtrahend : Nat
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/-- Definition 4.1.1 -/
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instance PreInt.instSetoid : Setoid PreInt where
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r a b := a.minuend + b.subtrahend = b.minuend + a.subtrahend
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iseqv := {
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refl := by grind
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symm := by grind
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trans := by grind
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}
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abbrev MyInt := Quotient PreInt.instSetoid
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abbrev MyInt.formalDiff (a b : Nat) : MyInt := Quotient.mk PreInt.instSetoid ⟨ a, b ⟩
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theorem MyInt.eq (a b c d : Nat) : formalDiff a b = formalDiff c d ↔ a + d = c + b :=
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⟨ Quotient.exact, by intro h; exact Quotient.sound h ⟩
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instance MyInt.instOfNat {n : Nat} : OfNat MyInt n where
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ofNat := formalDiff n 0
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instance MyInt.instNatCast : NatCast MyInt where
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natCast n := formalDiff n 0
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theorem MyInt.natCast_eq (n : Nat) : (n : MyInt) = formalDiff n 0 := rfl
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theorem MyInt.natCast_inj (n m : Nat) :
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(n : MyInt) = (m : MyInt) ↔ n = m := by
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rw [natCast_eq, natCast_eq, eq]; simp
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example (n m : Nat) : (n : MyInt) = (m : MyInt) ↔ n = m := by
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grind [MyInt.natCast_eq, MyInt.eq]
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@[grind]
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theorem MyInt.eq_0_of_cast_eq_0 (n : Nat) (h : (n : MyInt) = 0) : n = 0 := by
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rw [show (0 : MyInt) = ((0 : Nat) : MyInt) by rfl] at h
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rwa [natCast_inj] at h
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theorem MyInt.pos_iff_gt_0 {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
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intro ⟨ w, hw ⟩ h
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grind
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example {a : MyInt} : (∃ (n:Nat), n > 0 ∧ a = n) → a ≠ 0 := by
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grind
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