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.
61 lines
1.5 KiB
Text
61 lines
1.5 KiB
Text
opaque f : Nat → Nat
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opaque q : Nat → Prop
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opaque r : Nat → Prop
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@[simp] axiom ax1 (p : Prop) : (p ∧ True) ↔ p
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@[simp] axiom ax2 (x : Nat) : q (f x)
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@[simp] axiom ax3 (x : Nat) : ¬ r (f x)
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@[simp] axiom ax4 (p : Prop) : (p ∨ False) ↔ p
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theorem ex1 (x : Nat) (h : q x) : q x ∧ q (f x) := by
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simp [h]
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theorem ex2 (x : Nat) : q (f x) ∨ r (f x) := by
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simp
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@[simp] axiom ax5 (x : Nat) : 0 + x = x
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theorem ex3 (h : 0 + x = y) : f x = f y := by
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simp at h
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simp [h]
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theorem ex4 (x y z : Nat) (h : (x, z).1 = y) : f x = f y := by
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simp at h
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simp [h]
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theorem ex5
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(f : Nat → Nat → Nat)
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(g : Nat → Nat)
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(h₁ : ∀ x, f x x = x)
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(h₂ : ∀ x, g (g x) = x)
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: f (g (g x)) (f x x) = x :=
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by simp [h₁, h₂]
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@[simp] axiom ax6 (x : Nat) : x + 0 = x
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theorem ex6
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(f : Nat → Nat)
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(x y : Nat)
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: (fun (h : y = 0) => y + x) = (fun _ => x + 0) := by
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simp (config := { contextual := true })
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theorem ex7 (x : Nat) : (let y := x + 0; y + y) = x + x := by
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simp
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@[simp] theorem impTrue (p : Sort u) : (p → True) = True :=
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propext <| Iff.intro (fun _ => trivial) (fun _ _ => trivial)
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theorem ex8 (y x : Nat) : y = 0 → x + y = 0 → x = 0 := by
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simp (config := { contextual := true })
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theorem ex9 (y x : Nat) : y = 0 → x + y = 0 → x = 0 := by
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fail_if_success simp [-Nat.add_eq_zero_iff]
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intro h₁ h₂
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simp [h₁] at h₂
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simp [h₂]
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theorem ex10 (y x : Nat) : y = 0 → x + 0 = 0 → x = 0 := by
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simp
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theorem ex11 : ∀ x : Nat, 0 + x + 0 = x := by
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simp
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