295 lines
8.4 KiB
Text
295 lines
8.4 KiB
Text
example (a b : List Nat) : a = [] → b = [2] → a = b → False := by
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grind
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example (a b : List Nat) : a = b → a = [] → b = [2] → False := by
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grind
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example (a b : Bool) : a = true → b = false → a = b → False := by
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grind
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example (a b : Sum Nat Bool) : a = .inl c → b = .inr true → a = b → False := by
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grind
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example (a b : Sum Nat Bool) : a = b → a = .inl c → b = .inr true → a = b → False := by
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grind
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inductive Foo (α : Type) : Nat → Type where
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| a (v : α) : Foo α 0
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| b (n : α) (m : Nat) (v : Vector Nat m) : Foo α (2*m)
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example (h₁ : Foo.b x 2 v = f₁) (h₂ : Foo.b y 2 w = f₂) : f₁ = f₂ → x = y := by
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grind
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example (h₁ : Foo.a x = f₁) (h₂ : Foo.a y = f₂) : f₁ = f₂ → x = y := by
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grind
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example (h₁ : a :: b = x) (h₂ : c :: d = y) : x = y → a = c := by
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grind
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example (h : x = y) (h₁ : a :: b = x) (h₂ : c :: d = y) : a = c := by
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grind
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example (h : x = y) (h₁ : a :: b = x) (h₂ : c :: d = y) : b = d := by
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grind
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example (a b : Sum Nat Bool) : a = .inl x → b = .inl y → x ≠ y → a = b → False := by
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grind
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example (a b : Nat) : a = 1 → b = 2 → a = b → False := by
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grind
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example (a b c : Int) : a = 1 → c = -2 → a = b → c = b → False := by
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grind
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example (a b : Char) : a = 'h' → b = 'w' → a = b → False := by
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grind
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example (a b : String) : a = "hello" → b = "world" → a = b → False := by
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grind
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example (a b c : String) : a = c → a = "hello" → c = "world" → c = b → False := by
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grind
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example (a b c : BitVec 32) : a = c → a = 1#32 → c = 2#32 → c = b → False := by
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grind
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example (a b c : UInt32) : a = c → a = 1 → c = 200 → c = b → False := by
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grind
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structure Boo (α : Type) where
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a : α
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b : α
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c : α
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example (a b d : Nat) (f : Nat → Boo Nat) : (f d).1 ≠ a → f d = ⟨b, v₁, v₂⟩ → b = a → False := by
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grind
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def ex (a b c d : Nat) (f : Nat → Boo Nat) : (f d).2 ≠ a → f d = ⟨b, c, v₂⟩ → c = a → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat) : { a := f b, c, b := 4 : Boo Nat }.1 ≠ f a → f b = f c → a = c → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat) : p = { a := f b, c, b := 4 : Boo Nat } → p.1 ≠ f a → f b = f c → a = c → False := by
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grind
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example (a b c : Nat) (f : Nat → Nat) : p.1 ≠ f a → p = { a := f b, c, b := 4 : Boo Nat } → f b = f c → a = c → False := by
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grind
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/--
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info: [grind.debug.proj] { a := b, b := v₁, c := v₂ }.a
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-/
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#guard_msgs (info) in
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set_option trace.grind.debug.proj true in
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example (a b d e : Nat) (x y z : Boo Nat) (f : Nat → Boo Nat) : (f d).1 ≠ a → f d = ⟨b, v₁, v₂⟩ → x.1 = e → y.1 = e → z.1 = e → f d = x → f d = y → f d = z → b = a → False := by
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grind
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example (f : Nat → Nat) (a b c : Nat) : f (if a = b then x else y) = z → a = c → c = b → f x = z := by
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grind
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example (f : Nat → Nat) (a b c : Nat) : f (if a = b then x else y) = z → a = c → b ≠ c → f y = z := by
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grind
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namespace dite_propagator_test
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opaque R : Nat → Nat → Prop
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opaque f (a : Nat) (b : Nat) (_ : R a b) : Nat
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opaque g (a : Nat) (b : Nat) (_ : ¬ R a b) : Nat
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open Classical
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example (foo : Nat → Nat)
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(_ : foo (if h : R a c then f a c h else g a c h) = x)
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(_ : R a b)
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(_ : c = b) : foo (f a c (by grind)) = x := by
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grind
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example (foo : Nat → Nat)
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(_ : foo (if h : R a c then f a c h else g a c h) = x)
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(_ : ¬ R a b)
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(_ : c = b)
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: foo (g a c (by grind)) = x := by
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grind
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end dite_propagator_test
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/--
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info: [grind.eqc] x = 2 * a
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[grind.eqc] y = x
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[grind.eqc] (y = 2 * a) = False
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[grind.eqc] (y = 2 * a) = True
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-/
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#guard_msgs (info) in
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set_option trace.grind.eqc true in
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example (a : Nat) : let x := a + a; y = x → y = a + a := by
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grind
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/--
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info: [grind.eqc] x = 2 * a
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[grind.eqc] y = x
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[grind.eqc] (y = 2 * a) = False
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[grind.eqc] (y = 2 * a) = True
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-/
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#guard_msgs (info) in
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set_option trace.grind.eqc true in
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example (a : Nat) : let_fun x := a + a; y = x → y = a + a := by
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grind
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example (α : Type) (β : Type) (a₁ a₂ : α) (b₁ b₂ : β)
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(h₁ : α = β)
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(h₂ : cast h₁ a₁ = b₁)
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(h₃ : a₁ = a₂)
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(h₄ : b₁ = b₂)
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: HEq a₂ b₂ := by
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grind
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example (α : Type) (β : Type) (a₁ a₂ : α) (b₁ b₂ : β)
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(h₁ : α = β)
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(h₂ : h₁ ▸ a₁ = b₁)
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(h₃ : a₁ = a₂)
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(h₄ : b₁ = b₂)
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: HEq a₂ b₂ := by
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grind
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example (α : Type) (β : Type) (a₁ a₂ : α) (b₁ b₂ : β)
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(h₁ : α = β)
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(h₂ : Eq.recOn h₁ a₁ = b₁)
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(h₃ : a₁ = a₂)
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(h₄ : b₁ = b₂)
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: HEq a₂ b₂ := by
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grind
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example (α : Type) (β : Type) (a₁ a₂ : α) (b₁ b₂ : β)
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(h₁ : α = β)
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(h₂ : Eq.ndrec (motive := id) a₁ h₁ = b₁)
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(h₃ : a₁ = a₂)
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(h₄ : b₁ = b₂)
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: HEq a₂ b₂ := by
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grind
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example (α : Type) (β : Type) (a₁ a₂ : α) (b₁ b₂ : β)
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(h₁ : α = β)
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(h₂ : Eq.rec (motive := fun x _ => x) a₁ h₁ = b₁)
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(h₃ : a₁ = a₂)
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(h₄ : b₁ = b₂)
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: HEq a₂ b₂ := by
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grind
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/--
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info: [grind.assert] ∀ (a : α), a ∈ b → p a
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[grind.ematch.pattern] h₁: [@Membership.mem `[α] `[List α] `[List.instMembership] `[b] #1]
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[grind.ematch.pattern] h₁: [p #1]
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[grind.assert] w ∈ b
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[grind.assert] ¬p w
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[grind.ematch.instance] h₁: w ∈ b → p w
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[grind.assert] w ∈ b → p w
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-/
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#guard_msgs (info) in
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set_option trace.grind.ematch.pattern true in
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set_option trace.grind.ematch.instance true in
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set_option trace.grind.assert true in
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example (b : List α) (p : α → Prop) (h₁ : ∀ a ∈ b, p a) (h₂ : ∃ a ∈ b, ¬p a) : False := by
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grind
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/--
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info: [grind.assert] ∀ (x : α), Q x → P x
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[grind.ematch.pattern] h₁: [Q #1]
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[grind.ematch.pattern] h₁: [P #1]
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[grind.assert] ∀ (x : α), R x → False = P x
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[grind.ematch.pattern] h₂: [R #1]
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[grind.ematch.pattern] h₂: [P #1]
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[grind.assert] Q a
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[grind.assert] R a
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[grind.ematch.instance] h₁: Q a → P a
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[grind.ematch.instance] h₂: R a → False = P a
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[grind.assert] Q a → P a
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[grind.assert] R a → False = P a
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-/
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#guard_msgs (info) in
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set_option trace.grind.ematch.pattern true in
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set_option trace.grind.ematch.instance true in
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set_option trace.grind.assert true in
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example (P Q R : α → Prop) (h₁ : ∀ x, Q x → P x) (h₂ : ∀ x, R x → False = (P x)) : Q a → R a → False := by
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grind
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example (w : Nat → Type) (h : ∀ n, Subsingleton (w n)) : True := by
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grind
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example {P1 P2 : Prop} : (P1 ∧ P2) ↔ (P2 ∧ P1) := by
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grind
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example {P U V W : Prop} (h : P ↔ (V ↔ W)) (w : ¬ U ↔ V) : ¬ P ↔ (U ↔ W) := by
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grind
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example {P Q : Prop} (q : Q) (w : P = (P = ¬ Q)) : False := by
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grind
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example (P Q : Prop) : (¬P → ¬Q) ↔ (Q → P) := by
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grind
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example {α} (a b c : α) [LE α] :
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¬(¬a ≤ b ∧ a ≤ c ∨ ¬a ≤ c ∧ a ≤ b) ↔ a ≤ b ∧ a ≤ c ∨ ¬a ≤ c ∧ ¬a ≤ b := by
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simp_arith -- should not fail
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sorry
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example {α} (a b c : α) [LE α] :
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¬(¬a ≤ b ∧ a ≤ c ∨ ¬a ≤ c ∧ a ≤ b) ↔ a ≤ b ∧ a ≤ c ∨ ¬a ≤ c ∧ ¬a ≤ b := by
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grind
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example (x y : Bool) : ¬(x = true ↔ y = true) ↔ (¬(x = true) ↔ y = true) := by
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grind
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/--
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error: `grind` failed
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case grind
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p q : Prop
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a✝¹ : p = q
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a✝ : p
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⊢ False
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[grind] Diagnostics
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[facts] Asserted facts
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[prop] p = q
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[prop] p
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[eqc] True propositions
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[prop] p = q
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[prop] q
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[prop] p
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-/
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#guard_msgs (error) in
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set_option trace.grind.split true in
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example (p q : Prop) : (p ↔ q) → p → False := by
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grind -- should not split on (p ↔ q)
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/--
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error: `grind` failed
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case grind
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p q : Prop
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a✝¹ : p = ¬q
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a✝ : p
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⊢ False
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[grind] Diagnostics
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[facts] Asserted facts
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[prop] p = ¬q
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[prop] p
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[eqc] True propositions
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[prop] p = ¬q
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[prop] ¬q
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[prop] p
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[eqc] False propositions
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[prop] q
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-/
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#guard_msgs (error) in
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set_option trace.grind.split true in
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example (p q : Prop) : ¬(p ↔ q) → p → False := by
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grind -- should not split on (p ↔ q)
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example {a b : Nat} (h : a < b) : ¬ b < a := by
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grind
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example {m n : Nat} : m < n ↔ m ≤ n ∧ ¬ n ≤ m := by
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grind
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example {α} (f : α → Type) (a : α) (h : ∀ x, Nonempty (f x)) : Nonempty (f a) := by
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grind
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example {α β} (f : α → β) (a : α) : ∃ a', f a' = f a := by
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grind
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