203 lines
4.2 KiB
Text
203 lines
4.2 KiB
Text
abbrev f (a : α) := a
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set_option grind.debug true
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set_option grind.debug.proofs true
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/--
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error: `grind` failed
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case grind.1.2
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a b c : Bool
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p q : Prop
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left✝ : a = true
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left : p
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right : q
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h✝ : b = false
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h : c = true
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⊢ False[facts] Asserted facts
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[prop] a = true
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[prop] b = true ∨ c = true
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[prop] p
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[prop] q
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[prop] b = false ∨ a = false
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[prop] b = false
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[prop] c = true[eqc] True propositions
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[prop] b = true ∨ c = true
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[prop] p
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[prop] q
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[prop] b = false ∨ a = false
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[prop] b = false
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[prop] c = true[eqc] Equivalence classes
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[eqc] {b = true, a = false}
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[eqc] {b, false}
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[eqc] {a, c, true}
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-/
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#guard_msgs (error) in
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theorem ex (h : (f a && (b || f (f c))) = true) (h' : p ∧ q) : b && a := by
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grind
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open Lean.Grind.Eager in
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/--
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error: `grind` failed
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case grind.2.1
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a b c : Bool
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p q : Prop
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left✝ : a = true
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h✝ : c = true
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left : p
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right : q
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h : b = false
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⊢ False[facts] Asserted facts
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[prop] a = true
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[prop] c = true
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[prop] p
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[prop] q
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[prop] b = false[eqc] True propositions
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[prop] p
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[prop] q[eqc] Equivalence classes
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[eqc] {b, false}
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[eqc] {a, c, true}
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-/
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#guard_msgs (error) in
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theorem ex2 (h : (f a && (b || f (f c))) = true) (h' : p ∧ q) : b && a := by
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grind
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def g (i : Nat) (j : Nat) (_ : i > j := by omega) := i + j
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/--
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error: `grind` failed
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case grind
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i j : Nat
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h : j + 1 < i + 1
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h✝ : j + 1 ≤ i
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x✝ : ¬g (i + 1) j ⋯ = i + j + 1
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⊢ False[facts] Asserted facts
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[prop] j + 1 ≤ i
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[prop] ¬g (i + 1) j ⋯ = i + j + 1[eqc] True propositions
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[prop] j + 1 ≤ i[eqc] False propositions
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[prop] g (i + 1) j ⋯ = i + j + 1[offset] Assignment satisfying offset contraints
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[assign] j := 0
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[assign] i := 1
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[assign] g (i + 1) j ⋯ := 0
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[assign] i + j := 0
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-/
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#guard_msgs (error) in
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example (i j : Nat) (h : i + 1 > j + 1) : g (i+1) j = f ((fun x => x) i) + f j + 1 := by
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grind
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structure Point where
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x : Nat
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y : Int
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/--
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error: `grind` failed
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case grind
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a₁ : Point
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a₂ : Nat
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a₃ : Int
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as : List Point
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b₁ : Point
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bs : List Point
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b₂ : Nat
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b₃ : Int
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head_eq : a₁ = b₁
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x_eq : a₂ = b₂
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y_eq : a₃ = b₃
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tail_eq : as = bs
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⊢ False[facts] Asserted facts
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[prop] a₁ = b₁
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[prop] a₂ = b₂
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[prop] a₃ = b₃
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[prop] as = bs[eqc] Equivalence classes
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[eqc] {as, bs}
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[eqc] {a₃, b₃}
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[eqc] {a₂, b₂}
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[eqc] {a₁, b₁}
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-/
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#guard_msgs (error) in
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theorem ex3 (h : a₁ :: { x := a₂, y := a₃ : Point } :: as = b₁ :: { x := b₂, y := b₃} :: bs) : False := by
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grind
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def h (a : α) := a
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example (p : Prop) (a b c : Nat) : p → a = 0 → a = b → h a = h c → a = c ∧ c = a → a = b ∧ b = a → a = c := by
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grind
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set_option trace.grind.debug.proof true
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/--
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error: `grind` failed
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case grind.1
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α : Type
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a : α
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p q r : Prop
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h₁ : HEq p a
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h₂ : HEq q a
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h₃ : p = r
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left : ¬p ∨ r
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h : ¬r
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⊢ False[facts] Asserted facts
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[prop] HEq p a
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[prop] HEq q a
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[prop] p = r
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[prop] ¬p ∨ r
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[prop] ¬r ∨ p
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[prop] ¬r[eqc] True propositions
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[prop] p = r
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[prop] ¬p ∨ r
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[prop] ¬r ∨ p
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[prop] ¬p
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[prop] ¬r[eqc] False propositions
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[prop] a
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[prop] p
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[prop] q
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[prop] r
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case grind.2
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α : Type
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a : α
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p q r : Prop
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h₁ : HEq p a
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h₂ : HEq q a
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h₃ : p = r
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left : ¬p ∨ r
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h : p
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⊢ False[facts] Asserted facts
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[prop] HEq p a
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[prop] HEq q a
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[prop] p = r
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[prop] ¬p ∨ r
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[prop] ¬r ∨ p
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[prop] p[eqc] True propositions
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[prop] p = r
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[prop] ¬p ∨ r
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[prop] ¬r ∨ p
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[prop] a
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[prop] p
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[prop] q
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[prop] r[eqc] False propositions
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[prop] ¬p
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[prop] ¬r
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-/
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#guard_msgs (error) in
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example (a : α) (p q r : Prop) : (h₁ : HEq p a) → (h₂ : HEq q a) → (h₃ : p = r) → False := by
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grind
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example (a b : Nat) (f : Nat → Nat) : (h₁ : a = b) → (h₂ : f a ≠ f b) → False := by
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grind
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example (a : α) (p q r : Prop) : (h₁ : HEq p a) → (h₂ : HEq q a) → (h₃ : p = r) → q = r := by
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grind
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/--
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warning: declaration uses 'sorry'
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---
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info: [grind.issues] found congruence between
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g b
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and
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f a
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but functions have different types
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-/
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#guard_msgs in
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set_option trace.grind.issues true in
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set_option trace.grind.debug.proof false in
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example (f : Nat → Bool) (g : Int → Bool) (a : Nat) (b : Int) : HEq f g → HEq a b → f a = g b := by
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fail_if_success grind
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sorry
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