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leanprover / theorem_proving_in_lean4

Theorem Proving in Lean 4
https://leanprover.github.io/theorem_proving_in_lean4/
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ambiguous, possible interpretations on sample code in Quantifiers and Equality chapter #111

Open trj2059 opened 5 months ago

trj2059 commented 5 months ago

The below code from the Quantifiers and Equality chapter gives an "ambiguous, possible interpretations" error for this line: x ∣ y := h₁

you can see it if you paste the code into https://live.lean-lang.org/

def divides (x y : Nat) : Prop :=
  ∃ k, k*x = y

def divides_trans (h₁ : divides x y) (h₂ : divides y z) : divides x z :=
  let ⟨k₁, d₁⟩ := h₁
  let ⟨k₂, d₂⟩ := h₂
  ⟨k₁ * k₂, by rw [Nat.mul_comm k₁ k₂, Nat.mul_assoc, d₁, d₂]⟩

def divides_mul (x : Nat) (k : Nat) : divides x (k*x) :=
  ⟨k, rfl⟩

instance : Trans divides divides divides where
  trans := divides_trans

example (h₁ : divides x y) (h₂ : y = z) : divides x (2*z) :=
  calc
    divides x y     := h₁
    _ = z           := h₂
    divides _ (2*z) := divides_mul ..

infix:50 " ∣ " => divides

example (h₁ : divides x y) (h₂ : y = z) : divides x (2*z) :=
  calc
    x ∣ y   := h₁
    _ = z   := h₂
    _ ∣ 2*z := divides_mul ..