lean4-skills

# Lean 4 Theorem Proof Assistance

## Theorem to Prove
```lean
lemma vector_add_comm (v w : Vector ℕ) : v + w = w + v := sorry
```

## Current Attempt
```lean
lemma vector_add_comm (v w : Vector ℕ) : v + w = w + v := by
  induction v with
  | nil => rfl
  | cons hd tl ih =>
    rw [Vector.add_cons, Vector.add_cons]
    apply ih
    exact hd.add_comm
```

## Suggested Solution
```lean
lemma vector_add_comm (v w : Vector ℕ) : v + w = w + v := by
  induction v with
  | nil => rfl
  | cons hd tl ih =>
    rw [Vector.add_cons, Vector.add_cons]
    apply add_comm
    exact ih
```

The key insight was to use `add_comm` directly on the head elements rather than trying to apply the induction hypothesis first. This approach leverages Lean's built-in commutative addition property more effectively.