[voxl]

Something else important to note: this proof of commutativity of addition on natural numbers is definitely _not_ how you normally write these proofs in Lean.

Here is a closer approximation to how someone would actually write the proof in Lean:

  lemma add_comm (a b : ℕ) : a + b = b + a :=
  begin
    induction a with a IH,
    rw (add_zero b),
    rw (zero_add b),
    trivial,
    rw (add_succ b a),
    rw (succ_add a b),
    rw IH,
    trivial
  end

[prisonguard]

thank you for explaining, but do i need a special keyboard just to type out the natural number type?

[deadbeef57]

No, you can just type `\nat` and the Lean extension in VScode will turn it into `ℕ`. Similarly, you can type many LaTeX macros, and the will render in unicode. Examples: `\times` becomes `×` and `\to` becomes `→`, etc...

[nodogoto]

No, you just type \N. You can also use `nat` instead if you prefer.