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lean4game/server/nng/NNG/Levels/Multiplication/Level_2.lean

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import NNG.Levels.Multiplication.Level_1
Game "NNG"
World "Multiplication"
Level 2
Title "mul_one"
open MyNat
Introduction
"
In this level we'll need to use
* `one_eq_succ_zero : 1 = succ 0 `
which was mentioned back in Addition World (see \"Add\" tab in your inventory) and
which will be a useful thing to rewrite right now, as we
begin to prove a couple of lemmas about how `1` behaves
with respect to multiplication.
"
Statement MyNat.mul_one
"For any natural number $m$, we have $ m \\cdot 1 = m$."
(m : ) : m * 1 = m := by
rw [one_eq_succ_zero]
rw [mul_succ]
rw [mul_zero]
rw [zero_add]
rfl
LemmaTab "Mul"