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import NNG.Levels.AdvAddition.Level_7
Game "NNG"
World "AdvAddition"
Level 8
Title "eq_zero_of_add_right_eq_self"
open MyNat
Introduction
"
The lemma you're about to prove will be useful when we want to prove that $\\leq$ is antisymmetric.
There are some wrong paths that you can take with this one.
"
Statement MyNat.eq_zero_of_add_right_eq_self
"If $a$ and $b$ are natural numbers such that
$$ a + b = a, $$
then $b = 0$."
{a b : ℕ} : a + b = a → b = 0 := by
intro h
Hint (hidden := true) "Look at `add_left_cancel`."