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import NNG.Metadata
import NNG.MyNat.AdvAddition
Game "NNG"
World "AdvAddition"
Level 7
Title "add_right_cancel_iff"
open MyNat
Introduction
"
It's sometimes convenient to have the \"if and only if\" version
of theorems like `add_right_cancel`. Remember that you can use `split`
to split an `↔` goal into the `→` goal and the `←` goal.
## Pro tip:
`exact add_right_cancel _ _ _` means \"let Lean figure out the missing inputs\"
"
Statement --add_right_cancel_iff
"For all naturals $a$, $b$ and $t$,
$$ a + t = b + t\\iff a=b. $$
"
(t a b : ℕ) : a + t = b + t ↔ a = b := by
constructor
exact add_right_cancel _ _ _ -- done that way already,