This file contains ambiguous Unicode characters that may be confused with others in your current locale. If your use case is intentional and legitimate, you can safely ignore this warning. Use the Escape button to highlight these characters.
import NNG.Levels.AdvAddition.Level_6
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 `constructor`
to split an `↔` goal into the `→` goal and the `←` goal.
"
Statement MyNat.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
· Hint "Pro tip: `exact add_right_cancel _ _ _` means \"let Lean figure out the missing inputs\"."