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lean4game/server/nng/NNG/Levels/AdvAddition/Level_7.lean

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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 : ) : a + t = b + t ↔ a = b := by
constructor
· Hint "Pro tip: `exact add_right_cancel _ _ _` means \"let Lean figure out the missing inputs\"."
exact add_right_cancel _ _ _
· intro H
rw [H]
rfl
LemmaTab "Add"