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import NNG.Levels.AdvAddition.Level_3
Game "NNG"
World "AdvAddition"
Level 4
Title "eq_iff_succ_eq_succ"
open MyNat
Introduction
"
Here is an `iff` goal. You can split it into two goals (the implications in both
directions) using the `constructor` tactic, which is how you're going to have to start.
"
Statement
"Two natural numbers are equal if and only if their successors are equal.
"
(a b : ℕ) : succ a = succ b ↔ a = b := by
constructor
Hint "Now you have two goals. The first is exactly `succ_inj` so you can close
it with
```
exact succ_inj
```
"
· exact succ_inj
· Hint "The second one you could solve by looking up the name of the theorem
you proved in the last level and doing `exact <that name>`, or alternatively
you could get some more `intro` practice and seeing if you can prove it