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import NNG.Levels.AdvAddition.Level_12
Game "NNG"
World "AdvAddition"
Level 13
Title "ne_succ_self"
open MyNat
Introduction
"
The last level in Advanced Addition World is the statement
that $n\\not=\\operatorname{succ}(n)$.
"
Statement --ne_succ_self
"For any natural number $n$, we have
$$ n \\neq \\operatorname{succ}(n). $$"
(n : ℕ) : n ≠ succ n := by
Hint (hidden := true) "I would start a proof by induction on `n`."
induction n with d hd
· apply zero_ne_succ
· Hint (hidden := true) "If you have no clue, you could start with `rw [Ne, Not]`."
Branch
rw [Ne, Not]
intro hs
apply hd
apply succ_inj
exact hs
LemmaTab "Nat"
Conclusion
"
Congratulations. You've completed Advanced Addition World and can move on
to Advanced Multiplication World (after first doing
Multiplication World, if you didn't do it already).