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import NNG.Metadata
import NNG.MyNat.AdvAddition
Game "NNG"
World "AdvAddition"
Level 9
Title "succ_ne_zero"
open MyNat
Introduction
"
Levels 9 to 13 introduce the last axiom of Peano, namely
that $0\\not=\\operatorname{succ}(a)$. The proof of this is called `zero_ne_succ a`.
`zero_ne_succ (a : mynat) : 0 ≠ succ(a)`
The `symmetry` tactic will turn any goal of the form `R x y` into `R y x`,
if `R` is a symmetric binary relation (for example `=` or `≠`).
In particular, you can prove `succ_ne_zero` below by first using
`symmetry` and then `exact zero_ne_succ a`.
"
Statement -- succ_ne_zero
"Zero is not the successor of any natural number."