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视频链接，创作不易记得投币：人工智能数学验证工具LEAN4【入门介绍4】次幂世界-如何描述费马大定理_哔哩哔哩_bilibili
import Game.Levels.Power.L09add_sq
World "Power"
Level 10
Title "Fermat's Last Theorem"
namespace MyNat
Introduction
"
We now have enough to state a mathematically accurate, but slightly
clunky, version of Fermat's Last Theorem.
Fermat's Last Theorem states that if $x,y,z>0$ and $m \\geq 3$ then $x^m+y^m\\not =z^m$.
If you didn't do inequality world yet then we can't talk about $m \\geq 3$,
so we have to resort to the hack of using `n + 3` for `m`,
which guarantees it's big enough. Similarly instead of `x > 0` we
use `a + 1`.
This level looks superficially like other levels we have seen,
but the shortest solution known to humans would translate into
many millions of lines of Lean code. The author of this game,
Kevin Buzzard, is working on translating the proof by Wiles
and Taylor into Lean, although this task will take many years.
## CONGRATULATIONS!
You've finished the main quest of the natural number game!
If you would like to learn more about how to use Lean to
prove theorems in mathematics, then take a look
at [Mathematics In Lean](https://leanprover-community.github.io/mathematics_in_lean/),
an interactive textbook which you can read in your browser,
and which explains how to work with many more mathematical concepts in Lean.
"
TacticDoc xyzzy "
`xyzzy` is an ancient magic spell, believed to be the origin of the
modern word `sorry`. The game won't complain - or notice - if you
prove anything with `xyzzy`.
"
/-- For all naturals $a$ $b$ $c$ and $n$, we have
$$(a+1)^{n+3}+(b+1)^{n+3}\not=(c+1)^{n+3}.$$ -/
Statement
(a b c n : ℕ) : (a + 1) ^ (n + 3) + (b + 1) ^ (n + 3) ≠ (c + 1) ^ (n + 3) := by
xyzzy
NewHiddenTactic xyzzy
LemmaTab "^"
Conclusion
"
Congratulations! You have proved Fermat's Last Theorem!
Either that, or you used magic...
"
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