39 lines
866 B
Lean4
39 lines
866 B
Lean4
import Game.Levels.AdvAddition.Level_12
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World "AdvAddition"
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Level 13
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Title "ne_succ_self"
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open MyNat
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Introduction
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"
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The last level in Advanced Addition World is the statement
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that $n\\not=\\operatorname{succ}(n)$.
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"
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/-- For any natural number $n$, we have
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$$ n \\neq \\operatorname{succ}(n). $$ -/
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Statement --ne_succ_self
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(n : ℕ) : n ≠ succ n := by
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Hint (hidden := true) "I would start a proof by induction on `n`."
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induction n with d hd
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· apply zero_ne_succ
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· Hint (hidden := true) "If you have no clue, you could start with `rw [Ne, Not]`."
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Branch
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rw [Ne, Not]
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intro hs
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apply hd
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apply succ_inj
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exact hs
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LemmaTab "Nat"
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Conclusion
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"
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Congratulations. You've completed Advanced Addition World and can move on
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to Advanced Multiplication World (after first doing
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Multiplication World, if you didn't do it already).
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"
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