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import TestGame.Metadata
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import Std.Tactic.RCases
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import Mathlib.Tactic.Contrapose
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import Mathlib.Tactic.Use
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import Mathlib.Tactic.Ring
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import TestGame.ToBePorted
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Game "TestGame"
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World "Contradiction"
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Level 8
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Title "Kontraposition"
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Introduction
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"
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Lean Trick: Wenn das Goal nicht bereits eine Implikation ist, sondern man eine Annahme `h` hat, die
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Man gerne für die Kontraposition benützen würde, kann man mit `revert h` diese als
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Implikationsannahme ins Goal schreiben.
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"
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Statement
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"Ist n² ungerade, so ist auch n ungerade. Beweise durch Kontraposition."
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(n : ℕ) (h : odd (n ^ 2)): odd n := by
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revert h
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contrapose
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rw [not_odd]
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rw [not_odd]
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apply even_square
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Tactics contrapose rw apply revert
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Lemmas even odd not_even not_odd even_square
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