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import TestGame.Metadata
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import Std.Tactic.RCases
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import Mathlib.Tactic.LeftRight
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Game "TestGame"
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World "Contradiction"
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Level 4
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Title "Ad absurdum"
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Introduction
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"
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Im weiteren kann man auch Widersprüche erhalten, wenn man Annahmen der Form
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`A = B` hat, wo Lean weiss, dass `A und `B` unterschiedlich sind, z.B. `0 = 1` in `ℕ`
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oder auch Annahmen der Form `A ≠ A` (`\\ne`).
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"
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Statement
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"Ein Widerspruch impliziert alles."
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(A : Prop) (a b c : ℕ) (g₁ : a = b) (g₂ : b = c) (h : a ≠ c) : A := by
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rw [g₁] at h
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contradiction
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Message (A : Prop) (a : ℕ) (b : ℕ) (c : ℕ) (g₁ : a = b) (g₂ : b = c) (h : a ≠ c) : A =>
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"Recap: `rw [...] at h` hilft dir hier."
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Message (A : Prop) (a : ℕ) (b : ℕ) (c : ℕ) (g₁ : a = b) (g₂ : b = c) (h : b ≠ c) : A =>
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"`b ≠ c` muss man als `¬ (b = c)` lesen. Deshalb findet `contradiction` hier direkt
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einen Widerspruch."
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Tactics contradiction
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