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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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--set_option tactic.hygienic false
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Game "TestGame"
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World "TestWorld"
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Level 15
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Title "Oder - Bonus"
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Introduction
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"
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Wenn man hingegen ein ODER - `(h : A ∨ B)` - in den Annahmen hat, kann man dieses
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ähnlich wie beim UND mit `rcases h` aufteilen.
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ABER! Beim UND `(h : A ∧ B)` hat man dann zwei neue Annahmen erhalten, und diese hat man mit
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`rcases h with ⟨hA, hB⟩` benannt. Beim ODER `(h : A ∨ B)` kriegt man stattdessen zwei **Goals**
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wo man annimmt, dass entweder die linke oder rechte Seite von `h` war ist.
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Diese Annahme benennt man dann mit `rcases h with hA | hB`.
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"
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Statement
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(A B C D : Prop) (h : (A ∧ B) ∨ (D ∨ C)) : (A ∧ B) ∨ (C ∨ D) := by
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rcases h with ⟨ha, hb⟩ | (h | h)
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left
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constructor
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assumption
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assumption
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right
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right
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assumption
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right
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left
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assumption
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Message (A : Prop) (B : Prop) (C : Prop) (D : Prop) (h : (A ∧ B) ∨ (D ∨ C)) : (A ∧ B) ∨ (C ∨ D) =>
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"Man kann hier entweder in mehren Schritten `rcases` anwenden:
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```
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rcases h with h₁ | h₂
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rcases h₁ with ⟨hA, hB⟩
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[...]
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rcases h₂ with h | h
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```
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oder man kann dies in einem Schritt verschachteln:
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```
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rcases h with ⟨ha, hb⟩ | (h | h)
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```
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"
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Tactics left right assumption constructor rcases apply
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