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import NNG.Metadata
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import NNG.MyNat.Addition
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import Std.Tactic.RCases
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import Mathlib.Tactic.LeftRight
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Game "NNG"
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World "AdvProposition"
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Level 8
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Title ""
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open MyNat
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Introduction
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"
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"
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Statement and_or_distrib_left
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""
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(P Q R : Prop) : P ∧ (Q ∨ R) ↔ (P ∧ Q) ∨ (P ∧ R) := by
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constructor
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intro h
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rcases h with ⟨hp, hqr⟩
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rcases hqr with q | r
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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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constructor
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assumption
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assumption
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intro h
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rcases h with hpq | hpr
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rcases hpq with ⟨p, q⟩
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constructor
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assumption
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left
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assumption
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rcases hpr with ⟨hp, hr⟩
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constructor
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assumption
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right
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assumption
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Conclusion
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"
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"
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