47 lines
799 B
Lean4
47 lines
799 B
Lean4
import Game.Metadata
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import Game.MyNat.Addition
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Game "NNG"
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World "AdvProposition"
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Level 3
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Title "and_trans"
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open MyNat
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Introduction
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"
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Here is another exercise to `rcases` and `constructor`.
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"
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Statement --and_trans
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"If $P$, $Q$ and $R$ are true/false statements, then $P\\land Q$ and
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$Q\\land R$ together imply $P\\land R$."
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(P Q R : Prop) : P ∧ Q → Q ∧ R → P ∧ R := by
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Hint "Here's a trick:
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Your first steps would probably be
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```
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intro h
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rcases h with ⟨p, q⟩
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```
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i.e. introducing a new assumption and then immediately take it appart.
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In that case you could do that in a single step:
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```
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intro ⟨p, q⟩
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```
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"
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intro hpq
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rcases hpq with ⟨p, q⟩
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intro hqr
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rcases hqr with ⟨q', r⟩
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constructor
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assumption
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assumption
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Conclusion
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"
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"
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