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import Adam.Metadata
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import Mathlib.Data.Set.Basic
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import Mathlib.Algebra.Parity
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import Mathlib
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Game "Adam"
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World "SetTheory2"
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Level 5
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Title ""
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Introduction
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"
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Zu der Teilmengen-Schreibweise (`SetOf`) gibt es noch zwei spezielle
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Syntax, die abundzu auftreten.
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Der erste ist `{ x ∈ S | 0 ≤ x}` ( für z.B `(S : Set ℤ)`),
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welcher eine Abkürzung für `{ x : ℤ | x ∈ S ∧ 0 ≤ x}` ist.
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Entsprechend hilft auch hier `setOf_and`.
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"
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open Set
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Statement
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"" (S : Set ℤ) :
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{ x ∈ (S : Set ℤ) | 0 ≤ x} ⊆ S := by
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library_search
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NewTactic constructor intro rw assumption rcases simp tauto trivial
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