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36 lines
730 B
Plaintext
36 lines
730 B
Plaintext
import Adam.Metadata
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import Adam.Levels.SetTheory.L04_SubsetEmpty
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--import Mathlib.Data.Set.Basic
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import Mathlib.Init.Set
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import Mathlib.Tactic.Tauto
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import Mathlib.Tactic.PushNeg
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set_option tactic.hygienic false
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Game "Adam"
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World "SetTheory"
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Level 5
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Title "Empty"
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Introduction
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"
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Zeige folgendes Lemma, welches wir gleich brauchen werden:
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"
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open Set
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Statement Set.eq_empty_iff_forall_not_mem
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""
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{A : Type _} (s : Set A) :
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s = ∅ ↔ ∀ x, x ∉ s := by
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Hint "Das Lemma `subset_empty_iff` von letzter Aufgabe könnte hilfreich sein."
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rw [←subset_empty_iff]
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rfl -- This is quite a miracle :)
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NewTactic constructor intro rw assumption rcases simp tauto trivial
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NewLemma Set.subset_empty_iff
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LemmaTab "Set"
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