You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
|
|
|
|
|
import TestGame.Metadata
|
|
|
|
|
|
|
|
|
|
|
|
import Mathlib.Data.Set.Basic
|
|
|
|
|
|
|
|
|
|
|
|
Game "TestGame"
|
|
|
|
|
|
World "SetTheory"
|
|
|
|
|
|
Level 13
|
|
|
|
|
|
|
|
|
|
|
|
Title "Konkrete Mengen"
|
|
|
|
|
|
|
|
|
|
|
|
Introduction
|
|
|
|
|
|
"
|
|
|
|
|
|
Um zu überprüfen, dass gewisse Elemente in
|
|
|
|
|
|
konkreten Mengen enthalten sind, gibt es nicht direkt eine Taktik, aber ein
|
|
|
|
|
|
einfaches Rezept:
|
|
|
|
|
|
|
|
|
|
|
|
```
|
|
|
|
|
|
simp_rw [mem_insert_iff, mem_singleton_iff] at *
|
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
|
|
vereinfacht Aussagen der Form `6 ∈ { 0, 6, 1}` zu `(6 = 0) ∨ (6 = 6) ∨ (6 = 1)`,
|
|
|
|
|
|
und dann kann `tauto` diese Aussage beweisen.
|
|
|
|
|
|
|
|
|
|
|
|
Bei `⊆` kann man wie schon vorher zuerst mit `intro x hx` die Definition
|
|
|
|
|
|
auseinandernehmen und dann gleich vorgehen.
|
|
|
|
|
|
|
|
|
|
|
|
"
|
|
|
|
|
|
|
|
|
|
|
|
open Set
|
|
|
|
|
|
|
|
|
|
|
|
Statement
|
|
|
|
|
|
"" :
|
|
|
|
|
|
({2, 3, 5} : Set ℕ) ⊆ {4, 2, 5, 7, 3} := by
|
|
|
|
|
|
intro x hx
|
|
|
|
|
|
simp_rw [mem_insert_iff, mem_singleton_iff] at *
|
|
|
|
|
|
tauto
|
|
|
|
|
|
|
|
|
|
|
|
NewTactics simp_rw intro tauto rw
|
|
|
|
|
|
--Lemmas Subset.antisymm_iff empty_subset
|
