set theory levels

2023-02-02 14:44:58 +01:00
parent 73a44bd057
commit 404f346920
52 changed files with 1602 additions and 37 deletions
@@ -28,8 +28,7 @@ example (n : ℕ) : (∑ i : Fin (n + 1), ↑(2 * i - 1)) = n ^ 2 := by
  induction' n with n hn
  simp

-
-
+#check Finset.sum_comm

 Statement
 "Zeige $\\sum_{i = 0}^n i = \\frac{n ⬝ (n + 1)}{2}$."
@@ -0,0 +1,25 @@
+import TestGame.Metadata
+import Mathlib.Tactic.Ring
+import Mathlib
+
+import TestGame.ToBePorted
+
+Game "TestGame"
+World "Induction"
+Level 3
+
+Title "Induktion"
+
+Introduction
+"
+"
+
+
+Statement
+"Zeige $\\sum_{i = 0}^n i^3 = (\\sum_{i = 0}^n i^3)^2$."
+  (n : ℕ) : (∑ i : Fin (n + 1), (i : ℕ)^3) = (∑ i : Fin (n + 1), (i : ℕ))^2 := by
+  induction n
+  simp
+  sorry
+
+Tactics ring
@@ -0,0 +1,24 @@
+import Mathlib.Algebra.BigOperators.Basic
+import Mathlib
+
+import TestGame.Metadata
+
+set_option tactic.hygienic false
+
+Game "TestGame"
+World "Induction"
+Level 2
+
+Title "endliche Summe"
+
+Introduction
+"
+2^n > n^2   für   n ≥ 5
+"
+
+Statement
+"2^n > n^2   für   n ≥ 5"
+    (n : ℕ) : True := by
+  sorry
+
+Tactics rw simp ring
@@ -0,0 +1,24 @@
+import Mathlib.Algebra.BigOperators.Basic
+import Mathlib
+
+import TestGame.Metadata
+
+set_option tactic.hygienic false
+
+Game "TestGame"
+World "Induction"
+Level 2
+
+Title "endliche Summe"
+
+Introduction
+"
+n^3 + 2n ist durch 3 teilbar für alle ganzen Zahlen n
+"
+
+Statement
+"n^3 + 2n ist durch 3 teilbar für alle ganzen Zahlen n"
+    (n : ℤ) : True := by
+  sorry
+
+Tactics rw simp ring
@@ -0,0 +1,34 @@
+
+import Mathlib.Algebra.BigOperators.Basic
+import Mathlib
+
+import TestGame.Metadata
+
+set_option tactic.hygienic false
+
+Game "TestGame"
+World "Induction"
+Level 1
+
+Title "Simp"
+
+Introduction
+"
+"
+
+Statement
+""
+    (n : ℕ) : True := by
+  trivial
+
+Tactics simp
+
+
+-- Σ_i Σ_j ... = Σ_j Σ_i ...
+-- rw [sum_comm]
+example : ¬ ∀ (x : ℕ), x ≥ 10 := by
+  push_neg
+  use 5
+  simp
+
+¬ ∀ (...) ↔ ∃ (¬ ...)