add definitions

server/testgame/TestGame/LemmaDocs.lean

@@ -61,13 +61,13 @@ LemmaDoc not_forall as not_forall in "Logic"
 LemmaDoc not_exists as not_exists in "Logic"
 "`∀ (A : Prop), ¬(∃ x, A) ↔ ∀x, (¬A)`."
 
-LemmaDoc Even as Even in "Nat"
+DefinitionDoc Even
 "
 `even n` ist definiert als `∃ r, a = 2 * r`.
 Die Definition kann man mit `unfold even at *` einsetzen.
 "
 
-LemmaDoc Odd as Odd in "Nat"
+DefinitionDoc Odd
 "
 `odd n` ist definiert als `∃ r, a = 2 * r + 1`.
 Die Definition kann man mit `unfold odd at *` einsetzen.

server/testgame/TestGame/Levels/Contradiction/L01_Have.lean

@@ -66,4 +66,5 @@ Conclusion ""
 NewTactics «have»
 DisabledTactics «suffices»
 
-NewLemmas Even Odd not_even not_odd
+NewDefinitions Even Odd
+NewLemmas not_even not_odd

server/testgame/TestGame/Levels/Contradiction/L02_Suffices.lean

@@ -62,5 +62,5 @@ Conclusion ""
 
 NewTactics «suffices»
 DisabledTactics «have»
-
-NewLemmas Even Odd not_even not_odd
+NewDefinitions Even Odd
+NewLemmas not_even not_odd

server/testgame/TestGame/Levels/Contradiction/L05_Contrapose.lean

@@ -62,4 +62,5 @@ Hint (n : ℕ) : Even n → Even (n ^ 2) =>
 "Diese Aussage hast du bereits als Lemma bewiesen, schau mal in der Bibliothek."
 
 NewTactics contrapose rw apply
-NewLemmas Even Odd not_even not_odd even_square
+NewDefinitions Even Odd
+NewLemmas not_even not_odd even_square

server/testgame/TestGame/Levels/Contradiction/L06_Summary.lean

@@ -72,5 +72,5 @@ HiddenHint (n: ℕ) (h : Odd (n ^ 2)) (g : Even n) : Even (n ^ 2) =>
 
 
 NewTactics contradiction by_contra rw apply assumption -- TODO: suffices, have
-
-NewLemmas Odd Even not_odd not_even even_square
+NewDefinitions Even Odd
+NewLemmas not_odd not_even even_square

server/testgame/TestGame/Levels/Predicate/L06_Exists.lean

@@ -68,4 +68,4 @@ Hint (n : ℕ) (x : ℕ) (hx : n = x + x) : (x + x) ^ 2 = 2 * x ^ 2 + 2 * x ^ 2
 "Die Taktik `ring` löst solche Gleichungen."
 
 NewTactics unfold rcases use rw ring
-NewLemmas Even Odd
+NewDefinitions Even Odd

server/testgame/TestGame/Levels/Predicate/L08_PushNeg.lean

@@ -63,5 +63,5 @@ Hint (n : ℕ) : n + n = 2 * n => "Recap: `ring` löst Gleichungen in `ℕ`."
 Conclusion ""
 
 NewTactics push_neg intro use rw unfold ring
-
-NewLemmas Even Odd not_even not_odd not_exists not_forall
+NewDefinitions Even Odd
+NewLemmas not_even not_odd not_exists not_forall

server/testgame/TestGame/Levels/Predicate/L09_Summary.lean

@@ -51,5 +51,5 @@ Statement
 Conclusion ""
 
 NewTactics push_neg intro use rw unfold ring
-
-NewLemmas Even Odd not_even not_odd not_exists not_forall
+NewDefinitions Even Odd
+NewLemmas not_even not_odd not_exists not_forall