diff --git a/Game/Levels/World_two/L08_exercise.lean b/Game/Levels/World_two/L08_exercise.lean index 435d528..003763a 100644 --- a/Game/Levels/World_two/L08_exercise.lean +++ b/Game/Levels/World_two/L08_exercise.lean @@ -4,36 +4,13 @@ World "World_Two" Level 8 Title "Exercise" -Statement {α : Type*} (s t r : Set α): (s ∪ t) ∪ r = s ∪ (t ∪ r) := by +Statement {α : Type*} (s t : Set α) : s ⊆ t → s ∩ t = s := by + intro h ext x - rw [Set.mem_union] + rw [Set.mem_inter_iff] constructor - · rintro (h | h) - · rw [Set.mem_union] at * - rcases h with h | h - · left - exact h - · right - rw [Set.mem_union] - left - exact h - · rw [Set.mem_union, Set.mem_union] - right - right - exact h - · rintro (h | h) - · left - rw [Set.mem_union] - left - exact h - · rw [Set.mem_union] at * - rcases h with h | h - left - right - exact h - right - exact h + exact fun ha ↦ ha.1 + exact fun ha ↦ ⟨ha, h ha⟩ Conclusion "Level Completed!" -NewTactic left right diff --git a/Game/Levels/World_two/L09_subgroup.lean b/Game/Levels/World_two/L09_subgroup.lean new file mode 100644 index 0000000..54ebcde --- /dev/null +++ b/Game/Levels/World_two/L09_subgroup.lean @@ -0,0 +1,13 @@ +import Game.Metadata + +World "World_Two" +Level 9 +Title "Exercise" + +Statement {G : Type*} [Group G] (H : Subgroup G) : H.carrier ⊆ ⊤ := by + intro x _ + exact trivial + + +Conclusion "Level Completed!" +NewTheorem trivial