diff --git a/OneVariableCalculus/Exercises.lean b/OneVariableCalculus/Exercises.lean index 2319674..9e6a5bc 100644 --- a/OneVariableCalculus/Exercises.lean +++ b/OneVariableCalculus/Exercises.lean @@ -1 +1,2 @@ -import OneVariableCalculus.Exercises.Exercises_I_3_12 \ No newline at end of file +import OneVariableCalculus.Exercises.Exercises_I_3_12 +import OneVariableCalculus.Exercises.Exercises_1_7 \ No newline at end of file diff --git a/OneVariableCalculus/Exercises/Exercises_1_7.lean b/OneVariableCalculus/Exercises/Exercises_1_7.lean index 6eb4f6f..3bae1d6 100644 --- a/OneVariableCalculus/Exercises/Exercises_1_7.lean +++ b/OneVariableCalculus/Exercises/Exercises_1_7.lean @@ -1,6 +1,11 @@ /- Exercises 1.7 -/ +import OneVariableCalculus.Real.Geometry.Area +import OneVariableCalculus.Real.Geometry.Rectangle + +open Real +open Real.Geometry.Area -- ======================================== -- The properties of area in this set of exercises are to be deduced from the @@ -16,7 +21,20 @@ Exercises 1.7 -- (c) The union of a finite collection of line segments in a plane. -- ---------------------------------------- --- # TODO +example (p : Point) + : p.set_def ∈ 𝓜 + ∧ ((h : p.set_def ∈ 𝓜) → area h = 0) := + sorry + +example (S : Set Point) (hf : Set.Finite S) + : (⋃ p ∈ S, p.set_def) ∈ 𝓜 + ∧ ((h : (⋃ p ∈ S, p.set_def) ∈ 𝓜) → area h = 0) := + sorry + +example (S : Set LineSegment) (hf : Set.Finite S) + : (⋃ s ∈ S, s.set_def) ∈ 𝓜 + ∧ ((h : (⋃ s ∈ S, s.set_def) ∈ 𝓜) → area h = 0) := + sorry -- ---------------------------------------- -- Exercise 2