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fix gap in 3.1 #272

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Merged
merged 1 commit into from
Aug 4, 2025
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fix gap in 3.1 #272

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5 changes: 2 additions & 3 deletions analysis/Analysis/Section_11_4.lean
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Expand Up @@ -30,8 +30,7 @@ theorem IntegrableOn.smul {I: BoundedInterval} (c:ℝ) {f:ℝ → ℝ} (hf: Inte
sorry

theorem IntegrableOn.neg {I: BoundedInterval} {f:ℝ → ℝ} (hf: IntegrableOn f I) :
IntegrableOn (-f) I ∧ integ (-f) I = -integ f I := by
have := IntegrableOn.smul (-1) hf; simp_all; tauto
IntegrableOn (-f) I ∧ integ (-f) I = -integ f I := by have := IntegrableOn.smul (-1) hf; aesop

/-- Theorem 11.4.1(c) / Exercise 11.4.1 -/
theorem IntegrableOn.sub {I: BoundedInterval} {f g:ℝ → ℝ} (hf: IntegrableOn f I) (hg: IntegrableOn g I) :
Expand Down Expand Up @@ -189,7 +188,7 @@ theorem integ_of_mul_nonneg {I: BoundedInterval} {f g:ℝ → ℝ} (hf: Integrab
. peel hf_nonneg with x hx _; specialize hf'min _ hx; aesop
. exact hf'const.max hzero
. apply lt_of_lt_of_le hf'int (hf'const.integ_mono _ (hf'const.max hzero)); simp
intro _ _; simp
intro _; simp
obtain ⟨ f', hf'min, hf'const, hf'int, hf'_nonneg ⟩ := this
have : ∃ g', MinorizesOn g' g I ∧ PiecewiseConstantOn g' I ∧ integ g I - ε < PiecewiseConstantOn.integ g' I ∧ MajorizesOn g' 0 I := by
obtain ⟨ g', hg'min, hg'const, hg'int ⟩ := gt_of_lt_lower_integral hg.1 (show integ g I - ε < lower_integral g I by linarith)
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2 changes: 1 addition & 1 deletion analysis/Analysis/Section_3_1.lean
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Expand Up @@ -534,7 +534,7 @@ instance SetTheory.Set.instDistribLattice : DistribLattice Set where
le_inf := by sorry
le_sup_inf := by
intro X Y Z; change (X ∪ Y) ∩ (X ∪ Z) ⊆ X ∪ (Y ∩ Z)
rw [←union_inter_distrib_left]; exact subset_self _
rw [←union_inter_distrib_left]

/-- Sets have a minimal element. -/
instance SetTheory.Set.instOrderBot : OrderBot Set where
Expand Down