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2 changes: 1 addition & 1 deletion Analysis/Section_3_4.lean
Original file line number Diff line number Diff line change
Expand Up @@ -136,7 +136,7 @@ instance SetTheory.Set.inst_coe_of_fun {X Y:Set} : CoeOut (X → Y) Object where
theorem SetTheory.Set.coe_of_fun_inj {X Y:Set} (f g:X → Y) : (f:Object) = (g:Object) ↔ f = g := by
simp [coe_of_fun]

/-- Axiom 3.11 (Power set axiom) --/
/-- Axiom 3.11 (Power set axiom) -/
@[simp]
theorem SetTheory.Set.powerset_axiom {X Y:Set} (F:Object) :
F ∈ (X ^ Y) ↔ ∃ f: Y → X, f = F := SetTheory.powerset_axiom X Y F
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2 changes: 1 addition & 1 deletion Analysis/Section_5_4.lean
Original file line number Diff line number Diff line change
Expand Up @@ -275,7 +275,7 @@ theorem Real.LIM_mono {a b:ℕ → ℚ} (ha: (a:Sequence).IsCauchy) (hb: (b:Sequ
have := LIM_of_nonneg (a := b - a) (by intro n; simp [hmono n]) (Sequence.IsCauchy.sub hb ha)
rw [←Real.LIM_sub hb ha] at this; linarith

/-- Remark 5.4.11 --/
/-- Remark 5.4.11 -/
theorem Real.LIM_mono_fail :
∃ (a b:ℕ → ℚ), (a:Sequence).IsCauchy
∧ (b:Sequence).IsCauchy
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2 changes: 1 addition & 1 deletion Analysis/Section_7_1.lean
Original file line number Diff line number Diff line change
Expand Up @@ -230,7 +230,7 @@ theorem finite_series_of_le' {X':Type*} (f g: X' → ℝ) (X: Finset X') (h: ∀
theorem abs_finite_series_le' {X':Type*} (f: X' → ℝ) (X: Finset X') :
|∑ x ∈ X, f x| ≤ ∑ x ∈ X, |f x| := by sorry

/-- Lemma 7.1.13 --/
/-- Lemma 7.1.13 -/
theorem finite_series_of_finite_series {XX YY:Type*} (X: Finset XX) (Y: Finset YY)
(f: XX × YY → ℝ) :
∑ x ∈ X, ∑ y ∈ Y, f (x, y) = ∑ z ∈ X.product Y, f z := by
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2 changes: 1 addition & 1 deletion Analysis/Section_8_1.lean
Original file line number Diff line number Diff line change
Expand Up @@ -222,7 +222,7 @@ theorem CountablyInfinite.union {A:Type} {X Y: Set A} (hX: CountablyInfinite X)
CountablyInfinite (X ∪ Y: Set A) := by
sorry

/-- Corollary 8.1.11 --/
/-- Corollary 8.1.11 -/
theorem Int.countablyInfinite : CountablyInfinite ℤ := by
-- This proof is written to follow the structure of the original text.
have h1 : CountablyInfinite {n:ℤ | n ≥ 0} := by
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