File: Mathlib/NumberTheory/LSeries/Linearity.lean

full_name: LSeries.term_add
code: lemma LSeries.term_add (f g : ℕ → ℂ) (s : ℂ) : term (f + g) s = term f s + term g s 
goal: LSeries.term (f + g) s = LSeries.term f s + LSeries.term g s

full_name: LSeries.term_add_apply
code: lemma LSeries.term_add_apply (f g : ℕ → ℂ) (s : ℂ) (n : ℕ) :
    term (f + g) s n = term f s n + term g s n 
goal: LSeries.term (f + g) s n = LSeries.term f s n + LSeries.term g s n

full_name: LSeriesHasSum.add
code: lemma LSeriesHasSum.add {f g : ℕ → ℂ} {s a b : ℂ} (hf : LSeriesHasSum f s a)
    (hg : LSeriesHasSum g s b) :
    LSeriesHasSum (f + g) s (a + b) 
goal: LSeriesHasSum (f + g) s (a + b)

full_name: LSeriesSummable.add
code: lemma LSeriesSummable.add {f g : ℕ → ℂ} {s : ℂ} (hf : LSeriesSummable f s)
    (hg : LSeriesSummable g s) :
    LSeriesSummable (f + g) s 
goal: LSeriesSummable (f + g) s

full_name: LSeries_add
code: @[simp]
lemma LSeries_add {f g : ℕ → ℂ} {s : ℂ} (hf : LSeriesSummable f s) (hg : LSeriesSummable g s) :
    LSeries (f + g) s = LSeries f s + LSeries g s 
goal: LSeries (f + g) s = LSeries f s + LSeries g s

full_name: LSeries.term_neg
code: lemma LSeries.term_neg (f : ℕ → ℂ) (s : ℂ) : term (-f) s = -term f s 
goal: LSeries.term (-f) s = -LSeries.term f s

full_name: LSeries.term_neg_apply
code: lemma LSeries.term_neg_apply (f : ℕ → ℂ) (s : ℂ) (n : ℕ) : term (-f) s n = -term f s n 
goal: LSeries.term (-f) s n = -LSeries.term f s n

full_name: LSeriesHasSum.neg
code: lemma LSeriesHasSum.neg {f : ℕ → ℂ} {s a : ℂ} (hf : LSeriesHasSum f s a) :
    LSeriesHasSum (-f) s (-a) 
goal: LSeriesHasSum (-f) s (-a)

full_name: LSeriesSummable.neg
code: lemma LSeriesSummable.neg {f : ℕ → ℂ} {s : ℂ} (hf : LSeriesSummable f s) :
    LSeriesSummable (-f) s 
goal: LSeriesSummable (-f) s

full_name: LSeriesSummable.neg_iff
code: @[simp]
lemma LSeriesSummable.neg_iff {f : ℕ → ℂ} {s : ℂ} :
    LSeriesSummable (-f) s ↔ LSeriesSummable f s 
goal: LSeriesSummable (-f) s ↔ LSeriesSummable f s

full_name: LSeries_neg
code: @[simp]
lemma LSeries_neg (f : ℕ → ℂ) (s : ℂ) : LSeries (-f) s = -LSeries f s 
goal: LSeries (-f) s = -LSeries f s

full_name: LSeries.term_sub
code: lemma LSeries.term_sub (f g : ℕ → ℂ) (s : ℂ) : term (f - g) s = term f s - term g s 
goal: LSeries.term (f - g) s = LSeries.term f s - LSeries.term g s

full_name: LSeries.term_sub_apply
code: lemma LSeries.term_sub_apply (f g : ℕ → ℂ) (s : ℂ) (n : ℕ) :
    term (f - g) s n = term f s n - term g s n 
goal: LSeries.term (f - g) s n = LSeries.term f s n - LSeries.term g s n

full_name: LSeriesHasSum.sub
code: lemma LSeriesHasSum.sub {f g : ℕ → ℂ} {s a b : ℂ} (hf : LSeriesHasSum f s a)
    (hg : LSeriesHasSum g s b) :
    LSeriesHasSum (f - g) s (a - b) 
goal: LSeriesHasSum (f - g) s (a - b)

full_name: LSeriesSummable.sub
code: lemma LSeriesSummable.sub {f g : ℕ → ℂ} {s : ℂ} (hf : LSeriesSummable f s)
    (hg : LSeriesSummable g s) :
    LSeriesSummable (f - g) s 
goal: LSeriesSummable (f - g) s

full_name: LSeries_sub
code: @[simp]
lemma LSeries_sub {f g : ℕ → ℂ} {s : ℂ} (hf : LSeriesSummable f s) (hg : LSeriesSummable g s) :
    LSeries (f - g) s = LSeries f s - LSeries g s 
goal: LSeries (f - g) s = LSeries f s - LSeries g s

full_name: LSeries.term_smul
code: lemma LSeries.term_smul (f : ℕ → ℂ) (c s : ℂ) : term (c • f) s = c • term f s 
goal: LSeries.term (c • f) s = c • LSeries.term f s

full_name: LSeries.term_smul_apply
code: lemma LSeries.term_smul_apply (f : ℕ → ℂ) (c s : ℂ) (n : ℕ) :
    term (c • f) s n = c * term f s n 
goal: LSeries.term (c • f) s n = c * LSeries.term f s n

full_name: LSeriesHasSum.smul
code: lemma LSeriesHasSum.smul {f : ℕ → ℂ} (c : ℂ) {s a : ℂ} (hf : LSeriesHasSum f s a) :
    LSeriesHasSum (c • f) s (c * a) 
goal: LSeriesHasSum (c • f) s (c * a)

full_name: LSeriesSummable.smul
code: lemma LSeriesSummable.smul {f : ℕ → ℂ} (c : ℂ) {s : ℂ} (hf : LSeriesSummable f s) :
    LSeriesSummable (c • f) s 
goal: LSeriesSummable (c • f) s

full_name: LSeriesSummable.of_smul
code: lemma LSeriesSummable.of_smul {f : ℕ → ℂ} {c s : ℂ} (hc : c ≠ 0) (hf : LSeriesSummable (c • f) s) :
    LSeriesSummable f s 
goal: LSeriesSummable f s

full_name: LSeriesSummable.smul_iff
code: lemma LSeriesSummable.smul_iff {f : ℕ → ℂ} {c s : ℂ} (hc : c ≠ 0) :
    LSeriesSummable (c • f) s ↔ LSeriesSummable f s 
goal: LSeriesSummable (c • f) s ↔ LSeriesSummable f s

full_name: LSeries_smul
code: @[simp]
lemma LSeries_smul (f : ℕ → ℂ) (c s : ℂ) : LSeries (c • f) s = c * LSeries f s 
goal: LSeries (c • f) s = c * LSeries f s