url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | apply (hf d).subset | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun i => s.indicator f i) i)).Finite | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun i => s.indicator f i) i)) ⊆ support fun i => (coeff α d) (f i) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun i => s.indicator f i) i)).Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | intro i | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun i => s.indicator f i) i)) ⊆ support fun i => (coeff α d) (f i) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (i ∈ support fun i => (coeff α d) ((fun i => s.indicator f i) i)) → i ∈ support fun i => (coeff α d) (f i) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun i => s.indicator f i) i)) ⊆ support fun i => (coeff α d) (f i)
TACTIC... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | simp only [mem_support, ne_eq, not_imp_not] | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (i ∈ support fun i => (coeff α d) ((fun i => s.indicator f i) i)) → i ∈ support fun i => (coeff α d) (f i) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (coeff α d) (f i) = 0 → (coeff α d) (s.indicator f i) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (i ∈ support fun i => (coeff α d) ((fun i => s.indicator f i) i)) → i ∈ support fun i => (coeff α d... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | intro hi | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (coeff α d) (f i) = 0 → (coeff α d) (s.indicator f i) = 0 | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
hi : (coeff α d) (f i) = 0
⊢ (coeff α d) (s.indicator f i) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
⊢ (coeff α d) (f i) = 0 → (coeff α d) (s.indicator f i) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | cases' s.indicator_eq_zero_or_self f i with h h <;>
. simp only [h, hi, map_zero] | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
hi : (coeff α d) (f i) = 0
⊢ (coeff α d) (s.indicator f i) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
hi : (coeff α d) (f i) = 0
⊢ (coeff α d) (s.indicator f i) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.of_indicator | [371, 1] | [379, 32] | simp only [h, hi, map_zero] | case inr
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
hi : (coeff α d) (f i) = 0
h : s.indicator f i = f i
⊢ (coeff α d) (s.indicator f i) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
i : ι
hi : (coeff α d) (f i) = 0
h : s.indicator f i = f i
⊢ (coeff α d) (s.indicator f i) = 0
TAC... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.add_compl | [385, 1] | [388, 54] | rw [← sum_add (hf.of_indicator s) (hf.of_indicator (sᶜ))] | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ hf.sum = ⋯.sum + ⋯.sum | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ hf.sum = ⋯.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ hf.sum = ⋯.sum + ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.add_compl | [385, 1] | [388, 54] | exact sum_congr (s.indicator_self_add_compl f).symm | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ hf.sum = ⋯.sum | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ hf.sum = ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | intro d | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ StronglySummable (f ∘ Subtype.val) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
⊢ StronglySummable (f ∘ Subtype.val)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | apply Finite.of_finite_image _ (injOn_of_injective Subtype.coe_injective _) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | apply (hf d).subset | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)) ⊆ support fun i => (coeff α d) (f i) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)).Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | rintro i ⟨j, hj, rfl⟩ | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)) ⊆ support fun i => (coeff α d) (f i) | case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : j ∈ support fun i => (coeff α d) ((f ∘ Subtype.val) i)
⊢ (fun a => ↑a) j ∈ support fun i => (coeff α d) (f i) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
⊢ ((fun a => ↑a) '' support fun i => (coeff α d) ((f ∘ Subtype.val) i)) ⊆ support fun i => (coeff α d) (f i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | simp only [comp_apply, mem_support, ne_eq] at hj ⊢ | case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : j ∈ support fun i => (coeff α d) ((f ∘ Subtype.val) i)
⊢ (fun a => ↑a) j ∈ support fun i => (coeff α d) (f i) | case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : ¬(coeff α d) (f ↑j) = 0
⊢ ¬(coeff α d) (f ↑j) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : j ∈ support fun i => (coeff α d) ((f ∘ Subtype.val) i)
⊢ (fun a =>... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.on_subtype | [393, 1] | [400, 11] | exact hj | case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : ¬(coeff α d) (f ↑j) = 0
⊢ ¬(coeff α d) (f ↑j) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type u_3
inst✝ : Semiring α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
s : Set ι
d : σ →₀ ℕ
j : { x // x ∈ s }
hj : ¬(coeff α d) (f ↑j) = 0
⊢ ¬(coeff α d) (f ↑j) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.hasSum_coeff | [405, 1] | [410, 11] | apply hasSum_sum_of_ne_finset_zero | σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
⊢ HasSum (fun i => (coeff α d) (f i)) ((coeff α d) hf.sum) | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
⊢ ∀ b ∉ ⋯.toFinset, (coeff α d) (f b) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
⊢ HasSum (fun i => (coeff α d) (f i)) ((coeff α d) hf.sum)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.hasSum_coeff | [405, 1] | [410, 11] | intro b hb | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
⊢ ∀ b ∉ ⋯.toFinset, (coeff α d) (f b) = 0 | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : b ∉ ⋯.toFinset
⊢ (coeff α d) (f b) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
⊢ ∀ b ∉ ⋯.toFinset, (coeff α d) (f b) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.hasSum_coeff | [405, 1] | [410, 11] | rw [Finite.mem_toFinset, Function.mem_support, Classical.not_not] at hb | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : b ∉ ⋯.toFinset
⊢ (coeff α d) (f b) = 0 | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : (coeff α d) (f b) = 0
⊢ (coeff α d) (f b) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : b ∉ ⋯.toFinset
⊢ (coeff α d) (f b) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.hasSum_coeff | [405, 1] | [410, 11] | exact hb | case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : (coeff α d) (f b) = 0
⊢ (coeff α d) (f b) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
ι : Type u_3
inst✝¹ : Semiring α
inst✝ : TopologicalSpace α
f : ι → MvPowerSeries σ α
hf : StronglySummable f
d : σ →₀ ℕ
b : ι
hb : (coeff α d) (f b) = 0
⊢ (coeff α d) (f b) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | intro d | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ StronglySummable fun p => (homogeneousComponent w p) f | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)).Finite | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ StronglySummable fun p => (homogeneousComponent w p) f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | apply (finite_toSet {weight w d}).subset | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)).Finite | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) ⊆ ↑{(weight w) d} | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)).Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | intro p | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) ⊆ ↑{(weight w) d} | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (p ∈ support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) → p ∈ ↑{(weight w) d} | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) ⊆ ↑{(weight w) d}
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | rw [Function.mem_support, ne_eq, mem_coe, coeff_homogeneousComponent, Finset.mem_singleton,
ite_eq_right_iff, not_forall, exists_prop, and_imp] | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (p ∈ support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) → p ∈ ↑{(weight w) d} | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (weight w) d = p → ¬(coeff α d) f = 0 → p = (weight w) d | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (p ∈ support fun i => (coeff α d) ((fun p => (homogeneousComponent w p) f) i)) → p ∈ ↑{(weight w) d}
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | intro h _ | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (weight w) d = p → ¬(coeff α d) f = 0 → p = (weight w) d | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
h : (weight w) d = p
a✝ : ¬(coeff α d) f = 0
⊢ p = (weight w) d | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
⊢ (weight w) d = p → ¬(coeff α d) f = 0 → p = (weight w) d
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.homogeneous_components_self_stronglySummable | [425, 1] | [433, 15] | exact h.symm | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
h : (weight w) d = p
a✝ : ¬(coeff α d) f = 0
⊢ p = (weight w) d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.66393
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
p : ℕ
h : (weight w) d = p
a✝ : ¬(coeff α d) f = 0
⊢ p = (weight w) d
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | ext d | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f = ⋯.sum | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) ⋯.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f = ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | simp_rw [coeff_apply, StronglySummable.sum, coeff_homogeneousComponent] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) ⋯.sum | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) f else 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | rw [sum_eq_single (weight w d)] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) f else 0 | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else 0
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerS... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) f else 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | simp only [eq_self_iff_true, if_true] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else 0 | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = (coeff α d) f | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | rfl | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = (coeff α d) f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ f d = (coeff α d) f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | intro b _ h' | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ ∀ b ∈ ⋯.toFinset, b ≠ (weight w) d → (if (weight w) d = b then (coeff α d) f else 0) = 0 | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weight w) d = b then (coeff α d) f else 0) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ ∀ b ∈ ⋯.toFinset, b ≠ (weight w) d → (if (weight w) d = b then (coeff α d) f else 0) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | rw [if_neg (Ne.symm h')] | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weight w) d = b then (coeff α d) f else 0) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weight w) d = b then (coeff α d) f else 0) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components | [439, 1] | [448, 87] | simp only [Finite.mem_toFinset, Function.mem_support, Classical.not_not, imp_self] | case h.h₁
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (weight w) d ∉ ⋯.toFinset → (if (weight w) d = (weight w) d then (coeff α d) f else 0) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₁
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.68273
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (weight w) d ∉ ⋯.toFinset → (if (weight w) d = (weight w) d then (coeff α d) f else 0) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | intro hf | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ ∀ (hf : StronglySummable fun p => (homogeneousComponent w p) f), f = hf.sum | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
⊢ f = hf.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ ∀ (hf : StronglySummable fun p => (homogeneousComponent w p) f), f = hf.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | ext d | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
⊢ f = hf.sum | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) hf.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
⊢ f = hf.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | simp_rw [coeff_apply, StronglySummable.sum, coeff_homogeneousComponent] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) hf.sum | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) f else 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) hf.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | rw [sum_eq_single (weight w d)] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) f else 0 | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else 0
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = ∑ i ∈ ⋯.toFinset, if (weight w) d = i then (coeff α d) ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | simp only [eq_self_iff_true, if_true] | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else 0 | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = (coeff α d) f | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = if (weight w) d = (weight w) d then (coeff α d) f else ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | rfl | case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = (coeff α d) f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ f d = (coeff α d) f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | intro b _ h' | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ ∀ b ∈ ⋯.toFinset, b ≠ (weight w) d → (if (weight w) d = b then (coeff α d) f else 0) = 0 | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weight w) d = b then (coeff α d) f else 0) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ ∀ b ∈ ⋯.toFinset, b ≠ (weight w) d → (if (weight w) d = b ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | rw [if_neg (Ne.symm h')] | case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weight w) d = b then (coeff α d) f else 0) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₀
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
b : ℕ
a✝ : b ∈ ⋯.toFinset
h' : b ≠ (weight w) d
⊢ (if (weigh... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.as_sum_of_homogeneous_components' | [451, 1] | [461, 87] | simp only [Finite.mem_toFinset, Function.mem_support, Classical.not_not, imp_self] | case h.h₁
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ (weight w) d ∉ ⋯.toFinset → (if (weight w) d = (weight w) d then (coeff α d) f else 0) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h₁
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
ι : Type ?u.70732
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
hf : StronglySummable fun p => (homogeneousComponent w p) f
d : σ →₀ ℕ
⊢ (weight w) d ∉ ⋯.toFinset → (if (weight w) d = (weight w) ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | intro I | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
⊢ (support fun I => (coeff α d) (partialProduct f I)) ⊆ ↑(hf.unionOfSupportOfCoeffLe d).powerset | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (I ∈ support fun I => (coeff α d) (partialProduct f I)) → I ∈ ↑(hf.unionOfSupportOfCoeffLe d).powerset | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
⊢ (support fun I => (coeff α d) (partialProduct f I)) ⊆ ↑(hf.unionOfSup... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | simp only [mem_support, ne_eq, coe_powerset, Set.mem_preimage, Set.mem_powerset_iff,
Finset.coe_subset, not_imp_comm, Finset.not_subset] | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (I ∈ support fun I => (coeff α d) (partialProduct f I)) → I ∈ ↑(hf.unionOfSupportOfCoeffLe d).powerset | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (∃ x ∈ I, x ∉ hf.unionOfSupportOfCoeffLe d) → (coeff α d) (partialProduct f I) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (I ∈ support fun I => (coeff α d) (partialProduct f I)) ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | rintro ⟨i, hi, h⟩ | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (∃ x ∈ I, x ∉ hf.unionOfSupportOfCoeffLe d) → (coeff α d) (partialProduct f I) = 0 | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : i ∉ hf.unionOfSupportOfCoeffLe d
⊢ (coeff α d) (partialProduct f I) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
⊢ (∃ x ∈ I, x ∉ hf.unionOfSupportOfCoeffLe d) → (coeff α d... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | rw [StronglySummable.not_mem_unionOfSupportOfCoeffLe_iff] at h | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : i ∉ hf.unionOfSupportOfCoeffLe d
⊢ (coeff α d) (partialProduct f I) = 0 | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ (coeff α d) (partialProduct f I) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : i ∉ hf.unionOfSuppor... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | simp only [partialProduct, prod_eq_mul_prod_diff_singleton hi, coeff_mul] | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ (coeff α d) (partialProduct f I) = 0 | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ ∑ p ∈ antidiagonal d, (coeff α p.1) (f i) * (coe... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | apply sum_eq_zero | case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ ∑ p ∈ antidiagonal d, (coeff α p.1) (f i) * (coe... | case intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ ∀ x ∈ antidiagonal d, (coeff α x.1) (f i) * (c... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e)... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | rintro ⟨x, y⟩ | case intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
⊢ ∀ x ∈ antidiagonal d, (coeff α x.1) (f i) * (c... | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
⊢ (x, y) ∈ antidiagonal d → (coe... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | rw [mem_antidiagonal] | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
⊢ (x, y) ∈ antidiagonal d → (coe... | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
⊢ (x, y).1 + (x, y).2 = d → (coe... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | intro hxy | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
⊢ (x, y).1 + (x, y).2 = d → (coe... | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
hxy : (x, y).1 + (x, y).2 = d
⊢ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | rw [h x _, MulZeroClass.zero_mul] | case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
hxy : (x, y).1 + (x, y).2 = d
⊢ ... | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
hxy : (x, y).1 + (x, y).2 = d
⊢ x ≤ d | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.support_partialProduct_subset | [479, 1] | [494, 80] | simp only [← hxy, Finsupp.le_def, Finsupp.coe_add, Pi.add_apply, le_self_add] | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : σ →₀ ℕ
hxy : (x, y).1 + (x, y).2 = d
⊢ x ≤ d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
I : Finset ι
i : ι
hi : i ∈ I
h : ∀ e ≤ d, (coeff α e) (f i) = 0
x y : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.toStronglyMultipliable | [531, 1] | [534, 87] | classical
exact fun d => Finite.subset (finite_toSet _) (support_partialProduct_subset f hf d) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ StronglyMultipliable f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ StronglyMultipliable f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglySummable.toStronglyMultipliable | [531, 1] | [534, 87] | exact fun d => Finite.subset (finite_toSet _) (support_partialProduct_subset f hf d) | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ StronglyMultipliable f | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglySummable f
⊢ StronglyMultipliable f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rw [Finset.prod_one_add] | σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
⊢ ∏ i ∈ s, (1 + f i) = ⋯.sum | σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
⊢ ∑ t ∈ s.powerset, ∏ i ∈ t, f i = ⋯.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
⊢ ∏ i ∈ s, (1 + f i) = ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | ext d | σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
⊢ ∑ t ∈ s.powerset, ∏ i ∈ t, f i = ⋯.sum | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ (coeff α d) (∑ t ∈ s.powerset, ∏ i ∈ t, f i) = (coeff α d) ⋯.sum | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
⊢ ∑ t ∈ s.powerset, ∏ i ∈ t, f i = ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rw [map_sum, StronglySummable.coeff_sum d] | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ (coeff α d) (∑ t ∈ s.powerset, ∏ i ∈ t, f i) = (coeff α d) ⋯.sum | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∑ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) =
∑ i ∈ ?m.81701, (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) i)
case... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ (coeff α d) (∑ t ∈ s.powerset, ∏ i ∈ t, f i) = (coeff α d) ⋯.sum
TAC... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | apply sum_congr rfl | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∑ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) =
∑ i ∈ ?m.81701, (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) i) | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∀ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) = (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) x) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∑ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) =
∑ i ∈ ?m.81701, (... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | intro t ht | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∀ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) = (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) x) | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ (coeff α d) (∏ i ∈ t, f i) = (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ ∀ x ∈ s.powerset, (coeff α d) (∏ i ∈ x, f i) = (coeff α d) ({I | I ⊆... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | apply congr_arg | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ (coeff α d) (∏ i ∈ t, f i) = (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) | case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = {I | I ⊆ s}.indicator (partialProduct f) t | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ (coeff α d) (∏ i ∈ t, f i) = (coeff... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rw [indicator, if_pos] | case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = {I | I ⊆ s}.indicator (partialProduct f) t | case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = partialProduct f t
case h.h.hc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = {I | I ⊆ s}.indica... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rfl | case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = partialProduct f t
case h.h.hc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq ... | case h.h.hc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ t ∈ {I | I ⊆ s} | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ ∏ i ∈ t, f i = partialProduct f t... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | exact Finset.mem_powerset.mp ht | case h.h.hc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ t ∈ {I | I ⊆ s} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.hc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht : t ∈ s.powerset
⊢ t ∈ {I | I ⊆ s}
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | intro t | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) i)) ⊆ ↑s.powerset | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ (t ∈ support fun i => (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) i)) → t ∈ ↑s.powerset | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
⊢ (support fun i => (coeff α d) ({I | I ⊆ s}.indicator (partialProduct... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rw [mem_support, ne_eq, mem_coe, Finset.mem_powerset, not_imp_comm] | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ (t ∈ support fun i => (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) i)) → t ∈ ↑s.powerset | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ ¬t ⊆ s → (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ (t ∈ support fun i => (coeff α d) ({I | I ⊆ s}.indicato... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | intro ht' | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ ¬t ⊆ s → (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) = 0 | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
⊢ ¬t ⊆ s → (coeff α d) ({I | I ⊆ s}.indicator (partialPro... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | rw [indicator, if_neg, map_zero] | case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ (coeff α d) ({I | I ⊆ s}.indicator (partialProduct f) t) = 0 | case h.hnc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ t ∉ {I | I ⊆ s} | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ (coeff α d) ({I | I ⊆ s}.indicator (partia... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.finset_prod_eq | [543, 1] | [558, 14] | exact ht' | case h.hnc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ t ∉ {I | I ⊆ s} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.hnc
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
s : Finset ι
hf : StronglyMultipliable f
d : σ →₀ ℕ
t : Finset ι
ht' : ¬t ⊆ s
⊢ t ∉ {I | I ⊆ s}
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.prod_eq_sum_add_sum | [565, 1] | [568, 37] | rw [hf.prod_eq, ← hf.add_compl] | σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglyMultipliable f
s : Set ι
⊢ hf.prod = ⋯.sum + ⋯.sum | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝¹ : DecidableEq σ
inst✝ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
hf : StronglyMultipliable f
s : Set ι
⊢ hf.prod = ⋯.sum + ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.prod_eq_finset_prod_add | [573, 1] | [575, 53] | rw [hf.prod_eq_sum_add_sum s, hf.finset_prod_eq s] | σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
hf : StronglyMultipliable f
s : Finset ι
⊢ hf.prod = ∏ i ∈ s, (1 + f i) + ⋯.sum | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝² : DecidableEq σ
inst✝¹ : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝ : DecidableEq ι
hf : StronglyMultipliable f
s : Finset ι
⊢ hf.prod = ∏ i ∈ s, (1 + f i) + ⋯.sum
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | rw [hf.toStronglyMultipliable.prod_eq_finset_prod_add J, map_add, add_right_eq_self,
StronglySummable.coeff_sum_def] | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ (coeff α d) ⋯.prod = (coeff α d) (∏ i ∈ J, (1 + f i)) | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∑ i ∈ ⋯.toFinset, (coeff α d) ({I | I ⊆ J}ᶜ.indicator (partialProduct f) i) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ (coeff α d) ⋯.prod... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | apply sum_eq_zero | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∑ i ∈ ⋯.toFinset, (coeff α d) ({I | I ⊆ J}ᶜ.indicator (partialProduct f) i) = 0 | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∀ x ∈ ⋯.toFinset, (coeff α d) ({I | I ⊆ J}ᶜ.indicator (partialProduct f)... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∑ i ∈ ⋯.toFinset, ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | intro t _ | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∀ x ∈ ⋯.toFinset, (coeff α d) ({I | I ⊆ J}ᶜ.indicator (partialProduct f)... | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
⊢ (coeff α d) ({I | I ⊆ J}ᶜ.indicator (pa... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
⊢ ∀ x ∈ ⋯.toF... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | simp only [indicator, mem_compl_iff, mem_setOf_eq] | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
⊢ (coeff α d) ({I | I ⊆ J}ᶜ.indicator (pa... | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
⊢ (coeff α d) (if ¬t ⊆ J then partialProd... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | split_ifs with h | case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
⊢ (coeff α d) (if ¬t ⊆ J then partialProd... | case pos
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : t ⊆ J
⊢ (coeff α d) 0 = 0
case neg... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | . simp only [Finset.not_subset] at h
obtain ⟨i, hit, hiJ⟩ := h
simp only [partialProduct, prod_eq_mul_prod_diff_singleton hit, coeff_mul]
apply sum_eq_zero
rintro ⟨x, y⟩ hxy
rw [mem_antidiagonal] at hxy
rw [(hf.not_mem_unionOfSupportOfCoeffLe_iff d i).mp (fun hi => hiJ (hJ hi)) x _,
MulZeroClass.zero_mu... | case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : ¬t ⊆ J
⊢ (coeff α d) (partialProduc... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | rw [map_zero] | case pos
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : t ⊆ J
⊢ (coeff α d) 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | simp only [Finset.not_subset] at h | case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : ¬t ⊆ J
⊢ (coeff α d) (partialProduc... | case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : ∃ x ∈ t, x ∉ J
⊢ (coeff α d) (parti... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | obtain ⟨i, hit, hiJ⟩ := h | case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
h : ∃ x ∈ t, x ∉ J
⊢ (coeff α d) (parti... | case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | simp only [partialProduct, prod_eq_mul_prod_diff_singleton hit, coeff_mul] | case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉... | case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | apply sum_eq_zero | case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉... | case neg.intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | rintro ⟨x, y⟩ hxy | case neg.intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i... | case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.h
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | rw [mem_antidiagonal] at hxy | case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ ... | case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | rw [(hf.not_mem_unionOfSupportOfCoeffLe_iff d i).mp (fun hi => hiJ (hJ hi)) x _,
MulZeroClass.zero_mul] | case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ ... | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉ J
x y : σ →₀ ℕ
hxy :... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.intro.intro.h.mk
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/StronglySummable/Basic.lean | MvPowerSeries.StronglyMultipliable.coeff_prod_apply_eq_finset_prod | [582, 1] | [600, 82] | simp only [← hxy, Finsupp.le_def, Finsupp.coe_add, Pi.add_apply, le_self_add] | σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ∈ ⋯.toFinset
i : ι
hit : i ∈ t
hiJ : i ∉ J
x y : σ →₀ ℕ
hxy :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝³ : DecidableEq σ
inst✝² : CommRing α
ι : Type u_3
f : ι → MvPowerSeries σ α
inst✝¹ : DecidableEq ι
inst✝ : DecidableEq σ
hf : StronglySummable f
d : σ →₀ ℕ
J : Finset ι
hJ : hf.unionOfSupportOfCoeffLe d ⊆ J
t : Finset ι
a✝ : t ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | Ideal.sub_mem_ofRel_of_rel | [148, 1] | [151, 59] | rw [sub_add_cancel] | R✝ : Type ?u.35137
M : Type ?u.35140
inst✝³ : CommRing R✝
inst✝² : AddCommMonoid M
inst✝¹ : Module R✝ M
R : Type u_1
inst✝ : Ring R
r : R → R → Prop
a b : R
hr : r a b
⊢ a - b + b = a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R✝ : Type ?u.35137
M : Type ?u.35140
inst✝³ : CommRing R✝
inst✝² : AddCommMonoid M
inst✝¹ : Module R✝ M
R : Type u_1
inst✝ : Ring R
r : R → R → Prop
a b : R
hr : r a b
⊢ a - b + b = a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.mk_C | [173, 1] | [174, 53] | rw [← MvPolynomial.algebraMap_eq, AlgHom.commutes] | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
a : R
⊢ mk (C a) = (algebraMap R (DividedPowerAlgebra R M)) a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
a : R
⊢ mk (C a) = (algebraMap R (DividedPowerAlgebra R M)) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_eq_mkRingHom | [187, 1] | [190, 6] | rw [dp_def, ← mkAlgHom_coe R] | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
m : M
⊢ dp R n m = (mkRingHom (Rel R M)) (X (n, m)) | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
m : M
⊢ (mkAlgHom R (Rel R M)) (X (n, m)) = ↑(mkAlgHom R (Rel R M)) (X (n, m)) | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
m : M
⊢ dp R n m = (mkRingHom (Rel R M)) (X (n, m))
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_eq_mkRingHom | [187, 1] | [190, 6] | rfl | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
m : M
⊢ (mkAlgHom R (Rel R M)) (X (n, m)) = ↑(mkAlgHom R (Rel R M)) (X (n, m)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
m : M
⊢ (mkAlgHom R (Rel R M)) (X (n, m)) = ↑(mkAlgHom R (Rel R M)) (X (n, m))
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_zero | [193, 1] | [195, 41] | rw [dp_def, ← map_one (mkAlgHom R (Rel R M))] | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ dp R 0 m = 1 | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ (mkAlgHom R (Rel R M)) (X (0, m)) = (mkAlgHom R (Rel R M)) 1 | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ dp R 0 m = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_zero | [193, 1] | [195, 41] | exact RingQuot.mkAlgHom_rel R Rel.zero | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ (mkAlgHom R (Rel R M)) (X (0, m)) = (mkAlgHom R (Rel R M)) 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
m : M
⊢ (mkAlgHom R (Rel R M)) (X (0, m)) = (mkAlgHom R (Rel R M)) 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_smul | [198, 1] | [201, 32] | rw [dp_def, dp_def, ← map_smul] | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
r : R
n : ℕ
m : M
⊢ dp R n (r • m) = r ^ n • dp R n m | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
r : R
n : ℕ
m : M
⊢ (mkAlgHom R (Rel R M)) (X (n, r • m)) = r ^ n • (mkAlgHom R (Rel R M)) (X (n, m)) | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
r : R
n : ℕ
m : M
⊢ dp R n (r • m) = r ^ n • dp R n m
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | cases' Nat.eq_zero_or_pos n with hn hn | R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
⊢ dp R n 0 = if n = 0 then 1 else 0 | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = if n = 0 then 1 else 0
case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = if n = 0 then 1 else 0 | Please generate a tactic in lean4 to solve the state.
STATE:
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
⊢ dp R n 0 = if n = 0 then 1 else 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [if_pos hn] | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = if n = 0 then 1 else 0 | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = if n = 0 then 1 else 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [hn] | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = 1 | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R 0 0 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R n 0 = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [dp_zero] | case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R 0 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n = 0
⊢ dp R 0 0 = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [if_neg (ne_of_gt hn)] | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = if n = 0 then 1 else 0 | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = if n = 0 then 1 else 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [← zero_smul R (0 : M)] | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = 0 | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n (0 • 0) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n 0 = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [dp_smul] | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n (0 • 0) = 0 | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ 0 ^ n • dp R n 0 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ dp R n (0 • 0) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | unused_files/Init_copy.lean | DividedPowerAlgebra.dp_null | [204, 1] | [210, 36] | rw [zero_pow hn] | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ 0 ^ n • dp R n 0 = 0 | case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ 0 • dp R n 0 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
R : Type u_1
M : Type u_2
inst✝² : CommRing R
inst✝¹ : AddCommMonoid M
inst✝ : Module R M
n : ℕ
hn : n > 0
⊢ 0 ^ n • dp R n 0 = 0
TACTIC:
|
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