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/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | classical
induction s using Finset.induction_on with
| empty => simp only [Finset.sum_empty, IsNilpotent.zero]
| @insert b s hb hs =>
rw [Finset.sum_insert hb]
apply IsNilpotent.add
exact hf b (s.mem_insert_self b)
exact hs (fun b hb ↦ hf b (by exact Finset.mem_insert_of_mem hb)) | α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
s : Finset β
hf : ∀ b ∈ s, IsNilpotent (f b)
⊢ IsNilpotent (s.sum f) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
s : Finset β
hf : ∀ b ∈ s, IsNilpotent (f b)
⊢ IsNilpotent (s.sum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | induction s using Finset.induction_on with
| empty => simp only [Finset.sum_empty, IsNilpotent.zero]
| @insert b s hb hs =>
rw [Finset.sum_insert hb]
apply IsNilpotent.add
exact hf b (s.mem_insert_self b)
exact hs (fun b hb ↦ hf b (by exact Finset.mem_insert_of_mem hb)) | α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
s : Finset β
hf : ∀ b ∈ s, IsNilpotent (f b)
⊢ IsNilpotent (s.sum f) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
s : Finset β
hf : ∀ b ∈ s, IsNilpotent (f b)
⊢ IsNilpotent (s.sum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | simp only [Finset.sum_empty, IsNilpotent.zero] | case empty
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ b ∈ ∅, IsNilpotent (f b)
⊢ IsNilpotent (∅.sum f) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case empty
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ b ∈ ∅, IsNilpotent (f b)
⊢ IsNilpotent (∅.sum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | rw [Finset.sum_insert hb] | case insert
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent ((insert b s).sum f) | case insert
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b + ∑ x ∈ s, f x) | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent ((insert b s).sum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | apply IsNilpotent.add | case insert
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b + ∑ x ∈ s, f x) | case insert.ha
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b)
case insert.hb
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b + ∑ x ∈ s, f x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | exact hf b (s.mem_insert_self b) | case insert.ha
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b)
case insert.hb
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β... | case insert.hb
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (∑ x ∈ s, f x) | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.ha
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (f b)
case insert.hb
α : Type u_1
ins... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | exact hs (fun b hb ↦ hf b (by exact Finset.mem_insert_of_mem hb)) | case insert.hb
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (∑ x ∈ s, f x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.hb
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b : β
s : Finset β
hb : b ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b_1 ∈ insert b s, IsNilpotent (f b_1)
⊢ IsNilpotent (∑ x ∈ s, f x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finset_sum | [68, 1] | [78, 72] | exact Finset.mem_insert_of_mem hb | α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b✝ : β
s : Finset β
hb✝ : b✝ ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b ∈ insert b✝ s, IsNilpotent (f b)
b : β
hb : b ∈ s
⊢ b ∈ insert b✝ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
b✝ : β
s : Finset β
hb✝ : b✝ ∉ s
hs : (∀ b ∈ s, IsNilpotent (f b)) → IsNilpotent (s.sum f)
hf : ∀ b ∈ insert b✝ s, IsNilpotent (f b)
b : β
hb : b ∈ s
⊢ b ∈ insert b✝ s
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finsum | [80, 1] | [86, 56] | by_cases h : Set.Finite f.support | α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
⊢ IsNilpotent (_root_.finsum f) | case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (_root_.finsum f)
case neg
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : ¬(Function.support f).Finite
⊢ IsNilpotent (_ro... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
⊢ IsNilpotent (_root_.finsum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finsum | [80, 1] | [86, 56] | rw [finsum_def, dif_pos h] | case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (_root_.finsum f) | case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (∑ i ∈ h.toFinset, f i) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (_root_.finsum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finsum | [80, 1] | [86, 56] | exact IsNilpotent.finset_sum _ (fun b _ ↦ hf b) | case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (∑ i ∈ h.toFinset, f i) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : (Function.support f).Finite
⊢ IsNilpotent (∑ i ∈ h.toFinset, f i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | IsNilpotent.finsum | [80, 1] | [86, 56] | simp only [finsum_def, dif_neg h, IsNilpotent.zero] | case neg
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : ¬(Function.support f).Finite
⊢ IsNilpotent (_root_.finsum f) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_1
inst✝ : CommSemiring α
β : Type u_2
f : β → α
hf : ∀ (b : β), IsNilpotent (f b)
h : ¬(Function.support f).Finite
⊢ IsNilpotent (_root_.finsum f)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.monomial_one_eq | [102, 1] | [105, 82] | simp only [← MvPolynomial.coe_X, ← MvPolynomial.coe_pow, ← MvPolynomial.coe_monomial, MvPolynomial.monomial_eq, map_one, one_mul] | σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
⊢ (monomial R e) 1 = e.prod fun s n => X s ^ n | σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
⊢ ↑(e.prod fun n e => MvPolynomial.X n ^ e) = e.prod fun s n => ↑(MvPolynomial.X s ^ n) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
⊢ (monomial R e) 1 = e.prod fun s n => X s ^ n
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.monomial_one_eq | [102, 1] | [105, 82] | simp only [← MvPolynomial.coeToMvPowerSeries.ringHom_apply, ← map_finsupp_prod] | σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
⊢ ↑(e.prod fun n e => MvPolynomial.X n ^ e) = e.prod fun s n => ↑(MvPolynomial.X s ^ n) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
⊢ ↑(e.prod fun n e => MvPolynomial.X n ^ e) = e.prod fun s n => ↑(MvPolynomial.X s ^ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | rw [Finsupp.prod_congr (g2 := fun s n ↦ ((C σ R (algebraMap A R (a s)) * (X s : MvPowerSeries σ R)) ^ n))] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (e.prod fun s n => (a s • X s) ^ n) = (e.prod fun s n => a s ^ n) • (monomial R e) 1 | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (e.prod fun s n => ((C σ R) ((algebraMap A R) (a s)) * X s) ^ n) = (e.prod fun s n => a s ^ n) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : Com... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (e.prod fun s n => (a s • X s) ^ n) = (e.prod fun s n => a s ^ n) • (monomial R e) 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | simp only [mul_pow, Finsupp.prod_mul] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (e.prod fun s n => ((C σ R) ((algebraMap A R) (a s)) * X s) ^ n) = (e.prod fun s n => a s ^ n) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : Com... | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((e.prod fun a_1 b => (C σ R) ((algebraMap A R) (a a_1)) ^ b) * e.prod fun a b => X a ^ b) =
(e.prod fun s n => a s ^ n) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiri... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (e.prod fun s n => ((C σ R) ((algebraMap A R) (a s)) * X s) ^ n) = (e.prod fun s n => a s ^ n) • (monomial R e) 1
σ : Type u_1
A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | simp only [← map_pow, ← map_finsupp_prod] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((e.prod fun a_1 b => (C σ R) ((algebraMap A R) (a a_1)) ^ b) * e.prod fun a b => X a ^ b) =
(e.prod fun s n => a s ^ n) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiri... | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * e.prod fun a b => X a ^ b) =
(e.prod fun a_1 b => a a_1 ^ b) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemi... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((e.prod fun a_1 b => (C σ R) ((algebraMap A R) (a a_1)) ^ b) * e.prod fun a b => X a ^ b) =
(e.prod fun s n => a s ^ n) • (m... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | rw [← monomial_one_eq] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * e.prod fun a b => X a ^ b) =
(e.prod fun a_1 b => a a_1 ^ b) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemi... | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * (monomial R e) 1 =
(e.prod fun a_1 b => a a_1 ^ b) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ((C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * e.prod fun a b => X a ^ b) =
(e.prod fun a_1 b => a a_1 ^ b) • ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | rw [← smul_eq_C_mul, ← algebra_compatible_smul] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * (monomial R e) 1 =
(e.prod fun a_1 b => a a_1 ^ b) • (monomial R e) 1
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : ... | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ∀ x ∈ e.support, (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ (C σ R) ((algebraMap A R) (e.prod fun a_1 b => a a_1 ^ b)) * (monomial R e) 1 =
(e.prod fun a_1 b => a a_1 ^ b) • (monomial R... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | intro x _ | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ∀ x ∈ e.support, (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
x : σ
a✝ : x ∈ e.support
⊢ (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
⊢ ∀ x ∈ e.support, (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.prod_smul_X_eq_smul_monomial_one | [107, 1] | [118, 50] | rw [algebra_compatible_smul R, smul_eq_C_mul] | σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
x : σ
a✝ : x ∈ e.support
⊢ (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
A : Type u_2
inst✝² : CommSemiring A
R : Type u_3
inst✝¹ : CommSemiring R
inst✝ : Algebra A R
e : σ →₀ ℕ
a : σ → A
x : σ
a✝ : x ∈ e.support
⊢ (a x • X x) ^ e x = ((C σ R) ((algebraMap A R) (a x)) * X x) ^ e x
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.monomial_eq' | [120, 1] | [125, 74] | rw [prod_smul_X_eq_smul_monomial_one, ← map_smul, smul_eq_mul, mul_one] | σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : σ → R
⊢ (monomial R e) (e.prod fun s n => r s ^ n) = e.prod fun s e => (r s • X s) ^ e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : σ → R
⊢ (monomial R e) (e.prod fun s n => r s ^ n) = e.prod fun s e => (r s • X s) ^ e
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.monomial_smul_const | [127, 1] | [133, 68] | rw [prod_smul_X_eq_smul_monomial_one, ← map_smul, smul_eq_mul, mul_one] | σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : R
⊢ (monomial R e) (r ^ e.sum fun x n => n) = e.prod fun s e => (r • X s) ^ e | σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : R
⊢ (monomial R e) (r ^ e.sum fun x n => n) = (monomial R e) (e.prod fun s n => r ^ n) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : R
⊢ (monomial R e) (r ^ e.sum fun x n => n) = e.prod fun s e => (r • X s) ^ e
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.monomial_smul_const | [127, 1] | [133, 68] | simp only [Finsupp.sum, Finsupp.prod, Finset.prod_pow_eq_pow_sum] | σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : R
⊢ (monomial R e) (r ^ e.sum fun x n => n) = (monomial R e) (e.prod fun s n => r ^ n) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹ : DecidableEq σ
R : Type u_2
inst✝ : CommSemiring R
e : σ →₀ ℕ
r : R
⊢ (monomial R e) (r ^ e.sum fun x n => n) = (monomial R e) (e.prod fun s n => r ^ n)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_X | [203, 1] | [208, 45] | simp only [constantCoeff_X, IsNilpotent.zero] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
this : UniformSpace S := ⊥
s : σ
⊢ IsNilpotent ((const... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_zero | [210, 1] | [214, 41] | simp only [Pi.zero_apply, map_zero, IsNilpotent.zero] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
this : UniformSpace S := ⊥
x✝ : σ
⊢ IsNilpotent ((cons... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_add | [216, 1] | [225, 18] | simp only [Pi.add_apply, map_add] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_add | [216, 1] | [225, 18] | exact IsNilpotent.add (ha.const_coeff s) (hb.const_coeff s) | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_add | [216, 1] | [225, 18] | letI : UniformSpace S := ⊥ | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_add | [216, 1] | [225, 18] | convert Filter.Tendsto.add (ha.tendsto_zero) (hb.tendsto_zero) | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : SubstDomain a
hb : Su... | case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : Su... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_add | [216, 1] | [225, 18] | rw [add_zero] | case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a b : σ → MvPowerSeries τ S
ha : Su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5.h.e'_3
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
in... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.constantCoeff_smul | [228, 1] | [230, 6] | rfl | σ : Type u_1
inst✝¹¹ : DecidableEq σ
A : Type u_2
inst✝¹⁰ : CommSemiring A
R✝ : Type u_3
inst✝⁹ : CommRing R✝
inst✝⁸ : Algebra A R✝
τ : Type u_4
inst✝⁷ : DecidableEq τ
S✝ : Type u_5
inst✝⁶ : CommRing S✝
inst✝⁵ : Algebra A S✝
inst✝⁴ : Algebra R✝ S✝
inst✝³ : IsScalarTower A R✝ S✝
R : Type u_6
inst✝² : Semiring R
S : Type... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹¹ : DecidableEq σ
A : Type u_2
inst✝¹⁰ : CommSemiring A
R✝ : Type u_3
inst✝⁹ : CommRing R✝
inst✝⁸ : Algebra A R✝
τ : Type u_4
inst✝⁷ : DecidableEq τ
S✝ : Type u_5
inst✝⁶ : CommRing S✝
inst✝⁵ : Algebra A S✝
inst✝⁴ : Algebra R✝ S✝
inst✝³ : Is... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_mul | [232, 1] | [238, 76] | simp only [Pi.mul_apply, map_mul] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
b a : σ → MvPowerSeries τ S
ha : SubstDomain a
this : ... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
b a : σ → MvPowerSeries τ S
ha : SubstDomain a
this : ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_mul | [232, 1] | [238, 76] | exact Commute.isNilpotent_mul_right (Commute.all _ _) (ha.const_coeff _) | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
b a : σ → MvPowerSeries τ S
ha : SubstDomain a
this : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_smul | [240, 1] | [241, 59] | convert substDomain_mul _ ha | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
r : MvPowerSeries τ S
a : σ → MvPowerSeries τ S
ha : S... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_add | [289, 1] | [291, 37] | rw [← coe_substAlgHom ha, map_add] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f g : MvP... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_mul | [293, 1] | [295, 37] | rw [← coe_substAlgHom ha, map_mul] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f g : MvP... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_pow | [297, 1] | [299, 37] | rw [← coe_substAlgHom ha, map_pow] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_smul | [301, 1] | [303, 54] | rw [← coe_substAlgHom ha, AlgHom.map_smul_of_tower] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
r : A
f :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substAlgHom_X | [311, 1] | [313, 67] | rw [← MvPolynomial.coe_X, substAlgHom_coe, MvPolynomial.aeval_X] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
s : σ
⊢ (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substAlgHom_monomial | [315, 1] | [318, 81] | rw [← MvPolynomial.coe_monomial, substAlgHom_coe, MvPolynomial.aeval_monomial] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
e : σ →₀ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_coe | [320, 1] | [322, 45] | rw [← coe_substAlgHom ha, substAlgHom_coe] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
p : MvPol... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_X | [324, 1] | [326, 43] | rw [← coe_substAlgHom ha, substAlgHom_X] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
s : σ
⊢ s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_monomial | [328, 1] | [331, 50] | rw [← coe_substAlgHom ha, substAlgHom_monomial] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
e : σ →₀ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | letI : UniformSpace S := ⊥ | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | letI : UniformSpace R := ⊥ | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | have := ((hasSum_aeval ha.evalDomain f).map (coeff S e) (continuous_coeff e)) | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | erw [← this.tsum_eq, tsum_def] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | erw [dif_pos this.summable, if_pos (coeff_subst_finite ha f e)] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_subst | [348, 1] | [355, 6] | rfl | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.constantCoeff_subst | [357, 1] | [359, 70] | simp only [← coeff_zero_eq_constantCoeff_apply, coeff_subst ha f 0] | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.map_algebraMap_eq_subst_X | [361, 1] | [368, 79] | ext e | σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f : MvPow... | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.map_algebraMap_eq_subst_X | [361, 1] | [368, 79] | rw [coeff_map, coeff_subst substDomain_X f e, finsum_eq_single _ e] | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScal... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.map_algebraMap_eq_subst_X | [361, 1] | [368, 79] | rw [← MvPowerSeries.monomial_one_eq, coeff_monomial_same,
algebra_compatible_smul S, smul_eq_mul, mul_one] | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScal... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.map_algebraMap_eq_subst_X | [361, 1] | [368, 79] | intro d hd | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScal... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.map_algebraMap_eq_subst_X | [361, 1] | [368, 79] | rw [← MvPowerSeries.monomial_one_eq, coeff_monomial_ne hd.symm, smul_zero] | case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a
f ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝⁸ : DecidableEq σ
A : Type u_2
inst✝⁷ : CommSemiring A
R : Type u_3
inst✝⁶ : CommRing R
inst✝⁵ : Algebra A R
τ : Type u_4
inst✝⁴ : DecidableEq τ
S : Type u_5
inst✝³ : CommRing S
inst✝² : Algebra A S
inst✝¹ : Algebra R S
inst✝ : IsScal... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.comp_subst | [386, 1] | [393, 78] | rw [← comp_substAlgHom ha hε, AlgHom.coe_comp, coe_substAlgHom] | σ : Type u_1
inst✝¹⁸ : DecidableEq σ
A : Type u_2
inst✝¹⁷ : CommSemiring A
R : Type u_3
inst✝¹⁶ : CommRing R
inst✝¹⁵ : Algebra A R
τ : Type u_4
inst✝¹⁴ : DecidableEq τ
S : Type u_5
inst✝¹³ : CommRing S
inst✝¹² : Algebra A S
inst✝¹¹ : Algebra R S
inst✝¹⁰ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝¹⁸ : DecidableEq σ
A : Type u_2
inst✝¹⁷ : CommSemiring A
R : Type u_3
inst✝¹⁶ : CommRing R
inst✝¹⁵ : Algebra A R
τ : Type u_4
inst✝¹⁴ : DecidableEq τ
S : Type u_5
inst✝¹³ : CommRing S
inst✝¹² : Algebra A S
inst✝¹¹ : Algebra R S
inst✝¹⁰ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [coe_substAlgHom, constantCoeff_subst ha] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | apply IsNilpotent.finsum | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subst... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | intro d | case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subst... | case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subst... | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | by_cases hd : d = 0 | case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subst... | case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subs... | Please generate a tactic in lean4 to solve the state.
STATE:
case hf
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [← algebraMap_smul S, smul_eq_mul, mul_comm, ← smul_eq_mul, hd] | case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subs... | case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subs... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | exact IsNilpotent.smul (IsNilpotent.map hf _) _ | case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subs... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | apply IsNilpotent.smul | case neg
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : Subs... | case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : S... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [← ne_eq, Finsupp.ne_iff] at hd | case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : S... | case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : S... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | obtain ⟨t, hs⟩ := hd | case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : S... | case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [← Finsupp.prod_filter_mul_prod_filter_not (fun i ↦ i = t), map_mul,
mul_comm, ← smul_eq_mul] | case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
... | case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | apply IsNilpotent.smul | case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
... | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [Finsupp.prod_eq_single t] | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Alge... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | simp only [Finsupp.filter_apply_pos, map_pow] | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Alge... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | exact IsNilpotent.pow_of_pos (ha.const_coeff t) hs | case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Alge... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | intro t' htt' ht' | case neg.ha.intro.ha.h₀
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSerie... | case neg.ha.intro.ha.h₀
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSerie... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha.h₀
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | simp only [Finsupp.filter_apply, if_neg ht', ne_eq, not_true_eq_false] at htt' | case neg.ha.intro.ha.h₀
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSerie... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha.h₀
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | exact fun _ ↦ by rw [pow_zero] | case neg.ha.intro.ha.h₁
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSerie... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.ha.intro.ha.h₁
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : A... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.IsNilpotent_subst | [429, 1] | [449, 37] | rw [pow_zero] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_comp_subst | [472, 1] | [476, 48] | apply funext | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | case h
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstD... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.subst_comp_subst | [472, 1] | [476, 48] | simpa only [DFunLike.ext_iff, AlgHom.coe_comp, AlgHom.coe_restrictScalars', Function.comp_apply] using
substAlgHom_comp_substAlgHom (R := R) ha hb | case h
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstD... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_scale | [500, 1] | [507, 64] | convert substDomain_mul (fun s ↦ algebraMap A (MvPowerSeries σ R) (a s))
substDomain_X using 1 | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_scale | [500, 1] | [507, 64] | rw [Function.funext_iff] | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_scale | [500, 1] | [507, 64] | intro s | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_scale | [500, 1] | [507, 64] | simp only [Pi.smul_apply', Pi.mul_apply] | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.substDomain_scale | [500, 1] | [507, 64] | rw [algebra_compatible_smul (MvPowerSeries σ R), smul_eq_mul] | case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
i... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [AlgHom.ext_iff] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | intro f | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | simp only [AlgHom.coe_comp, Function.comp_apply, scale_algHom] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [substAlgHom_comp_substAlgHom_apply] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | congr | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [Function.funext_iff] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | intro s | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | simp only [Pi.smul_apply', Pi.mul_apply] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [AlgHom.map_smul_of_tower] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [← MvPolynomial.coe_X, substAlgHom_coe, MvPolynomial.aeval_X, MvPolynomial.coe_X] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | simp only [Pi.smul_apply', algebraMap_smul] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_algHom_comp | [517, 1] | [530, 28] | rw [← mul_smul, mul_comm] | case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case e_a.e_a
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.scale_scale_apply | [532, 1] | [534, 73] | simp only [← coe_scale_algHom, ← AlgHom.comp_apply, scale_algHom_comp] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a✝ : σ → MvPowerSeries τ S
ha : SubstDomain ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_scale | [536, 1] | [545, 63] | unfold scale | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_scale | [536, 1] | [545, 63] | rw [coeff_subst (substDomain_scale R _)] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_scale | [536, 1] | [545, 63] | simp only [Pi.smul_apply', smul_eq_mul, prod_smul_X_eq_smul_monomial_one] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_scale | [536, 1] | [545, 63] | simp only [LinearMap.map_smul_of_tower, Algebra.mul_smul_comm] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Substitutions.lean | MvPowerSeries.coeff_scale | [536, 1] | [545, 63] | rw [finsum_eq_single _ d] | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsScalarTower A R S
a : σ → MvPowerSeries τ S
ha : SubstDomain a... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
inst✝²³ : DecidableEq σ
A : Type u_2
inst✝²² : CommSemiring A
R : Type u_3
inst✝²¹ : CommRing R
inst✝²⁰ : Algebra A R
τ : Type u_4
inst✝¹⁹ : DecidableEq τ
S : Type u_5
inst✝¹⁸ : CommRing S
inst✝¹⁷ : Algebra A S
inst✝¹⁶ : Algebra R S
inst✝¹⁵ : IsS... |
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