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/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | exact mem_insert_self a s | case inl
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ,... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | simp only [mem_sigma, mem_univ, mem_sym_iff, true_and] at hm | case inr
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ,... | case inr
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ,... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | exact mem_insert_of_mem (hm i hi) | case inr
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ,... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | intro m hm | case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ... | case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add :... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | simp only [mem_sigma, mem_univ, mem_sym_iff, true_and] at hm | case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ... | case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add :... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | exact Sym.filter_ne_fill a m fun a_1 => ha (hm a a_1) | case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add :... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | intro m hm | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | simp only [mem_sym_iff, mem_insert] at hm | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | rw [Finset.prod_insert ha] | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | apply congr_arg₂ _ rfl | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | apply Finset.prod_congr rfl | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | intro i hi | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | apply congr_arg₂ _ _ rfl | case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range ... | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | conv_lhs => rw [← Sym.fill_filterNe a m, Sym.coe_fill] | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | simp only [Multiset.count_add, add_right_eq_self, Multiset.count_eq_zero,
Sym.mem_coe, Sym.mem_replicate, not_and] | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | exact fun _ => ne_of_mem_of_not_mem hi ha | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | intro m hm | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | convert sym_filterNe_mem a hm | A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ range n.succ, dpow x_3... | case h.e'_5.h.e'_3
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ ran... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux | [284, 1] | [345, 27] | rw [erase_insert ha] | case h.e'_5.h.e'_3
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → dpow n (x + y) = ∑ x_3 ∈ ran... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5.h.e'_3
A : Type u_1
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
dpow : ℕ → A → A
dpow_zero : ∀ {x : A}, x ∈ I → dpow 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dpow n 0 = 0
ι : Type u_2
inst✝ : DecidableEq ι
x : ι → A
dpow_add : ∀ (n... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk] at dpow_add | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_add :
∀ (n : ℕ) (x y : M),
dp n (x + y) =
∑ x_1 ∈ antidiagonal n,
match x_1 with
| (k, l... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
s : Finset ι
x : ι → M
n : ℕ
dpow_add :... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_add :
∀ (n : ℕ) (x y : M),
dp n (x + y) =
∑... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [sum_empty] | case empty
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | case empty
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case empty
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | by_cases hn : n = 0 | case empty
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case empty
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [hn] | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | haveI : Unique (Sym ι Nat.zero) := Sym.uniqueZero | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [dpow_zero, sum_unique_nonempty, prod_empty] | case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case pos.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [Nat.zero_eq, sym_zero, singleton_nonempty] | case pos.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [dpow_eval_zero hn] | case neg
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case neg
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply symm | case neg
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case neg.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | convert Finset.sum_empty | case neg.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ... | case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [sym_eq_empty] | case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | exact ⟨hn, rfl⟩ | case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_2.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp_rw [sum_insert ha, dpow_add n, sum_range, ih, mul_sum, sum_sigma'] | case insert
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n :... | case insert
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n :... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply symm | case insert
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n :... | case insert.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply sum_bij'
(fun m _ => Sym.filterNe a m)
(fun m _ => m.2.fill a m.1)
(fun m hm => Finset.mem_sigma.2 ⟨mem_univ _, _⟩)
(fun m hm => by
rw [mem_sym_iff]
intro i hi
rw [Sym.mem_fill_iff] at hi
cases hi with
| inl hi =>
rw [hi.2]
apply mem_insert_self
| inr hi... | case insert.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n... | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [mem_sym_iff] | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | intro i hi | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [Sym.mem_fill_iff] at hi | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | cases hi with
| inl hi =>
rw [hi.2]
apply mem_insert_self
| inr hi =>
simp only [mem_sigma, mem_univ, mem_sym_iff, true_and] at hm
exact mem_insert_of_mem (hm i hi) | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [hi.2] | case inl
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case inl
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply mem_insert_self | case inl
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [mem_sigma, mem_univ, mem_sym_iff, true_and] at hm | case inr
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | case inr
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | exact mem_insert_of_mem (hm i hi) | case inr
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | intro m hm | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [mem_sigma, mem_univ, mem_sym_iff, true_and] at hm | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | exact Sym.filter_ne_fill a m fun a_1 => ha (hm a a_1) | case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.right_inv
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | intro m hm | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [mem_sym_iff, mem_insert] at hm | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [Finset.prod_insert ha] | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply congr_arg₂ _ rfl | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply Finset.prod_congr rfl | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | intro i hi | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | apply congr_arg₂ _ _ rfl | case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ ... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert.a.h
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | conv_lhs => rw [← Sym.fill_filterNe a m, Sym.coe_fill] | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | simp only [Multiset.count_add, add_right_eq_self, Multiset.count_eq_zero,
Sym.mem_coe, Sym.mem_replicate, not_and] | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | exact fun _ => ne_of_mem_of_not_mem hi ha | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | intro m hm | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | convert sym_filterNe_mem a hm | A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add : ∀ (n : ℕ) (x y : M... | case h.e'_5.h.e'_3
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add :... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum_aux' | [357, 1] | [415, 27] | rw [erase_insert ha] | case h.e'_5.h.e'_3
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n 0 = 0
ι : Type u_3
inst✝ : DecidableEq ι
x : ι → M
dpow_add :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.e'_5.h.e'_3
A : Type ?u.63345
inst✝³ : CommSemiring A
I : Ideal A
hI : DividedPowers I
M : Type u_1
D : Type u_2
inst✝² : AddCommMonoid M
inst✝¹ : CommSemiring D
dp : ℕ → M → D
dpow_zero : ∀ (x : M), dp 0 x = 1
dpow_eval_zero : ∀ {n : ℕ}, n ≠ 0 → dp n ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | refine' dpow_sum_aux hI.dpow _ ?_ _ hx | A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ (n : ℕ), hI.dpow n (s.sum x) = ∑ k ∈ s.sym n, ∏ i ∈ s, hI.dpow (Multiset.count i ↑k) (x i) | case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ {x : A}, x ∈ I → hI.dpow 0 x = 1
case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ (n : ℕ), hI.dpow n (s.sum x) = ∑ k ∈ s.sym n, ∏ i ∈ s, hI.dpow (Multiset.count i ↑k) (x i)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | intro x | case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ {x : A}, x ∈ I → hI.dpow 0 x = 1 | case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx : ∀ i ∈ s, x✝ i ∈ I
x : A
⊢ x ∈ I → hI.dpow 0 x = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ {x : A}, x ∈ I → hI.dpow 0 x = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | exact hI.dpow_zero | case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx : ∀ i ∈ s, x✝ i ∈ I
x : A
⊢ x ∈ I → hI.dpow 0 x = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx : ∀ i ∈ s, x✝ i ∈ I
x : A
⊢ x ∈ I → hI.dpow 0 x = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | intro n x y hx hy | case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → hI.dpow n (x + y) = ∑ k ∈ antidiagonal n, hI.dpow k.1 x * hI.dpow k.2 y | case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx✝ : ∀ i ∈ s, x✝ i ∈ I
n : ℕ
x y : A
hx : x ∈ I
hy : y ∈ I
⊢ hI.dpow n (x + y) = ∑ k ∈ antidiagonal n, hI.dpow k.1 x * hI.dpow k.2 y | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ (n : ℕ) {x y : A}, x ∈ I → y ∈ I → hI.dpow n (x + y) = ∑ k ∈ antidiagonal n, hI.dpow k.1 x... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | rw [hI.dpow_add n hx hy,
Finset.Nat.sum_antidiagonal_eq_sum_range_succ (fun k l ↦ hI.dpow k x * hI.dpow l y)] | case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx✝ : ∀ i ∈ s, x✝ i ∈ I
n : ℕ
x y : A
hx : x ∈ I
hy : y ∈ I
⊢ hI.dpow n (x + y) = ∑ k ∈ antidiagonal n, hI.dpow k.1 x * hI.dpow k.2 y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_2
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x✝ : ι → A
hx✝ : ∀ i ∈ s, x✝ i ∈ I
n : ℕ
x y : A
hx : x ∈ I
hy : y ∈ I
⊢ hI.dpow n (x + y) = ∑ k ∈ antidiagonal n, hI.dpow k.1... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | intro n hn | case refine'_3
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ {n : ℕ}, n ≠ 0 → hI.dpow n 0 = 0 | case refine'_3
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
n : ℕ
hn : n ≠ 0
⊢ hI.dpow n 0 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_3
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
⊢ ∀ {n : ℕ}, n ≠ 0 → hI.dpow n 0 = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.dpow_sum | [422, 1] | [433, 31] | exact hI.dpow_eval_zero hn | case refine'_3
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
n : ℕ
hn : n ≠ 0
⊢ hI.dpow n 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_3
A : Type u_2
inst✝¹ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
inst✝ : DecidableEq ι
s : Finset ι
x : ι → A
hx : ∀ i ∈ s, x i ∈ I
n : ℕ
hn : n ≠ 0
⊢ hI.dpow n 0 = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.prod_dpow_self | [446, 1] | [455, 81] | induction' s using Finset.induction with i s hi ih | A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
s : Finset ι
n : ι → ℕ
a : A
ha : a ∈ I
⊢ ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a | case empty
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
⊢ ∏ i ∈ ∅, hI.dpow (n i) a = ↑(Nat.multinomial ∅ n) * hI.dpow (∅.sum n) a
case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
s : Finset ι
n : ι → ℕ
a : A
ha : a ∈ I
⊢ ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.prod_dpow_self | [446, 1] | [455, 81] | rw [Finset.prod_empty, Finset.sum_empty, hI.dpow_zero ha, Nat.multinomial_empty, Nat.cast_one,
mul_one] | case empty
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
⊢ ∏ i ∈ ∅, hI.dpow (n i) a = ↑(Nat.multinomial ∅ n) * hI.dpow (∅.sum n) a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case empty
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
⊢ ∏ i ∈ ∅, hI.dpow (n i) a = ↑(Nat.multinomial ∅ n) * hI.dpow (∅.sum n) a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.prod_dpow_self | [446, 1] | [455, 81] | rw [Finset.prod_insert hi, ih, ← mul_assoc, mul_comm (hI.dpow _ a), mul_assoc,
hI.dpow_mul _ _ ha, ← Finset.sum_insert hi, ← mul_assoc] | case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ∏ i ∈ insert i s, hI.dpow (n i) a = ↑(Nat.multinomial (insert i s) n) * hI.dpow ((insert i... | case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑ x ∈ insert i s, n x).choose (n i)) * hI.dpow (∑ x ∈ insert i... | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ∏ i ∈ insert i s, hI.dpow (n ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.prod_dpow_self | [446, 1] | [455, 81] | apply congr_arg₂ _ _ rfl | case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑ x ∈ insert i s, n x).choose (n i)) * hI.dpow (∑ x ∈ insert i... | A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑ x ∈ insert i s, n x).choose (n i)) = ↑(Nat.multinomial (insert i s) n) | Please generate a tactic in lean4 to solve the state.
STATE:
case insert
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/Basic.lean | DividedPowers.prod_dpow_self | [446, 1] | [455, 81] | rw [mul_comm, Nat.multinomial_insert hi, Finset.sum_insert hi, Nat.cast_mul] | A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑ x ∈ insert i s, n x).choose (n i)) = ↑(Nat.multinomial (insert i s) n) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_2
inst✝ : CommSemiring A
I : Ideal A
hI : DividedPowers I
ι : Type u_1
n : ι → ℕ
a : A
ha : a ∈ I
i : ι
s : Finset ι
hi : i ∉ s
ih : ∏ i ∈ s, hI.dpow (n i) a = ↑(Nat.multinomial s n) * hI.dpow (s.sum n) a
⊢ ↑(Nat.multinomial s n) * ↑((∑ x ∈ insert ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [Commute.add_pow' (Commute.all _ _), MvPolynomial.coeff_sum] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ MvPolynomial.coef... | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [nsmul_eq_smul, MvPolynomial.coeff_smul] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [Fin.isValue, Nat.cast_ite, Nat.cast_zero, hmon] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | split_ifs with hd | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
⊢ ∑ x ∈ Finset.anti... | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | intro u v | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
⊢ ∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1 | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1 | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
⊢ ∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.s... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [MvPolynomial.monomial_eq] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1 | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * (Finsupp.single 0 u + Finsupp.single 1 v).prod fun n e => MvPolynomial.X n ^ e | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + F... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [Finsupp.prod_of_support_subset _ (Finset.subset_univ _)] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * (Finsupp.single 0 u + Finsupp.single 1 v).prod fun n e => MvPolynomial.X n ^ e | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * ∏ x : Fin 2, MvPolynomial.X x ^ (Finsupp.single 0 u + Finsupp.single 1 v) x
case h
... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * (Finsupp.single 0 u + F... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [map_one, Fin.prod_univ_two, Fin.isValue, one_mul] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * ∏ x : Fin 2, MvPolynomial.X x ^ (Finsupp.single 0 u + Finsupp.single 1 v) x | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.X 0 ^ (Finsupp.single 0 u + Finsupp.single 1 v) 0 *
MvPolynomial.X 1 ^ (Finsupp.sing... | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.C 1 * ∏ x : Fin 2, MvPolynomi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [Fin.isValue, Finsupp.coe_add, Pi.add_apply,
Finsupp.single_eq_same, ne_eq, one_ne_zero, not_false_eq_true,
Finsupp.single_eq_of_ne, add_zero, zero_ne_one, zero_add] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.X 0 ^ (Finsupp.single 0 u + Finsupp.single 1 v) 0 *
MvPolynomial.X 1 ^ (Finsupp.sing... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v =
MvPolynomial.X 0 ^ (Finsupp.single 0 u + F... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | exact fun i _ ↦ by simp only [pow_zero] | case h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ ∀ i ∈ Finset.univ, MvPolynomial.X i ^ 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
⊢ ∀ i ∈ Finset.univ, MvPolynomial.X i ^ 0 = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [pow_zero] | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
i : Fin 2
x✝ : i ∈ Finset.univ
⊢ MvPolynomial.X i ^ 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n u v : ℕ
i : Fin 2
x✝ : i ∈ Finset.univ
⊢ MvPolynomial.X i ^ 0 = 1
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [Finset.sum_eq_single (d 0, d 1)] | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.mon... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [MvPolynomial.coeff_monomial, if_pos] | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.mon... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [Fin.isValue, nsmul_eq_mul, mul_one] | case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | case pos.hc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.mon... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | ext i | case pos.hc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | case pos.hc.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.hc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | match i with
| 0 => simp
| 1 => simp | case pos.hc.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.hc.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomia... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0, d 1) ∈ F... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp | A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0, d 1) ∈ F... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Fi... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | intro e _ hed | case pos.h₀
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | case pos.h₀
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [MvPolynomial.coeff_monomial, if_neg, smul_zero] | case pos.h₀
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | intro hde | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynom... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | apply hed | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynom... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [← hde] | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynom... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp | case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₀.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynom... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | intro hd' | case pos.h₁
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | case pos.h₁
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₁
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | contradiction | case pos.h₁
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h₁
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | apply Finset.sum_eq_zero | case neg
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d 0,... | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.mon... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | intro e he | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.m... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | simp only [Finset.mem_antidiagonal] at he | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.m... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ExponentialModule/Basic.lean | PowerSeries.coeff_add_pow | [64, 1] | [106, 19] | rw [MvPolynomial.coeff_monomial, if_neg, smul_zero] | case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd : (d ... | case neg.h.hnc
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.monomial (Finsupp.single 0 u + Finsupp.single 1 v)) 1
hd :... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
A : Type u_1
inst✝⁴ : CommRing A
R : Type u_2
inst✝³ : CommRing R
inst✝² : Algebra A R
S : Type u_3
inst✝¹ : CommRing S
inst✝ : Algebra A S
d : Fin 2 →₀ ℕ
n : ℕ
hmon :
∀ (u v : ℕ),
MvPolynomial.X 0 ^ u * MvPolynomial.X 1 ^ v = (MvPolynomial.m... |
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