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/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | rw [←lemEq] | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
lemEq : j + 1 = k :=
Eq.mpr (id (congrArg (fun _a => j + 1 = _a) (Eq.symm hyp)))
(Eq.mpr (id (congrArg (fun _a => j + 1 = _a) eqn)) (Eq.refl (j + 1)))
⊢ j < k | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
lemEq : j + 1 = k :=
Eq.mpr (id (congrArg (fun _a => j + 1 = _a) (Eq.symm hyp)))
(Eq.mpr (id (congrArg (fun _a => j + 1 = _a) eqn)) (Eq.refl (j + 1)))
⊢ j < j + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
lemEq : j + 1 = k :=
Eq.mpr (id (congrArg (fun _a => j + 1 = _a) (Eq.symm hyp)))
(Eq.mpr (id (congrArg (fun _a => j + 1 = _a) eqn)) (Eq.refl (j + 1)))
⊢ j < k
TACT... |
https://github.com/siddhartha-gadgil/Saturn.git | ddcebe3081f3f8f359fa4b804b9d09a1f1706c22 | Saturn/Skip.lean | skip_no_fixedpoints | [196, 1] | [217, 18] | apply Nat.lt_succ_self | k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
lemEq : j + 1 = k :=
Eq.mpr (id (congrArg (fun _a => j + 1 = _a) (Eq.symm hyp)))
(Eq.mpr (id (congrArg (fun _a => j + 1 = _a) eqn)) (Eq.refl (j + 1)))
⊢ j < j + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k j : Nat
c : ¬j < k
eqn : skip k j = j + 1 := skip_not_below_eq k j c
hyp : skip k j = k
lemEq : j + 1 = k :=
Eq.mpr (id (congrArg (fun _a => j + 1 = _a) (Eq.symm hyp)))
(Eq.mpr (id (congrArg (fun _a => j + 1 = _a) eqn)) (Eq.refl (j + 1)))
⊢ j < j + 1
... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_iff_ne_zero | [16, 1] | [18, 53] | simp only [ext_iff, ne_eq, coeff_zero, not_forall] | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
f : MvPowerSeries σ α
⊢ (∃ d, (coeff α d) f ≠ 0) ↔ f ≠ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
f : MvPowerSeries σ α
⊢ (∃ d, (coeff α d) f ≠ 0) ↔ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weight_apply | [37, 1] | [38, 26] | simp only [weight] | σ : Type u_1
α : Type ?u.2439
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (weight w) d = d.sum fun x => Mul.mul (w x) | σ : Type u_1
α : Type ?u.2439
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ { toFun := fun d => d.sum fun x y => w x * y, map_zero' := ⋯, map_add' := ⋯ } d = d.sum fun x => Mul.mul (w x) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.2439
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ (weight w) d = d.sum fun x => Mul.mul (w x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weight_apply | [37, 1] | [38, 26] | rfl | σ : Type u_1
α : Type ?u.2439
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ { toFun := fun d => d.sum fun x y => w x * y, map_zero' := ⋯, map_add' := ⋯ } d = d.sum fun x => Mul.mul (w x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.2439
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
⊢ { toFun := fun d => d.sum fun x y => w x * y, map_zero' := ⋯, map_add' := ⋯ } d = d.sum fun x => Mul.mul (w x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | simp only [weight_apply, Finsupp.sum] | σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
⊢ d x ≤ (weight w) d | σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
⊢ d x ≤ (weight w) d
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | by_cases hxd : x ∈ d.support | σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∉ d.su... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | simp only [Finsupp.mem_support_iff, Classical.not_not] at hxd | case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∉ d.support
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∉ d.support
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | rw [hxd] | case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ 0 ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | apply zero_le | case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ 0 ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : d x = 0
⊢ 0 ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | rw [Finset.sum_eq_add_sum_diff_singleton hxd] | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x) | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x) + ∑ x ∈ d.support \ {x}, Mul.mul (w x) (d x) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ ∑ x ∈ d.support, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | refine' le_trans _ (Nat.le_add_right _ _) | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x) + ∑ x ∈ d.support \ {x}, Mul.mul (w x) (d x) | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x) | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x) + ∑ x ∈ d.support \ {x}, Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weight | [41, 1] | [50, 16] | exact Nat.le_mul_of_pos_left _ (Nat.pos_of_ne_zero hx) | case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type ?u.2913
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
x : σ
hx : w x ≠ 0
d : σ →₀ ℕ
hxd : x ∈ d.support
⊢ d x ≤ Mul.mul (w x) (d x)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | classical
set fg := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n)) with hfg
suffices {f : σ →₀ ℕ | weight w f ≤ n} ⊆ ↑(fg.image fun uv => uv.fst) by
apply Set.Finite.subset _ this
apply Finset.finite_toSet
intro f hf
rw [hfg]
simp only [Finset.coe_image, Set.mem_image, Finset.mem_coe,
Fi... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
⊢ {f | (weight w) f ≤ n}.Finite | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
⊢ {f | (weight w) f ≤ n}.Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | set fg := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n)) with hfg | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
⊢ {f | (weight w) f ≤ n}.Finite | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
⊢ {f | (weight w) f ≤ n}.Finite
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | suffices {f : σ →₀ ℕ | weight w f ≤ n} ⊆ ↑(fg.image fun uv => uv.fst) by
apply Set.Finite.subset _ this
apply Finset.finite_toSet | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.an... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | intro f hf | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.an... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | rw [hfg] | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.a... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | simp only [Finset.coe_image, Set.mem_image, Finset.mem_coe,
Finset.mem_antidiagonal, Prod.exists, exists_and_right, exists_eq_right] | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.a... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | use Finsupp.equivFunOnFinite.symm (Function.const σ n) - f | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ ... | case h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.c... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.a... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | ext x | case h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.c... | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = F... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | simp only [Finsupp.coe_add, Finsupp.coe_tsub, Pi.add_apply, Pi.sub_apply,
Finsupp.equivFunOnFinite_symm_apply_toFun, Function.const_apply] | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | rw [add_comm] | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | apply Nat.sub_add_cancel | case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function... | case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Functi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg =... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | apply le_trans (le_weight w x (hw x) f) | case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Functi... | case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Functi... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | simpa only [Set.mem_setOf_eq] using hf | case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Functi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h.h
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f✝ : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | apply Set.Finite.subset _ this | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.an... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.finite_of_weight_le | [53, 1] | [71, 41] | apply Finset.finite_toSet | σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type ?u.4528
inst✝¹ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
inst✝ : Finite σ
hw : ∀ (x : σ), w x ≠ 0
n : ℕ
fg : Finset ((σ →₀ ℕ) × (σ →₀ ℕ)) := Finset.antidiagonal (Finsupp.equivFunOnFinite.symm (Function.const σ n))
hfg : fg = Finset.an... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | refine' not_iff_not.mp _ | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ↔ f ≠ 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (¬∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ↔ ¬f ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ↔ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | push_neg | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (¬∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ↔ ¬f ≠ 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) ↔ f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (¬∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ↔ ¬f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | constructor | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) ↔ f = 0 | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) → f = 0
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f = 0 → ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) ↔ f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | intro h | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) → f = 0 | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
⊢ f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0) → f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | ext d | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
⊢ f = 0 | case mp.h
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
⊢ f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | exact h _ d rfl | case mp.h
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.h
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | rintro rfl n d _ | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f = 0 → ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0 | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
n : ℕ
d : σ →₀ ℕ
_✝ : (weight w) d = n
⊢ (coeff α d) 0 = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f = 0 → ∀ (n : ℕ) (d : σ →₀ ℕ), (weight w) d = n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weight_iff_ne_zero | [74, 1] | [83, 23] | exact coeff_zero _ | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
n : ℕ
d : σ →₀ ℕ
_✝ : (weight w) d = n
⊢ (coeff α d) 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
n : ℕ
d : σ →₀ ℕ
_✝ : (weight w) d = n
⊢ (coeff α d) 0 = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_zero | [94, 9] | [95, 34] | rw [weightedOrder, dif_pos rfl] | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ weightedOrder w 0 = ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ weightedOrder w 0 = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | simp only [weightedOrder] | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ ↑(toNat (weightedOrder w f)) = weightedOrder w f ↔ f ≠ 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) ↔ f ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ ↑(toNat (weightedOrder w f)) = weightedOrder w f ↔ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | constructor | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) ↔ f ≠ 0 | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) → f ≠ 0
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f ≠ 0 → ↑(toNat (if x : f = 0 then ⊤ else ↑... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) ↔ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | split_ifs with h <;> intro H | case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) → f ≠ 0 | case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ f ≠ 0
case neg
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ¬f = 0
H : ↑(toNat ↑(Nat.find ⋯)) = ↑(Nat.find ⋯)
⊢ f ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ (↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)) → f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | exfalso | case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ f ≠ 0 | case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | apply ENat.coe_ne_top _ H | case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f = 0
H : ↑(toNat ⊤) = ⊤
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | exact h | case neg
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ¬f = 0
H : ↑(toNat ↑(Nat.find ⋯)) = ↑(Nat.find ⋯)
⊢ f ≠ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ¬f = 0
H : ↑(toNat ↑(Nat.find ⋯)) = ↑(Nat.find ⋯)
⊢ f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | intro h | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f ≠ 0 → ↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯) | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f ≠ 0
⊢ ↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯) | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ f ≠ 0 → ↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_finite_iff_ne_zero | [98, 1] | [107, 53] | simp only [h, not_false_iff, dif_neg, toNat_coe] | case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f ≠ 0
⊢ ↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : f ≠ 0
⊢ ↑(toNat (if x : f = 0 then ⊤ else ↑(Nat.find ⋯))) = if x : f = 0 then ⊤ else ↑(Nat.find ⋯)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weightedOrder | [113, 1] | [119, 25] | classical
simp_rw [weightedOrder, dif_neg ((weightedOrder_finite_iff_ne_zero _ f).mp h), Nat.cast_inj]
generalize_proofs h1
exact Nat.find_spec h1 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, ↑((weight w) d) = weightedOrder w f ∧ (coeff α d) f ≠ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, ↑((weight w) d) = weightedOrder w f ∧ (coeff α d) f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weightedOrder | [113, 1] | [119, 25] | simp_rw [weightedOrder, dif_neg ((weightedOrder_finite_iff_ne_zero _ f).mp h), Nat.cast_inj] | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, ↑((weight w) d) = weightedOrder w f ∧ (coeff α d) f ≠ 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, (weight w) d = Nat.find ⋯ ∧ (coeff α d) f ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, ↑((weight w) d) = weightedOrder w f ∧ (coeff α d) f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weightedOrder | [113, 1] | [119, 25] | generalize_proofs h1 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, (weight w) d = Nat.find ⋯ ∧ (coeff α d) f ≠ 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
h1 : ∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0
⊢ ∃ d, (weight w) d = Nat.find h1 ∧ (coeff α d) f ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ ∃ d, (weight w) d = Nat.find ⋯ ∧ (coeff α d) f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.exists_coeff_ne_zero_of_weightedOrder | [113, 1] | [119, 25] | exact Nat.find_spec h1 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
h1 : ∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0
⊢ ∃ d, (weight w) d = Nat.find h1 ∧ (coeff α d) f ≠ 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
h : ↑(toNat (weightedOrder w f)) = weightedOrder w f
h1 : ∃ n d, (weight w) d = n ∧ (coeff α d) f ≠ 0
⊢ ∃ d, (weight w) d = Nat.find h1 ∧ (coeff α d) f ≠ 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_le | [125, 1] | [130, 86] | rw [weightedOrder, dif_neg] | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ weightedOrder w f ≤ ↑((weight w) d) | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ↑(Nat.find ⋯) ≤ ↑((weight w) d)
case hnc
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ¬f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ weightedOrder w f ≤ ↑((weight w) d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_le | [125, 1] | [130, 86] | simp only [ne_eq, Nat.cast_le, Nat.find_le_iff] | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ↑(Nat.find ⋯) ≤ ↑((weight w) d) | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ∃ m ≤ (weight w) d, ∃ d, (weight w) d = m ∧ ¬(coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ↑(Nat.find ⋯) ≤ ↑((weight w) d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_le | [125, 1] | [130, 86] | exact ⟨weight w d, le_rfl, d, rfl, h⟩ | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ∃ m ≤ (weight w) d, ∃ d, (weight w) d = m ∧ ¬(coeff α d) f = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ∃ m ≤ (weight w) d, ∃ d, (weight w) d = m ∧ ¬(coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_le | [125, 1] | [130, 86] | exact (f.exists_coeff_ne_zero_of_weight_iff_ne_zero w).mp ⟨weight w d, d, rfl, h⟩ | case hnc
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ¬f = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hnc
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ ¬f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.coeff_of_lt_weightedOrder | [135, 1] | [137, 46] | contrapose! h | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : ↑((weight w) d) < weightedOrder w f
⊢ (coeff α d) f = 0 | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ weightedOrder w f ≤ ↑((weight w) d) | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : ↑((weight w) d) < weightedOrder w f
⊢ (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.coeff_of_lt_weightedOrder | [135, 1] | [137, 46] | exact weightedOrder_le w f h | σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ weightedOrder w f ≤ ↑((weight w) d) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
α : Type u_2
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
d : σ →₀ ℕ
h : (coeff α d) f ≠ 0
⊢ weightedOrder w f ≤ ↑((weight w) d)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | constructor | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ weightedOrder w f = ⊤ ↔ f = 0 | case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ weightedOrder w f = ⊤ → f = 0
case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ f = 0 → weightedOrder w f = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ weightedOrder w f = ⊤ ↔ f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | intro h | case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ weightedOrder w f = ⊤ → f = 0 | case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
⊢ f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ weightedOrder w f = ⊤ → f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | ext d | case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
⊢ f = 0 | case mp.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
⊢ f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | rw [(coeff α d).map_zero, coeff_of_lt_weightedOrder w] | case mp.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < weightedOrder w f | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | rw [h] | case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < weightedOrder w f | case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | exact WithTop.coe_lt_top _ | case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : weightedOrder w f = ⊤
d : σ →₀ ℕ
⊢ ↑((weight w) d) < ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | rintro rfl | case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ f = 0 → weightedOrder w f = ⊤ | case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ weightedOrder w 0 = ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
⊢ f = 0 → weightedOrder w f = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_top_iff | [142, 1] | [150, 31] | exact weightedOrder_zero w | case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ weightedOrder w 0 = ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
⊢ weightedOrder w 0 = ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | by_contra H | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
⊢ ↑n ≤ weightedOrder w f | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : ¬↑n ≤ weightedOrder w f
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
⊢ ↑n ≤ weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | rw [not_le] at H | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : ¬↑n ≤ weightedOrder w f
⊢ False | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : ¬↑n ≤ weightedOrder w f
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | have : ↑(toNat (f.weightedOrder w)) = f.weightedOrder w := by
rw [coe_toNat_eq_self] ; exact ne_top_of_lt H | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ False | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | obtain ⟨d, hd, hfd⟩ := exists_coeff_ne_zero_of_weightedOrder w f this | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ False | case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
hd : ↑((weight w) d) = weightedOrder w f
hfd : (coeff α d) f ≠ 0
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
⊢ False
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | rw [← hd, Nat.cast_lt] at H | case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
hd : ↑((weight w) d) = weightedOrder w f
hfd : (coeff α d) f ≠ 0
⊢... | case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
H : (weight w) d < n
hd : ↑((weight w) d) = weightedOrder w f
hfd : (coeff α d) f ≠ 0
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
hd : ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | exact hfd (h d H) | case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
H : (weight w) d < n
hd : ↑((weight w) d) = weightedOrder w f
hfd : (coeff α d) f ≠ 0
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
this : ↑(toNat (weightedOrder w f)) = weightedOrder w f
d : σ →₀ ℕ
H : (weight w) d < n
hd : ↑((wei... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | rw [coe_toNat_eq_self] | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ ↑(toNat (weightedOrder w f)) = weightedOrder w f | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ weightedOrder w f ≠ ⊤ | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ ↑(toNat (weightedOrder w f)) = weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.nat_le_weightedOrder | [155, 1] | [162, 20] | exact ne_top_of_lt H | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ weightedOrder w f ≠ ⊤ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
h : ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
H : weightedOrder w f < ↑n
⊢ weightedOrder w f ≠ ⊤
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | cases n | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ∞
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < n → (coeff α d) f = 0
⊢ n ≤ weightedOrder w f | case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ ⊤ ≤ weightedOrder w f
case coe
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ∞
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < n → (coeff α d) f = 0
⊢ n ≤ weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | rw [top_le_iff, weightedOrder_eq_top_iff] | case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ ⊤ ≤ weightedOrder w f | case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ ⊤ ≤ weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | ext d | case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ f = 0 | case top.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case top
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
⊢ f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | exact h d (coe_lt_top _) | case top.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case top.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ⊤ → (coeff α d) f = 0
d : σ →₀ ℕ
⊢ (coeff α d) f = (coeff α d) 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | apply nat_le_weightedOrder | case coe
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff α d) f = 0
⊢ ↑a✝ ≤ weightedOrder w f | case coe.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff α d) f = 0
⊢ ∀ (d : σ →₀ ℕ), (weight w) d < a✝ → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case coe
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff α d) f = 0
⊢ ↑a✝ ≤ weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder | [167, 1] | [173, 55] | simpa only [ENat.some_eq_coe, Nat.cast_lt] using h | case coe.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff α d) f = 0
⊢ ∀ (d : σ →₀ ℕ), (weight w) d < a✝ → (coeff α d) f = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case coe.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
a✝ : ℕ
h : ∀ (d : σ →₀ ℕ), ↑((weight w) d) < ↑a✝ → (coeff α d) f = 0
⊢ ∀ (d : σ →₀ ℕ), (weight w) d < a✝ → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | rcases eq_or_ne f 0 with (rfl | hf) | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
⊢ weightedOrder w f = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inl
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
n : ℕ
⊢ weightedOrder w 0 = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) 0 ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) 0 = 0
case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf... | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
⊢ weightedOrder w f = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | simp only [weightedOrder_zero, ENat.top_ne_coe, map_zero, ne_eq, not_true, and_false,
exists_false, implies_true, forall_const, and_true] | case inl
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
n : ℕ
⊢ weightedOrder w 0 = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) 0 ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inl
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f : MvPowerSeries σ α
n : ℕ
⊢ weightedOrder w 0 = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) 0 ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) 0 = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | simp only [weightedOrder, dif_neg hf, ne_eq, Nat.cast_inj, Nat.find_eq_iff] | case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ weightedOrder w f = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ((∃ d, (weight w) d = n ∧ ¬(coeff α d) f = 0) ∧ ∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔
(∃ d, (weight w) d = n ∧ ¬(coeff α d) f = 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ weightedOrder w f = ↑n ↔
(∃ d, (weight w) d = n ∧ (coeff α d) f ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | apply and_congr_right' | case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ((∃ d, (weight w) d = n ∧ ¬(coeff α d) f = 0) ∧ ∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔
(∃ d, (weight w) d = n ∧ ¬(coeff α d) f = 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ((∃ d, (weight w) d = n ∧ ¬(coeff α d) f = 0) ∧ ∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔
(∃ d, (weight w) d = n ∧ ¬(coeff α d) f... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | simp only [not_exists, not_and, Classical.not_not, imp_forall_iff] | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (n_1 : ℕ) (x : σ →₀ ℕ), n_1 < n → (weight w) x = n_1 → (coeff α x) f = 0) ↔
∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ n_1 < n, ¬∃ d, (weight w) d = n_1 ∧ ¬(coeff α d) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | rw [forall_swap] | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (n_1 : ℕ) (x : σ →₀ ℕ), n_1 < n → (weight w) x = n_1 → (coeff α x) f = 0) ↔
∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (y : σ →₀ ℕ), ∀ x < n, (weight w) y = x → (coeff α y) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (n_1 : ℕ) (x : σ →₀ ℕ), n_1 < n → (weight w) x = n_1 → (coeff α x) f = 0) ↔
∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | apply forall_congr' | case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (y : σ →₀ ℕ), ∀ x < n, (weight w) y = x → (coeff α y) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0 | case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ∀ (a : σ →₀ ℕ), (∀ x < n, (weight w) a = x → (coeff α a) f = 0) ↔ (weight w) a < n → (coeff α a) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ (∀ (y : σ →₀ ℕ), ∀ x < n, (weight w) y = x → (coeff α y) f = 0) ↔ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | intro d | case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ∀ (a : σ →₀ ℕ), (∀ x < n, (weight w) a = x → (coeff α a) f = 0) ↔ (weight w) a < n → (coeff α a) f = 0 | case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) ↔ (weight w) d < n → (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
⊢ ∀ (a : σ →₀ ℕ), (∀ x < n, (weight w) a = x → (coeff α a) f = 0) ↔ (weight w) a < n → (coeff α a) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | constructor | case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) ↔ (weight w) d < n → (coeff α d) f = 0 | case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) → (weight w) d < n → (coeff α d) f = 0
case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf ... | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) ↔ (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | intro h hd | case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) → (weight w) d < n → (coeff α d) f = 0 | case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : ∀ x < n, (weight w) d = x → (coeff α d) f = 0
hd : (weight w) d < n
⊢ (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ (∀ x < n, (weight w) d = x → (coeff α d) f = 0) → (weight w) d < n → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | exact h (weight w d) hd rfl | case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : ∀ x < n, (weight w) d = x → (coeff α d) f = 0
hd : (weight w) d < n
⊢ (coeff α d) f = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.mp
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : ∀ x < n, (weight w) d = x → (coeff α d) f = 0
hd : (weight w) d < n
⊢ (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | intro h m hm hd | case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ ((weight w) d < n → (coeff α d) f = 0) → ∀ x < n, (weight w) d = x → (coeff α d) f = 0 | case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : m < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
⊢ ((weight w) d < n → (coeff α d) f = 0) → ∀ x < n, (weight w) d = x → (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | rw [← hd] at hm | case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : m < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0 | case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : (weight w) d < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : m < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_eq_nat | [178, 1] | [194, 52] | exact h hm | case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : (weight w) d < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case inr.h.h.mpr
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f : MvPowerSeries σ α
n : ℕ
hf : f ≠ 0
d : σ →₀ ℕ
h : (weight w) d < n → (coeff α d) f = 0
m : ℕ
hm : (weight w) d < n
hd : (weight w) d = m
⊢ (coeff α d) f = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder_add | [198, 1] | [202, 46] | refine' le_weightedOrder w _ | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
⊢ min (weightedOrder w f) (weightedOrder w g) ≤ weightedOrder w (f + g) | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
⊢ ∀ (d : σ →₀ ℕ), ↑((weight w) d) < min (weightedOrder w f) (weightedOrder w g) → (coeff α d) (f + g) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
⊢ min (weightedOrder w f) (weightedOrder w g) ≤ weightedOrder w (f + g)
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.le_weightedOrder_add | [198, 1] | [202, 46] | simp (config := { contextual := true }) only [coeff_of_lt_weightedOrder w, lt_min_iff, map_add,
add_zero, eq_self_iff_true, imp_true_iff] | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
⊢ ∀ (d : σ →₀ ℕ), ↑((weight w) d) < min (weightedOrder w f) (weightedOrder w g) → (coeff α d) (f + g) = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
⊢ ∀ (d : σ →₀ ℕ), ↑((weight w) d) < min (weightedOrder w f) (weightedOrder w g) → (coeff α d) (f + g) = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | obtain ⟨n, hn⟩ := ne_top_iff_exists.mp (ne_top_of_lt H) | σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
⊢ weightedOrder w (f + g) = weightedOrder w f | case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ weightedOrder w (f + g) = weightedOrder w f | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
⊢ weightedOrder w (f + g) = weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | erw [← hn, weightedOrder_eq_nat] | case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ weightedOrder w (f + g) = weightedOrder w f | case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ (∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) (f + g) = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ weightedOrder w (f + g) = weightedOrder w f
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | obtain ⟨d, hd, hd'⟩ := ((weightedOrder_eq_nat w).mp hn.symm).1 | case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ (∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (coeff α d) (f + g) = 0 | case intro.intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
⊢ (∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d < n → (... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | constructor | case intro.intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0) ∧ ∀ (d : σ →₀ ℕ), (weight w) d... | case intro.intro.intro.left
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ ∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0
case intro.intro.intro.rig... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (∃ d, (weight w) d ... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | use d | case intro.intro.intro.left
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ ∃ d, (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0 | case h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.left
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ ∃ d, (weight w... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | use hd | case h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (weight w) d = n ∧ (coeff α d) (f + g) ≠ 0 | case right
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (coeff α d) (f + g) ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case h
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (weight w) d = n ∧ (coeff α d) (f +... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/MvPowerSeries/Order.lean | MvPowerSeries.weightedOrder_add_of_weightedOrder_lt.aux | [205, 9] | [221, 13] | rw [← hn, ← hd] at H | case right
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (coeff α d) (f + g) ≠ 0 | case right
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
H : ↑((weight w) d) < weightedOrder w g
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (coeff α d) (f + g) ≠ 0 | Please generate a tactic in lean4 to solve the state.
STATE:
case right
σ : Type u_2
α : Type u_1
inst✝ : Semiring α
w : σ → ℕ
f✝ f g : MvPowerSeries σ α
H : weightedOrder w f < weightedOrder w g
n : ℕ
hn : ↑n = weightedOrder w f
d : σ →₀ ℕ
hd : (weight w) d = n
hd' : (coeff α d) f ≠ 0
⊢ (coeff α d) (f + g) ≠ 0
TACTIC:... |
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