url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.IsHomogeneous.totalDegree_eq_weightedTotalDegree | [168, 1] | [174, 87] | rw [totalDegree, weightedTotalDegree, weightedDegree] | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ φ.totalDegree = weightedTotalDegree 1 φ | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ (φ.support.sup fun s => s.sum fun x e => e) = φ.support.sup fun s => (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom s | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ φ.totalDegree = weightedTotalDegree 1 φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.IsHomogeneous.totalDegree_eq_weightedTotalDegree | [168, 1] | [174, 87] | apply Finset.sup_congr rfl | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ (φ.support.sup fun s => s.sum fun x e => e) = φ.support.sup fun s => (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom s | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ ∀ a ∈ φ.support, (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ (φ.support.sup fun s => s.sum fun x e => e) = φ.support.sup fun s => (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom s
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.IsHomogeneous.totalDegree_eq_weightedTotalDegree | [168, 1] | [174, 87] | intro a _ | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ ∀ a ∈ φ.support, (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
a : σ →₀ ℕ
a✝ : a ∈ φ.support
⊢ (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
⊢ ∀ a ∈ φ.support, (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.IsHomogeneous.totalDegree_eq_weightedTotalDegree | [168, 1] | [174, 87] | simp only [Finsupp.total, Pi.one_apply, LinearMap.toAddMonoidHom_coe, Finsupp.coe_lsum,
LinearMap.coe_smulRight, LinearMap.id_coe, id_eq, Algebra.id.smul_eq_mul, mul_one] | σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
a : σ →₀ ℕ
a✝ : a ∈ φ.support
⊢ (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.33916
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.33925
φ ψ : MvPolynomial σ R
m n : ℕ
a : σ →₀ ℕ
a✝ : a ∈ φ.support
⊢ (a.sum fun x e => e) = (Finsupp.total σ ℕ ℕ 1).toAddMonoidHom a
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.IsHomogeneous.totalDegree | [178, 1] | [180, 85] | rw [totalDegree_eq_weightedTotalDegree, ← WithBot.coe_eq_coe, ←
weightedTotalDegree_coe _ φ h, IsWeightedHomogeneous.weighted_total_degree hφ h] | σ : Type u_1
τ : Type ?u.36379
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.36388
φ ψ : MvPolynomial σ R
m n : ℕ
hφ : φ.IsHomogeneous n
h : φ ≠ 0
⊢ φ.totalDegree = n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.36379
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.36388
φ ψ : MvPolynomial σ R
m n : ℕ
hφ : φ.IsHomogeneous n
h : φ ≠ 0
⊢ φ.totalDegree = n
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.homogeneousComponent_eq_zero | [269, 1] | [271, 51] | rw [totalDegree_eq_weightedTotalDegree] at h | σ : Type u_1
τ : Type ?u.51956
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.51965
n : ℕ
φ ψ : MvPolynomial σ R
h : φ.totalDegree < n
⊢ (homogeneousComponent n) φ = 0 | σ : Type u_1
τ : Type ?u.51956
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.51965
n : ℕ
φ ψ : MvPolynomial σ R
h : weightedTotalDegree 1 φ < n
⊢ (homogeneousComponent n) φ = 0 | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.51956
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.51965
n : ℕ
φ ψ : MvPolynomial σ R
h : φ.totalDegree < n
⊢ (homogeneousComponent n) φ = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.homogeneousComponent_eq_zero | [269, 1] | [271, 51] | exact weightedHomogeneousComponent_eq_zero n φ h | σ : Type u_1
τ : Type ?u.51956
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.51965
n : ℕ
φ ψ : MvPolynomial σ R
h : weightedTotalDegree 1 φ < n
⊢ (homogeneousComponent n) φ = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.51956
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.51965
n : ℕ
φ ψ : MvPolynomial σ R
h : weightedTotalDegree 1 φ < n
⊢ (homogeneousComponent n) φ = 0
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | ext1 d | σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
⊢ ∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ = φ | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ coeff d (∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ) = coeff d φ | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
⊢ ∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ = φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | suffices φ.totalDegree < degree d → 0 = coeff d φ by
simpa [coeff_sum, coeff_homogeneousComponent] | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ coeff d (∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ) = coeff d φ | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < degree d → 0 = coeff d φ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ coeff d (∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ) = coeff d φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | rw [degree_eq_weightedDegree] | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < degree d → 0 = coeff d φ | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < ∑ i ∈ d.support, d i → 0 = coeff d φ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < degree d → 0 = coeff d φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | intro h | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < ∑ i ∈ d.support, d i → 0 = coeff d φ | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
h : φ.totalDegree < ∑ i ∈ d.support, d i
⊢ 0 = coeff d φ | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
⊢ φ.totalDegree < ∑ i ∈ d.support, d i → 0 = coeff d φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | exact (coeff_eq_zero_of_totalDegree_lt h).symm | case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
h : φ.totalDegree < ∑ i ∈ d.support, d i
⊢ 0 = coeff d φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
h : φ.totalDegree < ∑ i ∈ d.support, d i
⊢ 0 = coeff d φ
TACTIC:
|
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.sum_homogeneousComponent | [275, 1] | [282, 49] | simpa [coeff_sum, coeff_homogeneousComponent] | σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
this : φ.totalDegree < degree d → 0 = coeff d φ
⊢ coeff d (∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ) = coeff d φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.53191
R : Type u_2
inst✝ : CommSemiring R
S : Type ?u.53200
n : ℕ
φ ψ : MvPolynomial σ R
d : σ →₀ ℕ
this : φ.totalDegree < degree d → 0 = coeff d φ
⊢ coeff d (∑ i ∈ range (φ.totalDegree + 1), (homogeneousComponent i) φ) = coeff d φ
TA... |
https://github.com/AntoineChambert-Loir/DividedPowers4.git | 18a13603ed0158d2880b6b0b0369d78417040a1d | DividedPowers/ForMathlib/Homogeneous.lean | MvPolynomial.decomposition.decompose'_eq | [321, 1] | [325, 6] | rfl | σ : Type u_1
τ : Type ?u.73574
R : Type u_2
inst✝² : CommSemiring R
S : Type ?u.73583
inst✝¹ : DecidableEq σ
inst✝ : DecidableEq R
⊢ DirectSum.Decomposition.decompose' = fun φ =>
(DirectSum.mk (fun i => ↥(homogeneousSubmodule σ R i)) (Finset.image (⇑degree) φ.support)) fun m =>
⟨(homogeneousComponent ↑m) φ, ⋯... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
σ : Type u_1
τ : Type ?u.73574
R : Type u_2
inst✝² : CommSemiring R
S : Type ?u.73583
inst✝¹ : DecidableEq σ
inst✝ : DecidableEq R
⊢ DirectSum.Decomposition.decompose' = fun φ =>
(DirectSum.mk (fun i => ↥(homogeneousSubmodule σ R i)) (Finset.image (⇑degre... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | Set.mem_toSubset' | [14, 1] | [17, 56] | rw [toSubset', Set.range_inclusion, Set.mem_setOf_eq] | X : Type u_1
s t : Set X
h : s ≤ t
x : ↑t
⊢ x ∈ s.toSubset' t h ↔ ↑x ∈ s | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type u_1
s t : Set X
h : s ≤ t
x : ↑t
⊢ x ∈ s.toSubset' t h ↔ ↑x ∈ s
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | Set.coe_toSubset | [25, 1] | [28, 8] | ext | X : Type u_1
s t : Set X
⊢ Subtype.val '' s.toSubset t = s ∩ t | case h
X : Type u_1
s t : Set X
x✝ : X
⊢ x✝ ∈ Subtype.val '' s.toSubset t ↔ x✝ ∈ s ∩ t | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type u_1
s t : Set X
⊢ Subtype.val '' s.toSubset t = s ∩ t
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | Set.coe_toSubset | [25, 1] | [28, 8] | sorry | case h
X : Type u_1
s t : Set X
x✝ : X
⊢ x✝ ∈ Subtype.val '' s.toSubset t ↔ x✝ ∈ s ∩ t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type u_1
s t : Set X
x✝ : X
⊢ x✝ ∈ Subtype.val '' s.toSubset t ↔ x✝ ∈ s ∩ t
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | toSubset_iUnion | [42, 1] | [45, 8] | ext | X : Type u_1
t : Set X
S : ℕ → Set X
⊢ (⋃ n, S n).toSubset t = ⋃ n, (S n).toSubset t | case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ x✝ ∈ (⋃ n, S n).toSubset t ↔ x✝ ∈ ⋃ n, (S n).toSubset t | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type u_1
t : Set X
S : ℕ → Set X
⊢ (⋃ n, S n).toSubset t = ⋃ n, (S n).toSubset t
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | toSubset_iUnion | [42, 1] | [45, 8] | rw [mem_toSubset] | case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ x✝ ∈ (⋃ n, S n).toSubset t ↔ x✝ ∈ ⋃ n, (S n).toSubset t | case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ ↑x✝ ∈ ⋃ n, S n ↔ x✝ ∈ ⋃ n, (S n).toSubset t | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ x✝ ∈ (⋃ n, S n).toSubset t ↔ x✝ ∈ ⋃ n, (S n).toSubset t
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | toSubset_iUnion | [42, 1] | [45, 8] | sorry | case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ ↑x✝ ∈ ⋃ n, S n ↔ x✝ ∈ ⋃ n, (S n).toSubset t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
X : Type u_1
t : Set X
S : ℕ → Set X
x✝ : ↑t
⊢ ↑x✝ ∈ ⋃ n, S n ↔ x✝ ∈ ⋃ n, (S n).toSubset t
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/ToSubset.lean | toSubset_compact | [47, 1] | [54, 8] | sorry | X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hsw : s ⊆ t
hs : IsCompact s
⊢ IsCompact (s.toSubset t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : Type u_1
Y : Type u_2
inst✝¹ : TopologicalSpace X
inst✝ : TopologicalSpace Y
s t : Set X
hsw : s ⊆ t
hs : IsCompact s
⊢ IsCompact (s.toSubset t)
TACTIC:
|
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | have h₁ : μ = μH[m] := by
have aux : μH[m] = volume := by
rw [← Fintype.card_fin m]
exact hausdorffMeasure_pi_real (ι := Fin m)
sorry | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | have h₂ : ν = μH[n] := by sorry | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | rw [h₁] at h₂s | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | have : μH[m] (f '' s) = 0 := by
have scifi : Convex ℝ U := sorry
apply locally_lipschitz_image_of_null_set_is_null_set_open (of_C1_on_open hU scifi hf) h₁s h₂s | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | rw [h₂, ← hd] | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | exact this | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | have aux : μH[m] = volume := by
rw [← Fintype.card_fin m]
exact hausdorffMeasure_pi_real (ι := Fin m) | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | sorry | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | rw [← Fintype.card_fin m] | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | exact hausdorffMeasure_pi_real (ι := Fin m) | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | sorry | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | have scifi : Convex ℝ U := sorry | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null | [22, 1] | [50, 13] | apply locally_lipschitz_image_of_null_set_is_null_set_open (of_C1_on_open hU scifi hf) h₁s h₂s | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null' | [52, 1] | [57, 77] | let hdiff := Iff.mpr contDiffOn_univ hf | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_null' | [52, 1] | [57, 77] | apply image_null_of_C1_of_null isOpen_univ hdiff μ ν hd (subset_univ s) hs | E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²² : NormedAddCommGroup E
inst✝²¹ : NormedSpace ℝ E
H : Type u_2
inst✝²⁰ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁹ : TopologicalSpace M
inst✝¹⁸ : ChartedSpace H M
inst✝¹⁷ : I.Boundaryless
inst✝¹⁶ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | let incl : E → E × (Fin (n-m) → ℝ) := fun x ↦ ⟨x, 0⟩ | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | let g' : E × (Fin (n-m) → ℝ) → F × (Fin (n-m) → ℝ) := fun ⟨y, _⟩ ↦ ⟨g y, 0⟩ | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | let pi : F × (Fin (n-m) → ℝ) → F := fun ⟨f, _⟩ ↦ f | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | have commutes: pi ∘ g' ∘ incl = g := by
ext y
rw [comp_apply, comp_apply] | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | obtain ⟨K''⟩ : Nonempty (PositiveCompacts (E × (Fin (n-m) → ℝ))) := PositiveCompacts.nonempty' | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | let μ' : Measure (E × (Fin (n-m) → ℝ)) := addHaarMeasure K'' | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : Smoot... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | have aux : μ' (incl '' U) = 0 := by sorry | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : Smoot... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | have : ν ((pi ∘ g' ∘ incl) '' U) = 0 := by
sorry | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : Smoot... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | rw [← commutes] | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : Smoot... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | exact this | case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : Smoot... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | ext y | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | case h
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ ... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | rw [comp_apply, comp_apply] | case h
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothMan... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | sorry | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_measure_zero_of_C1_dimension_increase | [59, 1] | [90, 13] | sorry | E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWithCorners I M
inst✝¹⁶ : FiniteDimensional ℝ E
inst✝¹⁵ : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²³ : NormedAddCommGroup E
inst✝²² : NormedSpace ℝ E
H : Type u_2
inst✝²¹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝²⁰ : TopologicalSpace M
inst✝¹⁹ : ChartedSpace H M
inst✝¹⁸ : I.Boundaryless
inst✝¹⁷ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | rw [← image_univ] | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | suffices hyp : ∀ x : M, MeasureZero J (f '' ((chartAt H x).source ∩ univ)) from
measure_zero_image_iff_chart_domains (J := J) hyp | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | intro x μ hμ y | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | let e := chartAt H x | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | let e' := chartAt G y | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | have aux : J ∘ e' '' (e'.source ∩ f '' e.source) = (J ∘ e' ∘ f) '' e.source := by sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | rw [inter_univ, aux] | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | let g : E → F := J ∘ e' ∘ f ∘ e.invFun ∘ I.invFun | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | have : (J ∘ ↑e' ∘ f '' e.source) = g '' (I '' e.target) := by sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | have hopen : IsOpen (I '' e.target) := by sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | have gdiff : ContDiffOn ℝ 1 g (I '' e.target) := by sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | rw [this] | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | apply image_measure_zero_of_C1_dimension_increase hopen μ gdiff hdim | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/Stuff.lean | image_null_of_C1_of_dimension_increase | [92, 1] | [114, 71] | sorry | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : Secon... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : I.Boundaryless
inst✝¹⁴ : SmoothManifoldWi... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | have h : ν = μH[n] := sorry | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | rw [h] | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | have : Convex ℝ U := sorry | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | have h : dimH (univ : Set E) = m := sorry | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | apply measure_zero_of_dimH_lt (d := n) rfl.absolutelyContinuous | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | image_measure_zero_of_C1_dimension_increase' | [24, 1] | [40, 33] | calc dimH (g '' U)
_ ≤ dimH U := hg.dimH_image_le this rfl.subset
_ ≤ m := h ▸ dimH_mono (subset_univ U) _ < n := Nat.cast_lt.mpr hmn | E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : FiniteDimensional ℝ E
inst✝¹⁴ : SecondCountableTopology M
inst... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²¹ : NormedAddCommGroup E
inst✝²⁰ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁹ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁸ : TopologicalSpace M
inst✝¹⁷ : ChartedSpace H M
inst✝¹⁶ : SmoothManifoldWithCorners I M
inst✝¹⁵ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | by_cases hyp: m < n | E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopology M
inst... | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | have hr : 1 ≤ (r : ℕ∞) := Nat.one_le_cast.mpr (Nat.one_le_of_lt hr) | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
in... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | have hless: μ (f '' s) ≤ 0 := calc
μ (f '' s)
_ ≤ μ (f '' w) := measure_mono (image_subset f hsw)
_ = 0 := image_measure_zero_of_C1_dimension_increase' hw μ (hf.of_le hr) hyp | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
in... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | simp only [nonpos_iff_eq_zero, zero_le] at hless ⊢ | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
in... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | exact hless | case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
in... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local | [44, 1] | [56, 10] | sorry | case neg
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
inst✝¹³ : FiniteDimensional ℝ E
inst✝¹² : SecondCountableTopolo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
E : Type u_1
inst✝¹⁹ : NormedAddCommGroup E
inst✝¹⁸ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁷ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁶ : TopologicalSpace M
inst✝¹⁵ : ChartedSpace H M
inst✝¹⁴ : SmoothManifoldWithCorners I M
in... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | obtain ⟨K''⟩ : Nonempty (PositiveCompacts F) := PositiveCompacts.nonempty' | E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopology M
inst... | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | let μ : Measure F := addHaarMeasure K'' | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | have ass : μ (f '' s) = 0 := sard_local hr hw hsw hf hf' h'f' μ | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | have : IsSigmaCompact s := isSigmaCompact_univ.of_isClosed_subset hs (subset_univ s) | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | have : IsSigmaCompact (f '' s) := this.image_of_continuousOn (hf.continuousOn.mono hsw) | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_local' | [62, 1] | [72, 49] | exact IsMeagre.of_isSigmaCompact_null this ass | case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
inst✝¹² : FiniteDimensional ℝ E
inst✝¹¹ : SecondCountableTopo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
E : Type u_1
inst✝¹⁸ : NormedAddCommGroup E
inst✝¹⁷ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁶ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁵ : TopologicalSpace M
inst✝¹⁴ : ChartedSpace H M
inst✝¹³ : SmoothManifoldWithCorners I M
... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | suffices hyp : ∀ x : M, MeasureZero J (f '' ((chartAt H x).source ∩ s)) from
measure_zero_image_iff_chart_domains (J := J) hyp | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | intro x | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | let e := chartAt H x | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | intro μ hμ y | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | let e' := chartAt G y | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | let w := e.extend I '' (e.source ∩ f ⁻¹' e'.source) | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | let s_better := (e.extend I) '' (s ∩ e.source ∩ f ⁻¹' e'.source) | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | let f_local := (J ∘ e') ∘ f ∘ (e.extend I).symm | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hwopen : IsOpen w := by
refine e.extend_isOpenMapOn_source I ?_ (inter_subset_left _ _)
exact e.open_source.inter (e'.open_source.preimage hf.continuous) | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hsw : s_better ⊆ w := by
apply image_subset
rw [inter_assoc]
apply inter_subset_right s _ | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hsbetter₀ : s_better ⊆ e.extend I '' e.source := by
apply image_subset
rw [inter_comm s, inter_assoc]
exact inter_subset_left _ _ | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have cor : ((e.extend I).symm ∘ e.extend I) '' (s ∩ e.source ∩ f ⁻¹' e'.source) = s ∩ e.source ∩ f ⁻¹' e'.source := by
have : (s ∩ e.source ∩ f ⁻¹' e'.source) ⊆ e.source := by
rw [inter_comm s, inter_assoc]
apply inter_subset_left
apply e.extend_left_inv' _ this | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hsbetter : (e.extend I).symm '' s_better = s ∩ e.source ∩ f ⁻¹' e'.source := by
calc (e.extend I).symm '' s_better
_ = ((e.extend I).symm ∘ (e.extend I)) '' (s ∩ e.source ∩ f ⁻¹' e'.source) := by simp only [comp.assoc, image_comp]
_ = s ∩ e.source ∩ f ⁻¹' e'.source := cor | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hsbetter₁ : (e.extend I).symm '' s_better ⊆ s := by
rw [hsbetter, inter_assoc]
exact inter_subset_left s _ | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
https://github.com/fpvandoorn/sard.git | f4a1bb550136e8591dcd20dca5bdcce766a958c7 | Sard/MainTheorem.lean | sard_boundaryless | [84, 1] | [250, 15] | have hsbetter₂ : (e.extend I).symm '' s_better ⊆ e.source := by
rw [hsbetter]
rw [inter_comm s, inter_assoc]
exact inter_subset_left _ _ | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : FiniteDimensional ℝ E
inst✝¹³ : SecondCountableTopology M
inst... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type u_1
inst✝²⁰ : NormedAddCommGroup E
inst✝¹⁹ : NormedSpace ℝ E
H : Type u_2
inst✝¹⁸ : TopologicalSpace H
I : ModelWithCorners ℝ E H
M : Type u_3
inst✝¹⁷ : TopologicalSpace M
inst✝¹⁶ : ChartedSpace H M
inst✝¹⁵ : SmoothManifoldWithCorners I M
inst✝¹⁴ : F... |
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