file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Multiset/Basic.lean | Multiset.subset_cons | [] | [
411,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.degreeLE_mono | [] | [
73,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_one | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.57133\nγ : Type ?u.57136\ninst✝ : CommMonoid α\ns t : Multiset α\na : α\nm : Multiset ι\nf g : ι → α\n⊢ prod (map (fun x => 1) m) = 1",
"tactic": "rw [map_const', prod_replicate, one_pow]"
}
] | [
193,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | Nat.cast_zero | [] | [
108,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.mul_mem_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.13003\nA : Type ?u.13006\na a₁ a₂ b c : G\ninst✝ : Group G\ns : Set G\nhs : IsSubgroup s\nh : a ∈ s\nhba : b * a ∈ s\n⊢ b ∈ s",
"tactic": "simpa using hs.mul_mem hba (hs.inv_mem h)"
}
] | [
151,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_inv_mul_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ 1 ≤ b⁻¹ * a ↔ b ≤ a",
"tactic": "rw [← mul_le_mul_iff_left b, mul_one, mul_inv_cancel_left]"
}
] | [
142,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_cthickening_subset | [
{
"state_after": "ι : Sort ?u.158407\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns✝ t : Set α\nx✝ : α\nhε : 0 ≤ ε\nhδ : 0 ≤ δ\ns : Set α\nx : α\n⊢ x ∈ cthickening ε (cthickening δ s) → x ∈ cthickening (ε + δ) s",
"state_before": "ι : Sort ?u.158407\nα : Type u\nβ : Type v\ninst✝ : Pseudo... | [
1506,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.dart_edge_eq_mk'_iff' | [
{
"state_after": "case mk.mk\nι : Sort ?u.98622\n𝕜 : Type ?u.98625\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na✝ b✝ c u✝ v✝ w : V\ne : Sym2 V\na b : V\nh : Adj G (a, b).fst (a, b).snd\nu v : V\n⊢ Dart.edge { toProd := (a, b), is_adj := h } = Quotient.mk (Sym2.Rel.setoid V) (u, ... | [
790,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Topology/Instances/Matrix.lean | summable_matrix_transpose | [] | [
308,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_of_forall_exists_gt | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : Preorder α\ninst✝ : Nonempty α\ns : Set α\nh : ∀ (a : α), ∃ b, b ∈ s ∧ a < b\ninhabited_h : Inhabited α\n⊢ Set.Infinite s",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝¹ : Preorder α\ninst✝ : Nonempty α\ns :... | [
1413,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_pair | [] | [
1000,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.differentiableWithinAt_iff_of_mem | [] | [
874,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_zero | [] | [
113,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_eq_iff_isCompl | [
{
"state_after": "α : Type u\nβ : Type ?u.54113\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : xᶜ = y\n⊢ IsCompl x (xᶜ)",
"state_before": "α : Type u\nβ : Type ?u.54113\nw x y z : α\ninst✝ : BooleanAlgebra α\nh : xᶜ = y\n⊢ IsCompl x y",
"tactic": "rw [← h]"
},
{
"state_after": "no goals",
"stat... | [
624,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.equicontinuousAt_iff | [] | [
56,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.inv_mem_iff | [] | [
193,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | mapsTo_tangentCone_pi | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_3\ninst✝⁹ : NontriviallyNormedField 𝕜\nE✝ : Type ?u.63756\ninst✝⁸ : NormedAddCommGroup E✝\ninst✝⁷ : NormedSpace 𝕜 E✝\nF : Type ?u.63851\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.63941\ninst✝⁴ : NormedAddCommGroup G\ninst✝... | [
209,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_coeff_of_ne | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\ni : ℕ\nhi : i ≠ natDegree f\n⊢ coeff (eraseLead f) i = coeff f i",
"tactic": "simp [eraseLead_coeff, hi]"
}
] | [
58,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.Ico_pred_singleton | [
{
"state_after": "no goals",
"state_before": "a✝ b c a : ℕ\nh : 0 < a\n⊢ Ico (a - 1) a = {a - 1}",
"tactic": "rw [← Icc_pred_right _ h, Icc_self]"
}
] | [
191,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Multiset/Fintype.lean | Multiset.toEnumFinset_subset_iff | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nm m₁ m₂ : Multiset α\nh : toEnumFinset m₁ ⊆ toEnumFinset m₂\n⊢ m₁ ≤ m₂",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nm m₁ m₂ : Multiset α\n⊢ toEnumFinset m₁ ⊆ toEnumFinset m₂ ↔ m₁ ≤ m₂",
"tactic": "refine' ⟨fun h ↦ _, Multiset.toEnumFinset... | [
154,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.toAffineEquiv_refl | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.card_univ | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_eq_derivFamily | [] | [
513,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | of_irreducible_map | [] | [
253,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_has_prop | [
{
"state_after": "case pos\nn : ℕ\nn1 : n ≠ 1\nn0 : n = 0\n⊢ Nat.minFacProp n (minFac n)\n\ncase neg\nn : ℕ\nn1 : n ≠ 1\nn0 : ¬n = 0\n⊢ Nat.minFacProp n (minFac n)",
"state_before": "n : ℕ\nn1 : n ≠ 1\n⊢ Nat.minFacProp n (minFac n)",
"tactic": "by_cases n0 : n = 0"
},
{
"state_after": "case neg\... | [
326,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_Ici | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.175688\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.175694\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.175789\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.175879\ninst✝¹ : NormedAddCommGroup ... | [
416,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.pow_le_pow | [
{
"state_after": "case intro\nR : Type u\nι : Type ?u.292952\ninst✝ : CommSemiring R\nI J K L : Ideal R\nm n : ℕ\nh : m ≤ n\nk : ℕ\nhk : n = m + k\n⊢ I ^ n ≤ I ^ m",
"state_before": "R : Type u\nι : Type ?u.292952\ninst✝ : CommSemiring R\nI J K L : Ideal R\nm n : ℕ\nh : m ≤ n\n⊢ I ^ n ≤ I ^ m",
"tactic"... | [
790,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.of_lt | [] | [
981,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_pos_iff_exists_ne_zero | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\n⊢ 0 < finrank K V ↔ 0 < ↑(finrank K V)",
"state_before": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRin... | [
323,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_of_right_le_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr : R\nhr : r ≤ 0\n⊢ ⌊r⁻¹⌋₊ < b ∨ b ≤ 1",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr : R\nhr : r ≤ 0\n⊢ clog b r = 0",
"tactic": "rw [clog, if_neg (... | [
209,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.132793\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : Group G\na : G\nm n : ℤ\n⊢ a ^ (m - n) = a ^ m * (a ^ n)⁻¹",
"tactic": "rw [sub_eq_add_neg, zpow_add, zpow_neg]"
}
] | [
245,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.coe_bot | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.extend_map | [
{
"state_after": "α : Type u_3\ninst✝⁴ : UniformSpace α\npkg : AbstractCompletion α\nβ : Type u_2\ninst✝³ : UniformSpace β\npkg' : AbstractCompletion β\nf✝ : α → β\nγ : Type u_1\ninst✝² : UniformSpace γ\ninst✝¹ : CompleteSpace γ\ninst✝ : SeparatedSpace γ\nf : β → γ\ng : α → β\nhf : UniformContinuous f\nhg : Uni... | [
231,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.zero_apply | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.to_fun_eq_coe | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_map_of_injective | [
{
"state_after": "case H₁\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q : MvPolynomial σ R\nf✝ : R →+* S₁\np : MvPolynomial σ R\nf : R →+* S₁\nhf : Injective ↑f\n⊢ support (↑(map f) p) ⊆ suppor... | [
1369,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_sup | [] | [
818,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
11
] |
Mathlib/Topology/Separation.lean | regularSpace_induced | [] | [
1603,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1601,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_div_cancel' | [
{
"state_after": "no goals",
"state_before": "a b : Int\nH : a ∣ b\n⊢ a * div b a = b",
"tactic": "rw [Int.mul_comm, Int.div_mul_cancel H]"
}
] | [
707,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
706,
11
] |
Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.mul_same | [
{
"state_after": "case a.h\nl : Type ?u.41930\nm : Type ?u.41933\nn : Type u_1\nR : Type ?u.41939\nα : Type u_2\ninst✝⁴ : DecidableEq l\ninst✝³ : DecidableEq m\ninst✝² : DecidableEq n\ninst✝¹ : Semiring α\ni j : n\nc : α\ni' j' : n\ninst✝ : Fintype n\nk : n\nd : α\na b : n\n⊢ (stdBasisMatrix i j c ⬝ stdBasisMat... | [
201,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.cons_reverseAux | [] | [
330,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_apply | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.cone_x | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.stronglyMeasurable_one | [] | [
168,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_mul | [] | [
1296,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.comp_const | [] | [
272,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.sups_infs_subset_right | [] | [
406,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.aleph0_lt_continuum | [] | [
79,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Set/Function.lean | Function.invFunOn_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.65525\nι : Sort ?u.65528\nπ : α → Type ?u.65533\ninst✝ : Nonempty α\ns : Set α\nf : α → β\na : α\nb : β\nh : ¬∃ a, a ∈ s ∧ f a = b\n⊢ invFunOn f s b = Classical.choice inst✝",
"tactic": "rw [invFunOn, dif_neg h]"
}
] | [
1227,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.pow_aux | [] | [
403,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
9
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.14510\nδ : Type ?u.14513\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g : β → α\na b : α\ns : Finset β\n⊢ HasSum (fun x => 0) 0",
"tactic": "simp [HasSum, tendsto_const_nhds]"
}
] | [
88,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_const_const | [] | [
262,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | T_pow | [] | [
137,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
9
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.Measure.toSignedMeasure_add | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.137383\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\ni : Set α\n⊢ MeasurableSet i → ↑(toSignedMeasure (μ + ν)) i = ↑(toSignedMeasure μ + toSignedMeasure ν) i",
"state_before": "α : Type u_1\nβ : Type ?u.137... | [
475,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | C_p_pow_dvd_bind₁_rename_wittPolynomial_sub_sum | [
{
"state_after": "case zero\np : ℕ\nR : Type ?u.932563\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℤ\nIH :\n ∀ (m : ℕ),\n m < Nat.zero →\n ↑(map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p (↑(map (Int.castRingHom ℚ)) Φ) m\n⊢ ↑C ↑(p ^ Nat.zer... | [
272,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_nat_cast | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x ↑Nat.zero = ↑Nat.zero\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q r ... | [
143,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.nat_cast_coeff_zero | [
{
"state_after": "case zero\nR✝ : Type u\nS : Type v\na b : R✝\nn m : ℕ\ninst✝¹ : Semiring R✝\np q r : R✝[X]\nR : Type u_1\ninst✝ : Semiring R\n⊢ coeff (↑Nat.zero) 0 = ↑Nat.zero\n\ncase succ\nR✝ : Type u\nS : Type v\na b : R✝\nn✝ m : ℕ\ninst✝¹ : Semiring R✝\np q r : R✝[X]\nR : Type u_1\ninst✝ : Semiring R\nn : ... | [
380,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | skewAdjoint.mem_iff | [
{
"state_after": "R : Type u_1\nA : Type ?u.105083\ninst✝¹ : AddCommGroup R\ninst✝ : StarAddMonoid R\nx : R\n⊢ x ∈ (skewAdjoint R).toAddSubmonoid.toAddSubsemigroup.carrier ↔ star x = -x",
"state_before": "R : Type u_1\nA : Type ?u.105083\ninst✝¹ : AddCommGroup R\ninst✝ : StarAddMonoid R\nx : R\n⊢ x ∈ skewAd... | [
467,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Set/Image.lean | Set.nontrivial_of_preimage | [] | [
1269,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1267,
1
] |
Mathlib/Data/List/Sort.lean | List.orderedInsert_nil | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.continuous_coe | [] | [
61,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.mk_byteIdx | [] | [
90,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
90,
9
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inr_sub | [] | [
369,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioc_succ_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : SuccOrder α\na b : α\nh : a < succ b\n⊢ Ioc a (succ b) = insert (succ b) (Ioc a b)",
"tactic": "simp_rw [← Ioi_inter_Iic, Iic_succ, inter_insert_of_mem (mem_Ioi.2 h)]"
}
] | [
457,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Topology/ContinuousOn.lean | pure_le_nhdsWithin | [] | [
169,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_le_mul_right | [] | [
284,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_eq_integral | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.1246877\n𝕜 : Type ?u.1246880\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : Norm... | [
1352,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_smul_left | [] | [
1007,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.fval_ex | [] | [
1780,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1779,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.Lex.inl_le_inr | [] | [
364,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.div_mem | [] | [
285,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
11
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | smul_orthogonalProjection_singleton | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.567907\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nv w : E\n⊢ ↑(↑(orthogonalProjection (Sub... | [
587,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.insertNth_comm | [
{
"state_after": "n : ℕ\nα : Type u_1\nβ : Type ?u.56356\nγ : Type ?u.56359\na✝ a b : α\ni j : Fin (n + 1)\nh : i ≤ j\nl : List α\nhl : List.length l = n\n⊢ ↑(insertNth b (Fin.succ j) (insertNth a i { val := l, property := hl })) =\n ↑(insertNth a (↑Fin.castSucc i) (insertNth b j { val := l, property := hl }... | [
572,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_of_isClosed | [
{
"state_after": "case hf\nα : Type ?u.149654\nβ : Type ?u.149657\nγ : Type u_1\nγ₂ : Type ?u.149663\nδ : Type u_2\nι : Sort y\ns t u : Set α\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : MeasurableSpace α\ninst✝¹⁰ : OpensMeasurableSpace α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : MeasurableSpace β\ninst✝⁷ : OpensMeasu... | [
347,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_lt_of_le_right | [
{
"state_after": "case a\nι : Type ?u.30542\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x✝ : α\ninst✝ : DecidablePred fun x => x < c\nhcb : c ≤ b\nx : α\n⊢ x ∈ filter (fun x => x < c) (Ico a b) ↔ x ∈ Ico a c",
"state_before": "ι : Type ?u.30542\nα : Type u_1\ninst✝² ... | [
329,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.noZeroDivisors | [
{
"state_after": "F : Type ?u.112165\nα : Type ?u.112168\nβ : Type ?u.112171\nR : Type ?u.112174\nS : Type ?u.112177\nS' : Type ?u.112180\ninst✝⁶ : Add R\ninst✝⁵ : Add S\ninst✝⁴ : Mul R\ninst✝³ : Mul S\nA : Type u_1\nB : Type u_2\ninst✝² : Ring A\ninst✝¹ : Ring B\ninst✝ : NoZeroDivisors B\ne : A ≃+* B\nx y : A\... | [
870,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
11
] |
Mathlib/GroupTheory/Perm/Fin.lean | Finset.univ_perm_fin_succ | [] | [
78,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongr_swap_one | [] | [
228,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_lt_of_one_le_of_nonneg | [] | [
775,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | MonoidWithZeroHom.ext_int | [] | [
292,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_add_left | [] | [
993,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
11
] |
Std/Data/Int/DivMod.lean | Int.emod_one | [
{
"state_after": "no goals",
"state_before": "a : Int\n⊢ a % 1 = 0",
"tactic": "simp [emod_def, Int.one_mul, Int.sub_self]"
}
] | [
350,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
349,
15
] |
Mathlib/Computability/Reduce.lean | ManyOneEquiv.congr_left | [] | [
266,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | PontryaginDual.map_mul | [] | [
473,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
8
] |
Mathlib/Combinatorics/Quiver/Push.lean | Quiver.Push.lift_obj | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.strict_mono | [] | [
564,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
11
] |
Mathlib/Order/SuccPred/Basic.lean | exists_pred_iterate_iff_le | [] | [
1416,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.normalize_of_nonpos | [
{
"state_after": "case inl\nh : 0 ≤ 0\n⊢ ↑normalize 0 = -0\n\ncase inr\nz : ℤ\nh✝ : z ≤ 0\nh : z < 0\n⊢ ↑normalize z = -z",
"state_before": "z : ℤ\nh : z ≤ 0\n⊢ ↑normalize z = -z",
"tactic": "obtain rfl | h := h.eq_or_lt"
},
{
"state_after": "no goals",
"state_before": "case inl\nh : 0 ≤ 0\n... | [
112,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.15924\nβ : Type u_1\ninst✝ : CommMonoid β\nf : Fin 1 → β\n⊢ ∏ i : Fin 1, f i = f 0",
"tactic": "simp"
}
] | [
107,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Topology/Constructions.lean | quotientMap_quotient_mk' | [] | [
1158,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.95909\nι : Type ?u.95912\nM : Type ?u.95915\nN : Type ?u.95918\nG✝ : Type ?u.95921\ninst✝¹ : Group G✝\ns✝ t : Set α\nf✝ g : α → G✝\na : α\nG : Type u_1\ninst✝ : AddGroup G\ns : Set α\nf : α → G\n⊢ indicator (sᶜ) f = f - indicator s f",
... | [
555,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_divInt | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ c✝ : ℚ\na b c : ℤ\nh : c = 0\n⊢ (a + b) /. c = a /. c + b /. c",
"tactic": "simp [h]"
},
{
"state_after": "a✝ b✝ c✝ : ℚ\na b c : ℤ\nh : ¬c = 0\n⊢ (a + b) * (c * c) = (a * c + b * c) * c",
"state_before": "a✝ b✝ c✝ : ℚ\na b c : ℤ\nh : ¬c = 0... | [
477,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.disjoint_list_sum_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.895297\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na✝ : α\nf g : α → β\na : Multiset α\nl : List (Multiset α)\n⊢ Disjoint a (List.sum l) ↔ ∀ (b : Multiset α), b ∈ l → Disjoint a b",
"tactic": "simpa only [@disjoint_comm _ a] using di... | [
2064,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2062,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.star_apply | [] | [
980,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Logic/Basic.lean | ULift.down_inj | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b : ULift α\nh : a = b\n⊢ a.down = b.down",
"tactic": "rw [h]"
}
] | [
76,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
9
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.card_compl_support_modEq | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np n : ℕ\nhp : Fact (Nat.Prime p)\nσ : Perm α\nhσ : σ ^ p ^ n = 1\n⊢ p ∣ sum (cycleType σ)\n\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np n : ℕ\nhp : Fact (Nat.Prime p)\nσ : Perm α\nhσ : σ ^ p ^ n = 1\n⊢ Finset.card (suppor... | [
333,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_strictMono | [] | [
339,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.isUnit_of_dvd | [] | [
168,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snorm_indicator_le | [
{
"state_after": "α : Type u_2\nE✝ : Type ?u.638627\nF : Type ?u.638630\nG : Type ?u.638633\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E✝\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ns : Set α\nhs : MeasurableSet s\nc : E✝\nf✝ : α → E✝\nhf : AEStro... | [
589,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | AssociatePrimes.mem_iff | [] | [
58,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
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