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/RingTheory/IntegrallyClosed.lean | integralClosure.isIntegrallyClosedOfFiniteExtension | [] | [
145,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_lt_of_right_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidablePred fun x => x < c\nhbc : b ≤ c\n⊢ filter (fun x => x < c) (Ico a b) = Ico a b",
"tactic": "rw [Ico, ← Finset.filter_val, Finset.Ico_filter_lt_of_right_le hbc]"
... | [
161,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_le_one_iff | [] | [
1552,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1551,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.lift_castAddHom | [] | [
1212,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Topology/Constructions.lean | inducing_prod_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type u_1\nδ : Type ?u.66912\nε : Type ?u.66915\nζ : Type ?u.66918\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : TopologicalSpa... | [
819,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_ne_bit1 | [] | [
158,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/Data/Nat/Digits.lean | Nat.base_pow_length_digits_le' | [
{
"state_after": "n b m : ℕ\nhm : m ≠ 0\nthis : digits (b + 2) m ≠ []\n⊢ (b + 2) ^ List.length (digits (b + 2) m) ≤ (b + 2) * m",
"state_before": "n b m : ℕ\nhm : m ≠ 0\n⊢ (b + 2) ^ List.length (digits (b + 2) m) ≤ (b + 2) * m",
"tactic": "have : digits (b + 2) m ≠ [] := digits_ne_nil_iff_ne_zero.mpr hm... | [
465,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_smul | [] | [
203,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous_eval | [] | [
219,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subsingleton.antitoneOn | [] | [
2681,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2680,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.disjoint_atTop_principal_Iio | [] | [
85,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Separation.lean | TopologicalSpace.IsTopologicalBasis.exists_mem_of_ne | [
{
"state_after": "case intro.intro.intro\nα : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\nb : Set (Set α)\nhb : IsTopologicalBasis b\nx y : α\nh : x ≠ y\na : Set α\nab : a ∈ b\nxa : x ∈ a\nha : a ⊆ {y_1 | y_1 ≠ y}\n⊢ ∃ a, a ∈ b ∧ x ∈ a ∧ ¬y ∈ a",
"state_before": "α : Type u\nβ : Type... | [
422,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Data/List/Basic.lean | List.get?_take | [
{
"state_after": "case zero\nι : Type ?u.170021\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l✝ : List α\nn m✝ : ℕ\nh✝ : m✝ < n\nl : List α\nm : ℕ\nh : m < zero\n⊢ get? (take zero l) m = get? l m\n\ncase succ\nι : Type ?u.170021\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l✝ : List α\nn✝ m✝... | [
2026,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2018,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_inf | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mulPosMono_iff_covariant_pos | [
{
"state_after": "case inl\nα : Type u_1\na✝ b✝ c✝ d : α\ninst✝¹ : MulZeroClass α\ninst✝ : PartialOrder α\nh✝ : CovariantClass { x // 0 < x } α (fun x y => y * ↑x) fun x x_1 => x ≤ x_1\na : { x // 0 ≤ x }\nb c : α\nh : b ≤ c\nha : 0 = ↑a\n⊢ b * ↑a ≤ c * ↑a\n\ncase inr\nα : Type u_1\na✝ b✝ c✝ d : α\ninst✝¹ : Mul... | [
464,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.zmod_cast_comp_toZModPow | [
{
"state_after": "case h\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\nm n : ℕ\nh : m ≤ n\n⊢ RingHom.ker (RingHom.comp (ZMod.castHom (_ : p ^ m ∣ p ^ n) (ZMod (p ^ m))) (toZModPow n)) = RingHom.ker (toZModPow m)",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\nm n : ℕ\nh... | [
444,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.locallyFinite | [] | [
236,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
11
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumLexAssoc_symm_apply_inr_inl | [] | [
682,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.one_sub_K_ne_top | [
{
"state_after": "α : Type ?u.2537\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\n⊢ ¬1 - ↑K = ⊤",
"state_before": "α : Type ?u.2537\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\n⊢ 1 - ↑K ≠ ⊤",
"tactic": "norm_cast"
},
{
"state_after": "no goals",
"sta... | [
65,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ exp 0 = 1",
"tactic": "simp [Real.exp]"
}
] | [
1134,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddGroupHom.completion_id | [
{
"state_after": "case H\nG : Type u_1\ninst✝² : SeminormedAddCommGroup G\nH : Type ?u.4520\ninst✝¹ : SeminormedAddCommGroup H\nK : Type ?u.4526\ninst✝ : SeminormedAddCommGroup K\nx : Completion G\n⊢ ↑(completion (id G)) x = ↑(id (Completion G)) x",
"state_before": "G : Type u_1\ninst✝² : SeminormedAddCommG... | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/CharP/Basic.lean | exists_add_pow_prime_pow_eq | [] | [
85,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.246220\nβ : Type ?u.246223\nγ : Type ?u.246226\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b c : Ordinal\na0 : a = 0\n⊢ a * (b - c) = a * b - a * c",
"tactic": "simp only [a0, zero_mul, sub_self]"
},
{
"state_after": "no goal... | [
973,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | RingHom.toRatAlgHom_toRingHom | [] | [
521,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_u_eq | [] | [
517,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.U_add_two | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.8331\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\n⊢ U R (n + 2) = 2 * X * U R (n + 1) - U R n",
"tactic": "rw [U]"
}
] | [
113,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.smul_empty | [] | [
436,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finAddFlip_apply_mk_right | [
{
"state_after": "case h.e'_2.h.e'_6.h.e'_2\nm n k : ℕ\nh₁ : m ≤ k\nh₂ : k < m + n\n⊢ k = ↑(↑(Fin.natAdd m) { val := k - m, isLt := (_ : k - m < n) })\n\nm n k : ℕ\nh₁ : m ≤ k\nh₂ : k < m + n\n⊢ k < n + m",
"state_before": "m n k : ℕ\nh₁ : m ≤ k\nh₂ : k < m + n\n⊢ ↑finAddFlip { val := k, isLt := h₂ } = { va... | [
385,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_list_sum | [] | [
2044,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2042,
1
] |
Mathlib/Algebra/Order/CompleteField.lean | ringHom_monotone | [
{
"state_after": "case intro\nF : Type ?u.192927\nα : Type ?u.192930\nβ : Type ?u.192933\nγ : Type ?u.192936\nR : Type u_1\nS : Type u_2\ninst✝¹ : OrderedRing R\ninst✝ : LinearOrderedRing S\nhR : ∀ (r : R), 0 ≤ r → ∃ s, s ^ 2 = r\nf : R →+* S\ns : R\nh : 0 ≤ s ^ 2\n⊢ 0 ≤ ↑f (s ^ 2)",
"state_before": "F : Ty... | [
369,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Order/Monotone/Odd.lean | strictAnti_of_odd_strictAntiOn_nonneg | [] | [
40,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/RingTheory/Finiteness.lean | AlgHom.Finite.of_surjective | [] | [
743,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.coeff_mk | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_self_eq_union | [] | [
2121,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2120,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.source_preimage_target | [] | [
228,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_sigma | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasZeroMorphisms C\nβ : Type w\nf : β → C\ninst✝ : HasCoproduct f\nh : IsSeparator (∐ f)\nX Y : C\nu v : X ⟶ Y\nhuv : ∀ (G : C), G ∈ Set.range f → ∀ (h : G ⟶ X), h ≫ u = h ≫ v\n⊢ u = v\n\ncase refine'_... | [
580,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitLower_eq_self | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type ?u.5739\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ splitLower I i x = ↑I ↔ upper I i ≤ x",
"tactic": "simp [splitLower, update_eq_iff]"
}
] | [
87,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_id | [] | [
803,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_multiset_sum | [] | [
105,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.const_smul' | [] | [
648,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/RingTheory/MvPolynomial/Tower.lean | MvPolynomial.aeval_algebraMap_apply | [
{
"state_after": "R : Type u_2\nA : Type u_4\nB : Type u_3\nσ : Type u_1\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring A\ninst✝⁴ : CommSemiring B\ninst✝³ : Algebra R A\ninst✝² : Algebra A B\ninst✝¹ : Algebra R B\ninst✝ : IsScalarTower R A B\nx : σ → A\np : MvPolynomial σ R\n⊢ ↑(eval₂Hom (algebraMap R B) (↑(al... | [
61,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_piecewise | [] | [
1095,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | hasCompactSupport_norm_iff | [] | [
2061,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2060,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_sSup' | [] | [
131,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.tendstoUniformlyOn_deriv_of_cthickening_subset | [
{
"state_after": "E : Type u_1\nι : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nU K : Set ℂ\nz : ℂ\nM r δ✝ : ℝ\nφ : Filter ι\nF : ι → ℂ → E\nf g : ℂ → E\nhf : TendstoLocallyUniformlyOn F f φ U\nhF : ∀ᶠ (n : ι) in φ, DifferentiableOn ℂ (F n) U\nδ : ℝ\nhδ : 0 < δ\nh... | [
134,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.mem_support_cycleOf_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.2518697\nα : Type u_1\nβ : Type ?u.2518703\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y : α\nhx : ↑f x ≠ x\n⊢ y ∈ support (cycleOf f x) ↔ SameCycle f x y",
"tactic": "rw [mem_support_cycleOf_iff, and_iff_left (mem_support.2 hx)]"... | [
1160,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haarMeasure_apply | [
{
"state_after": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : T2Space G\ninst✝² : TopologicalGroup G\ninst✝¹ : MeasurableSpace G\ninst✝ : BorelSpace G\nK₀ : PositiveCompacts G\ns : Set G\nhs : MeasurableSet s\n⊢ (↑(Content.outerMeasure (haarContent K₀)) ↑K₀)⁻¹ * ↑↑(Content.measure (haa... | [
618,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_and | [] | [
1474,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
] |
Mathlib/CategoryTheory/SingleObj.lean | CategoryTheory.SingleObj.comp_as_mul | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.deriv | [] | [
137,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
11
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | RieszExtension.exists_top | [
{
"state_after": "𝕜 : Type ?u.268240\nE : Type u_1\nF : Type ?u.268246\nG : Type ?u.268249\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : ConvexCone ℝ E\nf p : E →ₗ.[ℝ] ℝ\nhp_nonneg : ∀ (x : { x // x ∈ p.domain }), ↑x ∈ s → 0 ≤ ↑p x\nhp_dense : ∀ (y : E), ∃ x, ↑x + y ∈ s\nS : Set (E →ₗ.[ℝ] ℝ) := {p | ∀ (x :... | [
809,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_none_right | [
{
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65,
100
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src/lean/Init/Data/Nat/Basic.lean | Nat.ble_eq | [] | [
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124
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Mathlib/Algebra/Order/Floor.lean | abs_sub_round_div_natCast_eq | [
{
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Mathlib/Data/Real/Cardinality.lean | Cardinal.summable_cantor_function | [
{
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99,
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Mathlib/Data/Nat/PartENat.lean | PartENat.coe_lt_iff | [
{
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{
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309,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_append | [
{
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554,
40
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Mathlib/Data/Finset/Basic.lean | Finset.ssubset_iff_exists_cons_subset | [
{
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900,
46
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897,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_eq | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
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Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.comp.get_map | [
{
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}
] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.preimage_ball | [] | [
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38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Rel.lean | Rel.inv_def | [] | [
62,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Mathlib/Order/Monotone/Basic.lean | List.foldr_strictMono | [] | [
735,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
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Mathlib/Algebra/Periodic.lean | Function.Periodic.nsmul_eq | [] | [
270,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
11
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.map_nhds_eq | [
{
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351,
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345,
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Mathlib/Algebra/Field/Basic.lean | same_sub_div | [
{
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}
] | [
157,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.total_ne_of_not_mem_support | [
{
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639,
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Mathlib/Order/Filter/Basic.lean | Filter.bind_mono | [
{
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2758,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_sup_right | [] | [
1033,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
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Mathlib/Logic/Relation.lean | Reflexive.rel_of_ne_imp | [
{
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64,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Std/Data/List/Lemmas.lean | List.Sublist.subset | [] | [
405,
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401,
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Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_stabilizer | [
{
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563,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
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Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_div | [] | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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Mathlib/CategoryTheory/Sites/Coverage.lean | CategoryTheory.Coverage.toGrothendieck_eq_sInf | [
{
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"state_before": "C : Type u_1\ninst✝ : Category C\nK : ... | [
284,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.mul | [
{
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}
] | [
816,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
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Mathlib/Data/Set/Lattice.lean | Set.iUnion_setOf | [
{
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... | [
434,
19
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432,
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Mathlib/Algebra/Order/Group/Abs.lean | neg_abs_le_self | [
{
"state_after": "case inl\nα : Type u_1\ninst✝² : AddGroup α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\na✝ b c a : α\nh : 0 ≤ a\n⊢ -abs a ≤ a\n\ncase inr\nα : Type u_1\ninst✝² : AddGroup α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x x_1 => x ... | [
159,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Data/Fin/Basic.lean | Fin.mk_le_of_le_val | [] | [
298,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
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Mathlib/Data/Complex/ExponentialBounds.lean | Real.log_two_lt_d9 | [
{
"state_after": "no goals",
"state_before": "⊢ 1 / 10 ^ 10 + 287209 / 414355 < 0.6931471808",
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}
] | [
79,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.filter_add_filter | [
{
"state_after": "no goals",
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2081,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2079,
1
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Mathlib/CategoryTheory/Monad/Coequalizer.lean | CategoryTheory.Monad.beckCoequalizer_desc | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.l_le_l_iff | [] | [
836,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_x | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_X | [] | [
1445,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.right_not_mem_Ico | [] | [
145,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Topology/Constructions.lean | Inducing.prod_map | [
{
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807,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.rightRel_apply | [
{
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"tactic": "simp only [mul_inv_eq_iff_eq_mul, Subgroup.coe_inv, eq_inv_mul_iff_mul_eq]"
},
{
"state_after": "no goals",
"state_before": "α : Type u... | [
381,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Submodule.finrank_quotient_add_finrank | [
{
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"st... | [
764,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.isBounded_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.46280\nι : Type ?u.46283\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns✝ s : Set α\n⊢ IsBounded s ↔ ∃ C, ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s → dist x y ≤ C",
"tactic": "rw [isBounded_def, ← Filter.mem_sets, @Pse... | [
694,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_ne_top | [] | [
348,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_subset_of_subgraph | [] | [
760,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.inv_apply | [] | [
402,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection | [
{
"state_after": "case hv\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\np : P\n⊢ p -ᵥ ↑(↑(orthogonalProjec... | [
451,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
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Mathlib/CategoryTheory/Limits/Constructions/FiniteProductsOfBinaryProducts.lean | CategoryTheory.hasFiniteCoproducts_of_has_binary_and_initial | [
{
"state_after": "J : Type v\ninst✝⁴ : SmallCategory J\nC : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : HasInitial C\nn : ℕ\nK : Discrete (Fin n) ⥤ C\n⊢ HasColimit K",
"state_before": "J : Type v\ninst✝⁴ : SmallCategory J\nC : Type u\ninst✝³ : Categ... | [
258,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Std/Data/List/Lemmas.lean | List.chain_of_chain_cons | [] | [
1784,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1783,
1
] |
Mathlib/Data/Rat/BigOperators.lean | Rat.cast_sum | [] | [
39,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.preimage_interior | [] | [
632,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_diag | [] | [
371,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/LinearAlgebra/InvariantBasisNumber.lean | strongRankCondition_iff_succ | [
{
"state_after": "case refine'_1\nR : Type u\ninst✝ : Semiring R\nh : StrongRankCondition R\nn : ℕ\nf : (Fin (n + 1) → R) →ₗ[R] Fin n → R\nhf : Injective ↑f\n⊢ False\n\ncase refine'_2\nR : Type u\ninst✝ : Semiring R\nh : ∀ (n : ℕ) (f : (Fin (n + 1) → R) →ₗ[R] Fin n → R), ¬Injective ↑f\nn m : ℕ\nf : (Fin n → R) ... | [
106,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.nhdsWithin_coe_image | [] | [
293,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
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