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/LinearAlgebra/Basic.lean | LinearMap.map_sum | [] | [
179,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_target_subset_range | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_1\nM : Type u_2\nH : Type u_4\nE' : Type ?u.199765\nM' : Type ?u.199768\nH' : Type ?u.199771\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : Topologi... | [
1117,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.prodCongrRight_apply | [] | [
733,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_smul | [] | [
552,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Computability/Halting.lean | ComputablePred.halting_problem_re | [] | [
236,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.sigma_eq_empty | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : Type ?u.6768\ns s₁ s₂ : Finset ι\nt t₁ t₂ : (i : ι) → Finset (α i)\n⊢ Finset.sigma s t = ∅ ↔ ∀ (i : ι), i ∈ s → t i = ∅",
"tactic": "simp only [← not_nonempty_iff_eq_empty, sigma_nonempty, not_exists, not_and]"
}
] | [
68,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousWithinAt_iff'_left | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.198918\ninst✝¹ : UniformSpace α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\ns : Set β\n⊢ ContinuousWithinAt f s b ↔ Tendsto (fun x => (f x, f b)) (𝓝[s] b) (𝓤 α)",
"tactic": "rw [ContinuousW... | [
1946,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1944,
1
] |
Mathlib/Topology/Order/Basic.lean | Icc_mem_nhdsWithin_Iio | [] | [
487,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Functor.preservesEpimorphisms_of_map_exact | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\ninst✝⁴ : Abelian C\nA : Type u₁\nB : Type u₂\ninst✝³ : Category A\ninst✝² : Category B\ninst✝¹ : Abelian A\ninst✝ : Abelian B\nL : A ⥤ B\nh : ∀ ⦃X Y Z : A⦄ {f : X ⟶ Y} {g : Y ⟶ Z}, Exact f g → Exact (L.map f) (L.map g)\nX✝ Y✝ : A\nf : X✝ ⟶ Y✝\nhf : Epi f\nthis... | [
408,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_elem_of_subsingleton | [
{
"state_after": "m : Type ?u.185871\nn : Type u_1\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : Subsingleton n\nA : Matrix n n R\nk : n\nthis : Unique n\n⊢ det A = A k k",
"state_before": "m : Type ?u.185871\nn : Type u_1\n... | [
128,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/Matrix/Diagonal.lean | Matrix.range_diagonal | [
{
"state_after": "m : Type u_1\nn : Type ?u.147890\ninst✝³ : Fintype m\ninst✝² : Fintype n\nK : Type u\ninst✝¹ : Semifield K\ninst✝ : DecidableEq m\nw : m → K\n⊢ LinearMap.range (↑toLin' (diagonal w)) =\n ⨆ (i : m) (_ : w i ≠ 0), LinearMap.range (LinearMap.stdBasis K (fun x => K) i)",
"state_before": "m ... | [
77,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.hasSum_snd_expSeries_of_smul_comm | [
{
"state_after": "𝕜 : Type u_1\nR : Type u_2\nM : Type u_3\ninst✝¹⁶ : TopologicalSpace R\ninst✝¹⁵ : TopologicalSpace M\ninst✝¹⁴ : Field 𝕜\ninst✝¹³ : CharZero 𝕜\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : Algebra 𝕜 R\ninst✝⁹ : Module R M\ninst✝⁸ : Module Rᵐᵒᵖ M\ninst✝⁷ : SMulCommClass R Rᵐᵒᵖ M\nin... | [
81,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_Ico' | [
{
"state_after": "α : Type u\ninst✝ : DivisionRing α\nx : α\nhx : x ≠ 1\nm n : ℕ\nhmn : m ≤ n\n⊢ (x ^ n - x ^ m) / (x - 1) = (x ^ m - x ^ n) / (1 - x)",
"state_before": "α : Type u\ninst✝ : DivisionRing α\nx : α\nhx : x ≠ 1\nm n : ℕ\nhmn : m ≤ n\n⊢ ∑ i in Ico m n, x ^ i = (x ^ m - x ^ n) / (1 - x)",
"ta... | [
363,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Set/Function.lean | Set.le_piecewise | [] | [
1418,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.self_act_eq_iff_eq | [
{
"state_after": "case mp\nR : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ x ◃ x = y ◃ y → x = y\n\ncase mpr\nR : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ x = y → x ◃ x = y ◃ y",
"state_before": "R : Type u_1\ninst✝ : Rack R\nx y : R\n⊢ x ◃ x = y ◃ y ↔ x = y",
"tactic": "constructor"
},
{
"state_after": "c... | [
315,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.sigmaFiniteTrim_mono | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3499652\nγ : Type ?u.3499655\nδ : Type ?u.3499658\nι : Type ?u.3499661\nR : Type ?u.3499664\nR' : Type ?u.3499667\nm✝ m0✝ : MeasurableSpace α\nμ✝ : Measure α\ns : Set α\nm m₂ m0 : MeasurableSpace α\nμ : Measure α\nhm : m ≤ m0\nhm₂ : m₂ ≤ m\ninst✝ : SigmaFinite (trim μ... | [
4441,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4425,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.coe_image | [] | [
1380,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_neg_add_lt_right | [
{
"state_after": "a b c : Int\nh : a + -c < b\n⊢ a < b + c",
"state_before": "a b c : Int\nh : -c + a < b\n⊢ a < b + c",
"tactic": "rw [Int.add_comm] at h"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : a + -c < b\n⊢ a < b + c",
"tactic": "exact Int.lt_add_of_sub_right... | [
1097,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1095,
11
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_prod_symm | [
{
"state_after": "α : Type u_1\nα' : Type ?u.5365024\nβ : Type u_2\nβ' : Type ?u.5365030\nγ : Type ?u.5365033\nE : Type ?u.5365036\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
770,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indep_of_indep_of_le_left | [] | [
194,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Std/Data/Fin/Lemmas.lean | Fin.ofNat'_zero_val | [] | [
9,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
9,
9
] |
Mathlib/Analysis/Convex/Star.lean | starConvex_sUnion | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.8711\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 F\nx : E\ns t : Set E\nS : Set (Set E)\nhS : ∀ (s : Set E), s ∈ S → StarConvex 𝕜 x s\n⊢ StarConvex 𝕜 x (⋃ (i : ↑S), ↑i)",
"s... | [
141,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Logic/Basic.lean | PLift.down_injective | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b : α\nx✝ : { down := a }.down = { down := b }.down\n⊢ { down := a } = { down := b }",
"tactic": "congr"
}
] | [
80,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ENNReal.measurable_toReal | [] | [
1861,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1860,
1
] |
Mathlib/CategoryTheory/Preadditive/Schur.lean | CategoryTheory.finrank_hom_simple_simple_eq_zero_iff | [
{
"state_after": "C : Type u_3\ninst✝⁹ : Category C\ninst✝⁸ : Preadditive C\n𝕜 : Type u_1\ninst✝⁷ : Field 𝕜\ninst✝⁶ : IsAlgClosed 𝕜\ninst✝⁵ : Linear 𝕜 C\ninst✝⁴ : HasKernels C\nX Y : C\ninst✝³ : FiniteDimensional 𝕜 (X ⟶ X)\ninst✝² : FiniteDimensional 𝕜 (X ⟶ Y)\ninst✝¹ : Simple X\ninst✝ : Simple Y\n⊢ finra... | [
210,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableOn.const_sub | [] | [
640,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_add_of_lt_aleph0 | [
{
"state_after": "case a\nα β : Type u\na : Cardinal\nb : Cardinal\nha : a < ℵ₀\nhb : b < ℵ₀\n⊢ ↑(↑toNat (lift a + lift b)) = ↑(↑toNat a + ↑toNat b)",
"state_before": "α β : Type u\na : Cardinal\nb : Cardinal\nha : a < ℵ₀\nhb : b < ℵ₀\n⊢ ↑toNat (lift a + lift b) = ↑toNat a + ↑toNat b",
"tactic": "apply ... | [
1829,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1823,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubgroup_eq | [] | [
541,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.mono_of_mem | [] | [
359,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_mul_rpow_measure_univ | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.4103402\nG : Type ?u.4103405\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq✝ : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np q : ℝ≥0∞\nhpq : p ≤ q\nf : α → E\nhf : AEStronglyMeasurabl... | [
1093,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Order/Filter/Interval.lean | Filter.HasBasis.tendstoIxxClass | [] | [
122,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Adjunction.injective_of_map_injective | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u_2\ninst✝³ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\ninst✝² : Full G\ninst✝¹ : Faithful G\nI : D\nhI : Injective (G.obj I)\nX Y : D\nf : X ⟶ I\ng : X ⟶ Y\ninst✝ : Mono g\n⊢ ∃ h, g ≫ h = f",
"state_before": "C : Type u₁\ninst✝³ : Category C... | [
335,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_submodule_le_one_iff | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1061352\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module K V\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K V₁\ninst✝¹ : AddCommGroup V'\ninst✝ : Module K ... | [
1254,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.complete_of_convergent_controlled_sequences | [] | [
332,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Set/Basic.lean | Set.eq_empty_or_nonempty | [] | [
626,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.log_neg_I | [
{
"state_after": "no goals",
"state_before": "⊢ log (-I) = -(↑π / 2) * I",
"tactic": "simp [log]"
}
] | [
107,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/List/Sigma.lean | List.lookup_ext | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl l₁✝ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\nl₀ l₁ : List (Sigma β)\nnd₀ : NodupKeys l₀\nnd₁ : NodupKeys l₁\nh : ∀ (x : α) (y : β x), y ∈ dlookup x l₀ ↔ y ∈ dlookup x l₁\nx✝ : Sigma β\na : α\nb : β a\n⊢ { fst := a, snd := b } ∈ l... | [
247,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.blocks_partial_sum | [
{
"state_after": "case zero\nn : ℕ\nc : CompositionAsSet n\ni : ℕ\nh✝ : i < Finset.card c.boundaries\nh : Nat.zero < Finset.card c.boundaries\n⊢ sum (take Nat.zero (blocks c)) = ↑(↑(boundary c) { val := Nat.zero, isLt := h })\n\ncase succ\nn : ℕ\nc : CompositionAsSet n\ni✝ : ℕ\nh✝ : i✝ < Finset.card c.boundarie... | [
958,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.le_tsub_iff_left | [] | [
110,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
11
] |
Mathlib/Data/Bool/AllAny.lean | List.all_iff_forall | [
{
"state_after": "case nil\nα : Type u_1\np✝ : α → Prop\ninst✝ : DecidablePred p✝\nl : List α\na : α\np : α → Bool\n⊢ all [] p = true ↔ ∀ (a : α), a ∈ [] → p a = true\n\ncase cons\nα : Type u_1\np✝ : α → Prop\ninst✝ : DecidablePred p✝\nl✝ : List α\na✝ : α\np : α → Bool\na : α\nl : List α\nih : all l p = true ↔ ... | [
33,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.cast_symm | [] | [
315,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
9
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.tan_angle_add_of_inner_eq_zero | [
{
"state_after": "case pos\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x = 0\n⊢ Real.tan (angle x (x + y)) = ‖y‖ / ‖x‖\n\ncase neg\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : ¬x = ... | [
164,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.dualBasis_apply | [] | [
443,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_sInf | [
{
"state_after": "no goals",
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Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakSpace.map_apply | [] | [
332,
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Mathlib/LinearAlgebra/Alternating.lean | MultilinearMap.domCoprod_alternization_coe | [
{
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Mathlib/Data/Finset/NAry.lean | Finset.image_image₂_distrib_right | [
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Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.Monic.isPrimitive | [
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Mathlib/Data/Num/Lemmas.lean | PosNum.natSize_pos | [
{
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584,
77
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Mathlib/Algebra/Invertible.lean | invOf_mul_self' | [] | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.algebra_adjoin_le_adjoin | [] | [
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Mathlib/Topology/Category/CompHaus/Basic.lean | CompHaus.mono_iff_injective | [
{
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Mathlib/Algebra/Hom/Aut.lean | MulAut.smul_def | [] | [
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Mathlib/Logic/Encodable/Lattice.lean | Encodable.iUnion_decode₂ | [] | [
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.generalizedEigenspace_restrict | [
{
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Mathlib/Algebra/GroupPower/Order.lean | pow_le_pow_iff' | [] | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.HasAntitoneBasis.subbasis_with_rel | [
{
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Mathlib/Data/Nat/Cast/Basic.lean | MonoidWithZeroHom.ext_nat | [] | [
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Mathlib/Data/Set/Function.lean | MonotoneOn.congr | [
{
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Mathlib/Data/PFun.lean | PFun.core_res | [
{
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | continuousAt_extChartAt_symm' | [] | [
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Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.sInf_image_Icc_le | [
{
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Mathlib/Data/Multiset/Basic.lean | Multiset.cons_subset_cons | [] | [
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_C_mul | [
{
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195,
53
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Mathlib/Data/Nat/Prime.lean | Nat.Prime.pow_minFac | [
{
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630,
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Mathlib/Order/LiminfLimsup.lean | Filter.limsup_sdiff | [
{
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Mathlib/Data/List/Infix.lean | List.cons_prefix_iff | [
{
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Mathlib/Data/Finset/Basic.lean | Finset.nonempty_of_ne_empty | [] | [
604,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.norm_weightedSMul_le | [] | [
243,
62
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236,
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Mathlib/Computability/Halting.lean | Nat.Partrec'.comp₁ | [
{
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] | [
368,
55
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Mathlib/Data/Multiset/Basic.lean | Multiset.count_add | [] | [
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15
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Mathlib/MeasureTheory/Function/EssSup.lean | essSup_mono_measure' | [] | [
205,
63
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202,
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Std/Classes/LawfulMonad.lean | SatisfiesM.bind | [
{
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.snoc_smul | [
{
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_dvd_lcm | [] | [
782,
73
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781,
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Mathlib/Algebra/Order/Chebyshev.lean | AntivaryOn.card_smul_sum_le_sum_smul_sum | [
{
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.lift_index_right | [
{
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17
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198,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_one | [
{
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}
] | [
644,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Multiset/Powerset.lean | Multiset.map_single_le_powerset | [
{
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_add | [] | [
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74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_eq_top_iff | [
{
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622,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformly.continuous | [] | [
908,
42
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906,
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Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.exp_def_of_smul_comm | [
{
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1
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Mathlib/Data/Seq/Computation.lean | Computation.Results.len_unique | [
{
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537,
94
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_quotientMap_iff | [
{
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1103,
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Mathlib/Logic/Unique.lean | unique_iff_subsingleton_and_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Sort u\nx✝ : Nonempty (Unique α)\nu : Unique α\n⊢ Subsingleton α ∧ Nonempty α",
"tactic": "constructor <;> exact inferInstance"
},
{
"state_after": "α : Sort u\nx✝ : Subsingleton α ∧ Nonempty α\nhs : Subsingleton α\nhn : Nonempty α\ninhabited_h :... | [
187,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/List/Count.lean | List.count_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\na b : α\n⊢ count a (List.erase [] b) = count a [] - if a = b then 1 else 0",
"tactic": "simp"
},
{
"state_after": "α : Type u_1\nl✝ : List α\ninst✝ : DecidableEq α\na b c : α\nl : List α\n⊢ count a (if... | [
348,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.nat_cast_imK | [] | [
989,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_emod | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a % b % b = a % b",
"tactic": "conv => rhs; rw [← emod_add_ediv a b, add_mul_emod_self_left]"
}
] | [
495,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
494,
9
] |
Mathlib/Data/ZMod/Defs.lean | Fin.left_distrib_aux | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nx✝² x✝¹ x✝ : Fin n\na : ℕ\nha : a < n\nb : ℕ\nhb : b < n\nc : ℕ\nhc : c < n\n⊢ a * (b + c) ≡ a * b + a * c [MOD n]",
"tactic": "rw [mul_add]"
}
] | [
65,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
9
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableAt.add_const | [] | [
210,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffOn_all_iff_nat | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : NormedAdd... | [
696,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | derivWithin.neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL : Filter �... | [
222,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.inf | [] | [
566,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_span_pair | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₂ : Type ?u.166899\nK : Type ?u.166902\nM : Type u_1\nM₂ : Type ?u.166908\nV : Type ?u.166911\nS : Type ?u.166914\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* ... | [
487,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_uniformizer | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\nϖ : R\nhϖ : Irreducible ϖ\n⊢ ↑(addVal R) ϖ = 1",
"tactic": "simpa only [one_mul, eq_self_iff_true, Units.val_one, pow_one, forall_true_left, Nat.cast_one]\n using addVa... | [
433,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.nmem_hyperfilter_of_finite | [] | [
492,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.mem_range | [] | [
107,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.coe_toEmbedding | [] | [
828,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | multiplicity_factor_dvd_iso_eq_multiplicity_of_mem_normalizedFactors | [
{
"state_after": "case h\nM : Type u_1\ninst✝⁸ : CancelCommMonoidWithZero M\nN : Type u_2\ninst✝⁷ : CancelCommMonoidWithZero N\ninst✝⁶ : Unique Mˣ\ninst✝⁵ : Unique Nˣ\ninst✝⁴ : UniqueFactorizationMonoid M\ninst✝³ : UniqueFactorizationMonoid N\ninst✝² : DecidableEq M\ninst✝¹ : DecidableRel fun x x_1 => x ∣ x_1\n... | [
460,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
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