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/Polynomial/Expand.lean | Polynomial.of_irreducible_expand_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : ℕ\nhp : p ≠ 0\nf : R[X]\nn : ℕ\nhf : Irreducible (↑(expand R (p ^ Nat.zero)) f)\n⊢ Irreducible f",
"tactic": "rwa [pow_zero, expand_one] at hf"
},
{
"state_after": "R : Type u\ninst✝¹ : CommRin... | [
294,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
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Mathlib/Logic/Function/Basic.lean | Function.injective_surjInv | [] | [
516,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
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src/lean/Init/SimpLemmas.lean | eq_true_of_decide | [] | [
23,
32
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
22,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_Iio | [] | [
151,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInvEquiv_symm_eq_inv | [
{
"state_after": "no goals",
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"tactic": "rw [← mul_right_inj (x : M), mul_right_inv, mul_leftInvEquiv_symm]"
}
] | [
253,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_succ | [] | [
123,
6
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122,
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Mathlib/Topology/ContinuousOn.lean | ContinuousOn.piecewise | [] | [
1165,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
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Mathlib/Topology/Instances/Discrete.lean | discreteTopology_iff_orderTopology_of_pred_succ' | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : PartialOrder α\ninst✝³ : PredOrder α\ninst✝² : SuccOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : NoMaxOrder α\nh : DiscreteTopology α\n⊢ inst✝⁵ = generateFrom {s | ∃ a, s = Ioi a ∨ s = Iio a}\n\ncase refine'_2\nα : Type u_1\ninst✝⁵ ... | [
69,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/MeasureTheory/Covering/DensityTheorem.lean | IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝⁴ : IsUnifLocDoublingMeasure μ\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nE : Type ?u.1198936\ninst✝ : NormedA... | [
154,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Std/Data/Int/Lemmas.lean | Int.succ_ofNat_pos | [] | [
851,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
850,
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Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.compatiblePreservingOfFlat | [
{
"state_after": "case Compatible\nC✝ : Type u₁\ninst✝⁵ : Category C✝\nD✝ : Type u₂\ninst✝⁴ : Category D✝\nA : Type u₃\ninst✝³ : Category A\nJ : GrothendieckTopology C✝\nK✝ : GrothendieckTopology D✝\nL : GrothendieckTopology A\nG✝ : C✝ ⥤ D✝\nhG : CompatiblePreserving K✝ G✝\nℱ : SheafOfTypes K✝\nZ : C✝\nT : Pres... | [
159,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/IntegrallyClosed.lean | isIntegrallyClosed_iff_isIntegralClosure | [
{
"state_after": "case mp\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\n⊢ (∀ {x : K}, IsIntegral R x → ∃ y, ↑(algebraMap R K) y = x) → IsIntegralClosure R R K\n\ncase mpr\nR : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsD... | [
78,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.limsup_trim | [
{
"state_after": "α : Type u_1\nE : Type ?u.3170438\nF : Type ?u.3170441\nG : Type ?u.3170444\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nhm : m ≤ m0\nf : α → ℝ≥0∞\nhf : Measurable f\n⊢ sInf {a | ∀ᵐ (n :... | [
975,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.sub_congr_left | [] | [
1789,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1788,
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Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_add_le_tsub_add_tsub | [
{
"state_after": "α : Type u_1\nβ : Type ?u.17481\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ a + b - d - c ≤ a - c + (b - d)",
"state_before": "α : Type u_1\nβ : Type ?u.1748... | [
180,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
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Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.pos | [] | [
124,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_modEq_x2n_add | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn j : ℕ\n⊢ xn a1 n * xn a1 (n + j) + (Pell.d a1 * yn a1 n * yn a1 (n + j) + xn a1 j) ≡ 0 + 0 [MOD xn a1 n]",
"state_before": "a : ℕ\na1 : 1 < a\nn j : ℕ\n⊢ xn a1 (2 * n + j) + xn a1 j ≡ 0 [MOD xn a1 n]",
"tactic": "rw [two_mul, add_assoc, xn_add, add_assoc, ← zero_ad... | [
605,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasInitialChangeDiagram | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX : C\nF₁ : Discrete PEmpty ⥤ C\nF₂ : Discrete PEmpty ⥤ C\nh : HasColimit F₁\n⊢ (X : Discrete PEmpty) → F₂.obj X ⟶ ((Functor.const (Discrete PEmpty)).obj (colimit F₁)).obj X",
"tactic": "aesop_cat"
},
{
"state_after":... | [
286,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.lt_map_map_zero | [] | [
516,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.zero_modByMonic | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Ring R\np✝ q p : R[X]\n⊢ (if h : Monic p then\n (if h_1 : degree p ≤ degree 0 ∧ 0 ≠ 0 then\n let z := ↑C (leadingCoeff 0) * X ^ (natDegree 0 - natDegree p);\n let_fun _wf := (_ : degree (0 - ↑C (lead... | [
178,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_eq_of_range_eq | [] | [
1698,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_ne_zero_iff | [] | [
854,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.map_pullback | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nX✝ Y✝ Z✝ : C\nD : Type u₂\ninst✝³ : Category D\ninst✝² : HasPullbacks C\nX Y Z W : C\nf : X ⟶ Y\ng : X ⟶ Z\nh : Y ⟶ W\nk : Z ⟶ W\ninst✝¹ : Mono h\ninst✝ : Mono g\ncomm : f ≫ h = g ≫ k\nt : IsLimit (PullbackCone.mk f g comm)\n⊢ ∀ (p : Subobject Y), (map g).obj ... | [
666,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
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] |
Mathlib/Data/Set/Function.lean | Set.BijOn.comp | [] | [
977,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.C_comp | [] | [
551,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
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Mathlib/Logic/Unique.lean | PUnit.default_eq_unit | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | LinearIsometryEquiv.reflections_generate_dim_aux | [
{
"state_after": "case zero\n𝕜 : Type ?u.1021326\nE : Type ?u.1021329\nF : Type u_1\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✝ : FiniteDimensional ℝ F\nn : ℕ\nφ✝ : F ≃ₗᵢ[ℝ] F\nhn✝ ... | [
1207,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
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Mathlib/LinearAlgebra/Basis.lean | Basis.map_equiv | [
{
"state_after": "case a\nι : Type u_1\nι' : Type u_4\nR : Type u_2\nR₂ : Type ?u.557598\nK : Type ?u.557601\nM : Type u_3\nM' : Type u_5\nM'' : Type ?u.557610\nV : Type u\nV' : Type ?u.557615\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\ninst✝² : Module R M'\nb... | [
700,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
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Mathlib/LinearAlgebra/Dual.lean | Submodule.sup_dualAnnihilator_le_inf | [
{
"state_after": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nW U V : Submodule R M\n⊢ U ⊓ V ≤ dualCoannihilator (dualAnnihilator U) ⊓ dualCoannihilator (dualAnnihilator V)",
"state_before": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddComm... | [
925,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | ContDiff.norm | [] | [
215,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/Logic/IsEmpty.lean | isEmpty_subtype | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort ?u.2853\nγ : Sort ?u.2856\np : α → Prop\n⊢ IsEmpty (Subtype p) ↔ ∀ (x : α), ¬p x",
"tactic": "simp only [← not_nonempty_iff, nonempty_subtype, not_exists]"
}
] | [
166,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.im_to_real | [] | [
844,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
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Mathlib/Analysis/Normed/Field/Basic.lean | nnnorm_pow_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.129705\nγ : Type ?u.129708\nι : Type ?u.129711\ninst✝¹ : SeminormedRing α\ninst✝ : NormOneClass α\na : α\nn : ℕ\n⊢ ‖a ^ Nat.zero‖₊ ≤ ‖a‖₊ ^ Nat.zero",
"tactic": "simp only [Nat.zero_eq, pow_zero, nnnorm_one, le_rfl]"
}
] | [
372,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.of_le_succ | [] | [
237,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/Logic/Basic.lean | exists_or_eq_left | [] | [
790,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
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] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.95878\nE : Type u_2\nF : Type ?u.95884\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nht : NullMeasurableSet t\nhts : s ⊆ t\nh't : ∀ᵐ ... | [
380,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
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Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.Γ_map_op | [] | [
294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/RingTheory/NonZeroDivisors.lean | mul_left_mem_nonZeroDivisors_eq_zero_iff | [
{
"state_after": "no goals",
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60,
62
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousLinearMap.continuous_integral_comp_L1 | [
{
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1077,
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Mathlib/Order/CompleteLattice.lean | le_iSup | [] | [
752,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivComm_symm | [
{
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612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
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] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | completeSpace_coe_iff_isComplete | [
{
"state_after": "no goals",
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"tactic": "rw [Subtype.range_coe]"
}
] | [
325,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | le_mul_of_le_one_right | [
{
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"state_before": "α : Type u\nβ : Type ?u.41755\ninst✝ : OrderedRing α\na b c d : α\nha : a ≤ 0\nh : b ≤ 1\n⊢ a ≤ a * b",
"tactic": "simpa only [mul_one] using mul_le_mul_of_nonpos_left h ha"
}
] | [
405,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_apply_apply_zpow_self | [
{
"state_after": "ι : Type ?u.2245333\nα : Type u_1\nβ : Type ?u.2245339\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y : α\nf : Perm α\nx : α\nk : ℤ\n⊢ ↑f (↑(f ^ k) x) = ↑(f ^ (k + 1)) x\n\nι : Type ?u.2245333\nα : Type u_1\nβ : Type ?u.2245339\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g ... | [
1021,
19
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1017,
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Mathlib/Data/List/Basic.lean | List.foldr_cons | [] | [
2412,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2410,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuous_iff_continuous_comp_left | [
{
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Mathlib/Logic/Relation.lean | Relation.TransGen.mono | [] | [
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Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_neg | [
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209,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.coe_vadd | [] | [
524,
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523,
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_iff_convex | [] | [
442,
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441,
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.sum_hom_add_index | [] | [
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Hom.ext | [] | [
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_image_linearMap | [
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Mathlib/Algebra/Hom/Group.lean | map_mul_eq_one | [
{
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Mathlib/Data/List/Basic.lean | List.zipRight_cons_cons | [] | [
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Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_lt_of_one_le' | [] | [
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75
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806,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_conj | [
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622,
96
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_neg_eq_smul | [
{
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Iic_eq_integral_Iio | [] | [
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Mathlib/Topology/MetricSpace/Baire.lean | dense_iInter_of_Gδ | [
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Mathlib/Data/Real/EReal.lean | EReal.sign_mul | [
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.tendsto_at | [] | [
180,
82
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Mathlib/Data/List/Cycle.lean | Cycle.not_mem_nil | [] | [
537,
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536,
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Mathlib/MeasureTheory/Lattice.lean | AEMeasurable.sup | [] | [
161,
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159,
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Std/Data/List/Lemmas.lean | List.eq_nil_or_concat | [] | [
314,
49
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310,
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Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.mul | [] | [
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13
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Mathlib/Data/Fintype/Card.lean | finite_iff_nonempty_fintype | [] | [
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | measurableSet_of_differentiableWithinAt_Ici | [
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Mathlib/Data/Set/Basic.lean | Set.nontrivial_of_mem_mem_ne | [] | [
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22
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Mathlib/Data/Multiset/Bind.lean | Multiset.prod_bind | [
{
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... | [
190,
74
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Mathlib/Data/List/Zip.lean | List.map_snd_zip | [
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.smul_const | [] | [
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Mathlib/Analysis/MeanInequalities.lean | Real.inner_le_Lp_mul_Lq_tsum_of_nonneg | [
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_mul_of_one_le_right' | [] | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_def | [] | [
469,
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468,
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Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.add_omega | [
{
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_of_mem_maximalAtlas | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_congr | [
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Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.ofQuotientStabilizer_mem_orbit | [] | [
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Mathlib/Topology/Algebra/ConstMulAction.lean | continuousAt_const_smul_iff₀ | [] | [
316,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | SemilinearMapClass.bound_of_shell_semi_normed | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospan_map_inr | [] | [
242,
54
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Mathlib/Order/MinMax.lean | Max.right_comm | [] | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_cons_some | [] | [
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Mathlib/Order/LiminfLimsup.lean | Filter.cofinite.blimsup_set_eq | [
{
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Mathlib/Algebra/BigOperators/Basic.lean | ofAdd_list_prod | [
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Mathlib/Algebra/Star/Basic.lean | eq_star_of_eq_star | [
{
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104,
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasurableSet.nullMeasurableSet | [] | [
107,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.sup_eq_union | [] | [
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93
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Mathlib/Data/Set/Basic.lean | Set.forall_of_forall_insert | [] | [
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Mathlib/Data/Seq/Parallel.lean | Computation.exists_of_mem_parallel | [
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_smul_closedBall | [
{
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Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.Functor.map_neg | [] | [
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.image | [
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Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_mul | [
{
"state_after": "case a.h\nα : Type u_1\nβ : Type ?u.17976\nm : Type ?u.17979\nn : Type u_2\nR : Type ?u.17985\ninst✝² : Semiring α\ninst✝¹ : Fintype n\ninst✝ : AddGroup n\nv w : n → α\ni j : n\n⊢ (circulant v ⬝ circulant w) i j = circulant (mulVec (circulant v) w) i j",
"state_before": "α : Type u_1\nβ : ... | [
134,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_attach | [
{
"state_after": "ι : Type ?u.328587\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\na : α\nh : a ∈ l\nthis : ∃ a_1, a_1 ∈ attach l ∧ ↑a_1 = a\n⊢ { val := a, property := h } ∈ attach l",
"state_before": "ι : Type ?u.328587\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\... | [
3137,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3133,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.rel_flip_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.440899\nγ : Type ?u.440902\nδ : Type ?u.440905\nr : α → β → Prop\np : γ → δ → Prop\ns t : Multiset α\n⊢ Rel (flip fun x x_1 => x = x_1) s t ↔ s = t",
"tactic": "rw [rel_flip, rel_eq, eq_comm]"
}
] | [
2709,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2708,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.WF.mk' | [
{
"state_after": "case refine_1\nα : Type u_1\nβ : Type u_2\nn : Nat\ninst✝³ : BEq α\ninst✝² : Hashable α\nh✝ : 0 < n\ninst✝¹ : LawfulHashable α\ninst✝ : PartialEquivBEq α\nx✝ : AssocList α β\nh : x✝ ∈ (Bucket.mk n).val.data\n⊢ List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) (AssocList.toList x✝)\n\ncase re... | [
44,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.HasBasis.liminf_eq_iSup_iInf | [] | [
768,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/Part.lean | Part.dom_iff_mem | [] | [
104,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
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