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/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.inf_le_left | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.463632\nδ : Type ?u.463635\ninst✝⁵ : MeasurableSpace α\nμ ν : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : SemilatticeInf β\ninst✝ : ContinuousInf β\nf g : α →ₘ[μ] β\n⊢ ↑(f ⊓ g) ≤ᵐ[μ] ↑f",
... | [
508,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
11
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_eq_zero_of_empty | [] | [
224,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
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Std/Data/Rat/Lemmas.lean | Rat.sub_def' | [
{
"state_after": "no goals",
"state_before": "a b : Rat\n⊢ a - b = mkRat (a.num * ↑b.den - b.num * ↑a.den) (a.den * b.den)",
"tactic": "rw [sub_def, normalize_eq_mkRat]"
}
] | [
234,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
233,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_pred_right | [
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ n * pred m = n * m - n",
"tactic": "rw [Nat.mul_comm, mul_pred_left, Nat.mul_comm]"
}
] | [
704,
49
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
703,
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Mathlib/Order/Disjoint.lean | IsCompl.le_left_iff | [] | [
539,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.coe_restrictScalarsIsometry | [] | [
1261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.isNilpotent_range_toEndomorphism_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk : ℕ\nN : LieSubmodule R L M\n⊢ IsNilpotent R { x // x ∈ Lie... | [
346,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.mul_nonneg | [
{
"state_after": "d : ℕ\na b : ℤ√↑d\n⊢ Nonneg a → Nonneg b → Nonneg (a * b)",
"state_before": "d : ℕ\na b : ℤ√↑d\n⊢ 0 ≤ a → 0 ≤ b → 0 ≤ a * b",
"tactic": "simp_rw [← nonneg_iff_zero_le]"
},
{
"state_after": "no goals",
"state_before": "d : ℕ\na b : ℤ√↑d\n⊢ Nonneg a → Nonneg b → Nonneg (a * b... | [
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19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Continuous.exp | [] | [
162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/Algebra/BigOperators/Fin.lean | List.prod_take_ofFn | [
{
"state_after": "no goals",
"state_before": "case zero\nα : Type u_1\nβ : Type ?u.208372\ninst✝ : CommMonoid α\nn : ℕ\nf : Fin n → α\n⊢ prod (take Nat.zero (ofFn f)) = ∏ j in Finset.filter (fun j => ↑j < Nat.zero) univ, f j",
"tactic": "simp"
},
{
"state_after": "case pos\nα : Type u_1\nβ : Typ... | [
477,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_mul | [] | [
387,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.edist_efixedPoint_lt_top' | [] | [
235,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.is_prime_iff | [
{
"state_after": "case inl\na✝ b : Cardinal\nn m : ℕ\na : Cardinal\nh : ℵ₀ ≤ a\n⊢ Prime a ↔ ℵ₀ ≤ a ∨ ∃ p, a = ↑p ∧ Nat.Prime p\n\ncase inr\na✝ b : Cardinal\nn m : ℕ\na : Cardinal\nh : a < ℵ₀\n⊢ Prime a ↔ ℵ₀ ≤ a ∨ ∃ p, a = ↑p ∧ Nat.Prime p",
"state_before": "a✝ b : Cardinal\nn m : ℕ\na : Cardinal\n⊢ Prime a ... | [
143,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | ContinuousLinearMap.coe_mkOfIsCompactOperator | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
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Mathlib/Topology/Connected.lean | ConnectedComponents.coe_ne_coe | [] | [
1451,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1449,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_le_mul_self_of_le_of_neg_le | [] | [
1184,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAt_apply | [
{
"state_after": "case a\nι : Type u_1\nB : Type u_2\nF : Type u_3\nX : Type ?u.44757\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nZ : FiberBundleCore ι B F\ni : ι\nb : B\na : F\np : TotalSpace Z\n⊢ p.fst ∈ baseSet Z (indexAt Z p.fst)",
"state_before": "ι : Type u_1... | [
693,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
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] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.trim_measurableSet_eq | [
{
"state_after": "no goals",
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"t... | [
4372,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.subset_negative_null_set | [
{
"state_after": "α : Type u_1\nβ : Type ?u.51571\ninst✝² : MeasurableSpace α\ns : SignedMeasure α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nu v w : Set α\nhu : MeasurableSet u\nhv : MeasurableSet v\nhw : MeasurableSet w\nhsu : VectorMeasure.restrict 0 u ≤ VectorMeasure.restrict (... | [
303,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.π_desc | [] | [
983,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
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Mathlib/Order/Lattice.lean | Ne.inf_lt_or_inf_lt | [] | [
560,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
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] |
Std/Data/String/Lemmas.lean | String.data_join | [
{
"state_after": "no goals",
"state_before": "ss : List String\n⊢ (join ss).data = List.join (List.map data ss)",
"tactic": "rw [join_eq]"
}
] | [
481,
15
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.limit_π_isIso_of_is_strict_terminal | [
{
"state_after": "case refine'_1\nC : Type u\ninst✝⁴ : Category C\ninst✝³ : HasStrictTerminalObjects C\nI : C\nJ : Type v\ninst✝² : SmallCategory J\nF : J ⥤ C\ninst✝¹ : HasLimit F\ni : J\nH : (j : J) → j ≠ i → IsTerminal (F.obj j)\ninst✝ : Subsingleton (i ⟶ i)\n⊢ (X : J) → ((Functor.const J).obj (F.toPrefunctor... | [
240,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/Algebra/Star/Pointwise.lean | Set.star_empty | [] | [
45,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | mem_balancedCore_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.1285\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns t : Set E\nx : E\n⊢ x ∈ balancedCore 𝕜 s ↔ ∃ t, Balanced 𝕜 t ∧ t ⊆ s ∧ x ∈ t",
"tactic": "simp_rw [balancedCore, mem_sUnion, mem_setOf_eq, and_assoc]"
}
] | [
85,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.lt_radius_of_isBigO | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.147148\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np : FormalMultilinear... | [
244,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbit_eq_univ | [] | [
176,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.w | [] | [
126,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Data/Finsupp/ToDfinsupp.lean | Dfinsupp.toFinsupp_single | [
{
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"state_before": "ι : Type u_1\nR : Type ?u.8500\nM : Type u_2\ninst✝² : Deci... | [
129,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.toSubalgebra_eq_top | [] | [
632,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
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Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean | CategoryTheory.IsKernelPair.id_of_mono | [] | [
72,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
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Mathlib/Data/Option/Basic.lean | Option.orElse_none' | [
{
"state_after": "no goals",
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"tactic": "cases x <;> rfl"
}
] | [
283,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
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Mathlib/Algebra/Lie/BaseChange.lean | LieAlgebra.ExtendScalars.bracket_leibniz_lie | [
{
"state_after": "R : Type u\nA : Type w\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : LieRing L\ninst✝ : LieAlgebra R L\nx y z : A ⊗[R] L\n⊢ ↑(↑(LieAlgebra.ExtendScalars.bracket' R A L) x) (↑(↑(LieAlgebra.ExtendScalars.bracket' R A L) y) z) =\n ↑(↑(LieAlgebra.ExtendSc... | [
110,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
9
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Mathlib/Data/Set/Basic.lean | Set.subset_univ | [] | [
679,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
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] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.NullMeasurableSet.subtype_coe | [] | [
1413,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1410,
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] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumAssoc_apply_inl_inr | [] | [
362,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
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Mathlib/Topology/Constructions.lean | nhds_inr | [] | [
956,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_toReal_le | [] | [
249,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Topology/Inseparable.lean | SeparationQuotient.image_mk_closure | [] | [
512,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_integral_norm | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\n𝕜 : Type ?u.197555\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\np : ℝ≥0∞\nG : Type ?u.197657\nF' : Type ?u.197660\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : NormedAddCommGroup F'\ninst✝⁴ : NormedSpace ℝ F'\nm ... | [
442,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Topology/NhdsSet.lean | subset_interior_iff_mem_nhdsSet | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7780\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ s ⊆ interior t ↔ t ∈ 𝓝ˢ s",
"tactic": "simp_rw [mem_nhdsSet_iff_forall, subset_interior_iff_nhds]"
}
] | [
60,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
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Mathlib/Order/Hom/Lattice.lean | OrderHomClass.coe_to_lattice_hom | [] | [
1191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
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Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.singleton_mem_nhds_of_units | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
104,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Std/Data/Array/Lemmas.lean | getElem?_fin | [] | [
18,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.coeff_zero_eq_eval_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np✝ q r : R[X]\nx : R\np : R[X]\n⊢ coeff p 0 = coeff p 0 * 0 ^ 0",
"tactic": "simp"
},
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n... | [
504,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_one | [] | [
280,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_apply | [] | [
1696,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1695,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_congr_fun | [] | [
163,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.normalizedFactors_prod | [
{
"state_after": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\na : α\nane0 : a ≠ 0\n⊢ Multiset.prod\n (Multiset.map (↑normalize) (Classical.choose (_ : ∃ f, (∀ (b : α), b ∈ f → Prime b) ∧ Multiset.prod f ~ᵤ a... | [
578,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
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Mathlib/Algebra/Algebra/Subalgebra/Pointwise.lean | Subalgebra.pointwise_smul_toSubring | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/LinearAlgebra/Contraction.lean | zero_prodMap_dualTensorHom | [
{
"state_after": "no goals",
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114,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.nodup_antidiagonal | [] | [
67,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Data/List/MinMax.lean | List.index_of_argmin | [] | [
230,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.coe_range | [
{
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206,
100
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205,
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Mathlib/Topology/OmegaCompletePartialOrder.lean | isωSup_ωSup | [
{
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122,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/GroupTheory/Index.lean | Subgroup.mul_mem_iff_of_index_two | [
{
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205,
69
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199,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | smul_closedBall_one | [
{
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] | [
202,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_eq_bot | [] | [
159,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_zero_iff_degree_lt | [
{
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165,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.congr_fun | [] | [
184,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
11
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Mathlib/Order/Atoms.lean | sSup_atoms_le_eq | [
{
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390,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
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Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.mk_coe | [] | [
797,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
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Mathlib/Data/Set/Intervals/Monotone.lean | Antitone.Iic | [] | [
65,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
11
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Mathlib/RingTheory/Polynomial/Pochhammer.lean | factorial_mul_pochhammer | [
{
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"tactic": "rw_mod_cast [pochhammer_nat_eq_ascFactorial, Nat.factorial_mul_ascFactorial]"
}
] | [
198,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Std/Data/List/Lemmas.lean | List.get_set | [
{
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"tactic": "if h : m = n then subst m; simp else simp [h]"
},
{
"... | [
846,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
844,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.integral_sin_mul_sin_mul_cos_pow_eq | [
{
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154,
87
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95,
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Mathlib/Order/Bounds/Basic.lean | Monotone.image_lowerBounds_subset_lowerBounds_image | [] | [
1278,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
1
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Std/Data/String/Lemmas.lean | String.Pos.zero_addString_byteIdx | [
{
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"tactic": "simp only [addString_byteIdx, byteIdx_zero, Nat.zero_add]"
}
] | [
131,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
130,
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] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_strictAntiOn | [] | [
636,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.complex_ofReal_eval_U | [] | [
62,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.nat_odd_mul_antiperiodic | [
{
"state_after": "no goals",
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"tactic": "rw [← add_assoc, h, h.periodic.nat_mul]"
}
] | [
394,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.star_smul | [] | [
680,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.compl₁₂_id_id | [
{
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358,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteVerts_inter_verts_set_right_eq | [
{
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"tactic": "ext <;> simp (config := { contextual := true }) [imp_false]"
}
] | [
1254,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1253,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.tendsto_nhdsWithin_nhdsWithin | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.199771\ninst✝¹ : PseudoEMetricSpace α\nx✝² y z : α\nε✝ ε₁ ε₂ : ℝ≥0∞\ns t✝ : Set α\ninst✝ : PseudoEMetricSpace β\nf : α → β\nt : Set β\na : α\nb : β\nε : ℝ≥0∞\nx✝¹ : 0 < ε\nδ : ℝ≥0∞\nx✝ : 0 < δ\nx : α\n⊢ edist x a < δ → x ∈ s → edist (f x) b < ε ∧ f x ∈ t ↔ x... | [
669,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
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Mathlib/MeasureTheory/Integral/RieszMarkovKakutani.lean | rieszContentAux_sup_le | [
{
"state_after": "case h\nX : Type u_1\ninst✝ : TopologicalSpace X\nΛ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0\nK1 K2 : Compacts X\n⊢ ∀ (ε : ℝ≥0), 0 < ε → rieszContentAux Λ (K1 ⊔ K2) ≤ rieszContentAux Λ K1 + rieszContentAux Λ K2 + ε",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\nΛ : (X →ᵇ ℝ≥0) →ₗ[ℝ≥0] ℝ≥0\nK1... | [
116,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | HomotopyCategory.quotient_map_out_comp_out | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : Preadditive V\nc : ComplexShape ι\nC D E : HomotopyCategory V c\nf : C ⟶ D\ng : D ⟶ E\n⊢ (quotient V c).map (Quot.out f ≫ Quot.out g) = f ≫ g",
"tactic": "simp"
}
] | [
113,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsClosed.mem_of_ge_of_forall_exists_gt | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁶ : ConditionallyCompleteLinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : ConditionallyCompleteLinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology β\ninst✝ : Nonempty γ\na b : α\ns : Set α\nhs : IsClosed (s ∩... | [
357,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.Integrable.withDensityᵥ_trim_absolutelyContinuous | [
{
"state_after": "α : Type u_1\nβ : Type ?u.164970\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf g : α → E\nm m0 : MeasurableSpace α\nμ : Measure α\nhm : m ≤ m0\nhfi : Integrable f\nj : Set α\nhj₁ : MeasurableSet j\nh... | [
210,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.exists_upcrossings_of_not_bounded_under | [
{
"state_after": "α : Type ?u.206583\nβ : Type ?u.206586\nγ : Type ?u.206589\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx✝ y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Type u_1\nl : Filter ι\nx : ι → ℝ\nhf : liminf (fun i => ↑(↑Real.nnabs (x i))) l ≠ ⊤\nhbdd : (¬IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun i => x i) ∨ ¬IsBoundedUnd... | [
752,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitFlipCompLimIsoLimitCompLim_hom_π_π | [
{
"state_after": "J K : Type v\ninst✝⁶ : SmallCategory J\ninst✝⁵ : SmallCategory K\nC : Type u\ninst✝⁴ : Category C\nF : J ⥤ K ⥤ C\ninst✝³ : HasLimitsOfShape J C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimitsOfShape (J × K) C\ninst✝ : HasLimitsOfShape (K × J) C\nj : J\nk : K\n⊢ ((limitUncurryIsoLimitCompLim... | [
240,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.predAbove_left_monotone | [
{
"state_after": "n m : ℕ\ni : Fin (n + 1)\na b : Fin n\nH : a ≤ b\n⊢ (if h : ↑castSucc a < i then pred i (_ : i ≠ 0) else castLT i (_ : ↑i < n)) ≤\n if h : ↑castSucc b < i then pred i (_ : i ≠ 0) else castLT i (_ : ↑i < n)",
"state_before": "n m : ℕ\ni : Fin (n + 1)\na b : Fin n\nH : a ≤ b\n⊢ (fun p => ... | [
2288,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2280,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.fst_sumFinsuppLEquivProdFinsupp | [] | [
946,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝³ : Category C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ coprod.inl ≫ (pushoutZeroZeroIso X Y).inv = pushout.inl",
"tactic": "simp [Iso.comp_inv_eq]"
}
] | [
225,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.le_liminf_of_le | [] | [
449,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_singleton' | [] | [
1803,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Data/DList/Basic.lean | Std.DList_lazy | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iInter₂_div_subset | [] | [
801,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLUB_singleton | [] | [
625,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
624,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.radius_eq_top_of_forall_nnreal_isBigO | [] | [
170,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basisFun_apply | [
{
"state_after": "no goals",
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285,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.exists_finset_of_mem_supr' | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_3\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nι : Type u_1\nf : ι → IntermediateField F E\nx : E\nhx : x ∈ ⨆ (i : ι), f i\ni : ι\n⊢ f i ≤ ⨆ (i : (i : ι) × { x // x ∈ f i }), F⟮↑i.snd⟯",
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651,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_ofScientific_of_true | [
{
"state_after": "α : Type u_1\ninst✝ : DivisionRing α\nσα : OfScientific α\nx✝¹ x✝ : ℕ\nnum✝ : ℤ\ndenom✝ : ℕ\nσh : OfScientific.ofScientific = fun m s e => ↑(Rat.ofScientific m s e)\ninv✝ : Invertible ↑denom✝\neq : ↑(mkRat (↑x✝¹) (10 ^ x✝)) = ↑num✝ * ⅟↑denom✝\n⊢ ↑(mkRat (↑x✝¹) (10 ^ x✝)) = ↑num✝ * ⅟↑denom✝",
... | [
596,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balancedSz_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.7958\nl : ℕ\n⊢ BalancedSz l 0 ↔ l ≤ 1",
"tactic": "simp (config := { contextual := true }) [BalancedSz]"
}
] | [
198,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/WithBot.lean | WithTop.lt_top_iff_ne_top | [] | [
1090,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
11
] |
Mathlib/Algebra/Group/Conj.lean | ConjClasses.mem_carrier_mk | [] | [
317,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Topology/ContinuousOn.lean | tendsto_nhdsWithin_iff | [] | [
462,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_to_inv | [] | [
1059,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Data/Real/Basic.lean | Real.cauchy_sub | [
{
"state_after": "x y : ℝ\na b : Cauchy abs\n⊢ ({ cauchy := a } - { cauchy := b }).cauchy = ({ cauchy := a } + -{ cauchy := b }).cauchy",
"state_before": "x y : ℝ\na b : Cauchy abs\n⊢ ({ cauchy := a } - { cauchy := b }).cauchy = { cauchy := a }.cauchy - { cauchy := b }.cauchy",
"tactic": "rw [sub_eq_add... | [
167,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Ring/Defs.lean | mul_add_eq_mul_add_iff_sub_mul_add_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonUnitalNonAssocRing α\na b c d e : α\n⊢ a * e + c = b * e + d ↔ a * e + c = d + b * e",
"tactic": "simp [add_comm]"
},
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ :... | [
393,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
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