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/FiniteType.lean | MonoidAlgebra.finiteType_iff_fg | [] | [
611,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
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Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.prop | [] | [
120,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbs_empty | [] | [
69,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.Regular.coe_compl | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Order/Hom/Basic.lean | RelEmbedding.toOrderHom_injective | [] | [
770,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
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Mathlib/Data/Vector3.lean | vectorAll_iff_forall | [] | [
255,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
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Mathlib/Algebra/Quaternion.lean | Quaternion.zero_re | [] | [
849,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Field/Basic.lean | div_nonneg_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.136348\nα : Type u_1\nβ : Type ?u.136354\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\n⊢ 0 ≤ a / b ↔ 0 ≤ a ∧ 0 ≤ b ∨ a ≤ 0 ∧ b ≤ 0",
"tactic": "simp [division_def, mul_nonneg_iff]"
}
] | [
689,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | Continuous.tendsto | [] | [
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49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_arrow_comp_eq_zero | [
{
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"state_before": "C : Type u\ninst✝⁴ : Category C\nX✝ Y✝ Z✝ : C\nf✝ : X✝ ⟶ Y✝\ninst✝³ : HasImage f✝\ninst✝² : HasZeroMorphisms C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝¹ : HasImage f\ninst✝ : Epi (factorThruImageSubobject f)\nh : f ≫ g = 0\n⊢ factorThruImageSubobject f ≫ arrow (i... | [
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Mathlib/Order/Bounds/Basic.lean | upperBounds_Ioo | [] | [
772,
33
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771,
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Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.measure_inter_notConvergentSeq_eq_zero | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nι : Type u_1\nm : MeasurableSpace α\ninst✝² : MetricSpace β\nμ : Measure α\nn✝ : ℕ\ni j : ι\ns : Set α\nε : ℝ\nf : ι → α → β\ng : α → β\ninst✝¹ : SemilatticeSup ι\ninst✝ : Nonempty ι\nn : ℕ\nhfg : ↑↑μ {a | ¬(a ∈ s → ∀ (ε : ℝ), ε > 0 → ∃ N, ∀ (n : ι), n ≥ N → dist (f... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/TuringMachine.lean | Turing.TM2to1.stk_nth_val | [
{
"state_after": "K : Type u_1\nΓ : K → Type u_2\nL : ListBlank ((k : K) → Option (Γ k))\nk : K\nS : List (Γ k)\nn : ℕ\nhL : ListBlank.map (proj k) L = ListBlank.mk (List.reverse (List.map some S))\n⊢ Option.iget (Option.map some (List.get? (List.reverse S) n)) = List.get? (List.reverse S) n",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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src/lean/Init/Data/Nat/Div.lean | Nat.mod_eq_sub_mod | [] | [
120,
52
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Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_eq_zero_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b : α\nh : gcd a b = 0\nca : α\nha : a = gcd a b * ca\n⊢ a = 0 ∧ b = 0",
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"tacti... | [
402,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Basic.lean | Int.cast_sum | [] | [
2250,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Parity.lean | Even.tsub | [
{
"state_after": "case intro\nF : Type ?u.56414\nα : Type u_1\nβ : Type ?u.56420\nR : Type ?u.56423\ninst✝³ : CanonicallyLinearOrderedAddMonoid α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\ninst✝ : ContravariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\nn : α\nhn : Even n\na : α\n⊢ Even (a + a - n)",
... | [
231,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.subtype | [] | [
1184,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.sum_repr | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.811955\n𝕜 : Type u_2\ninst✝⁹ : IsROrC 𝕜\nE : Type u_3\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.811984\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type ?u.812002\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ :... | [
441,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
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Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.dvd | [
{
"state_after": "R : Type ?u.83807\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n m : ℕ\nhn : ∃ p k, Nat.Prime p ∧ 0 < k ∧ p ^ k = n\nhm : m ∣ n\nhm₁ : m ≠ 1\n⊢ ∃ p k, Nat.Prime p ∧ 0 < k ∧ p ^ k = m",
"state_before": "R : Type ?u.83807\ninst✝ : CommMonoidWithZero R\nn✝ p : R\nk n m : ℕ\nhn : IsPrimePow n\nh... | [
107,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.ediv_dvd_of_dvd | [
{
"state_after": "case inl\na b : ℤ\nn : ℕ\nt : ℤ\nhst : 0 ∣ t\n⊢ t / 0 ∣ t\n\ncase inr\na b : ℤ\nn : ℕ\ns t : ℤ\nhst : s ∣ t\nhs : s ≠ 0\n⊢ t / s ∣ t",
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"tactic": "rcases eq_or_ne s 0 with (rfl | hs)"
},
{
"state_after": "case ... | [
494,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.tendsto_cobounded | [] | [
236,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/MeasureTheory/Group/Arithmetic.lean | Finset.measurable_prod | [
{
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941,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_single | [
{
"state_after": "l : Type ?u.165555\nm : Type u_1\nn : Type ?u.165561\no : Type ?u.165564\nm' : o → Type ?u.165569\nn' : o → Type ?u.165574\nR : Type ?u.165577\nS : Type ?u.165580\nα : Type v\nβ : Type w\nγ : Type ?u.165587\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : DecidableEq m\ninst✝ : NonUnitalNonAs... | [
841,
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837,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mem_span_iff_total | [] | [
660,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_range_eq_span_range_vsub_right_ne | [
{
"state_after": "k : Type u_2\nV : Type u_1\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\ni₀ : ι\n⊢ Submodule.span k ((fun x => x -ᵥ p i₀) '' (p '' (univ \\ {i₀}))) = Submodule.span k (range fun i => p ↑i -ᵥ p i₀)",
"state_be... | [
1143,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
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Mathlib/Algebra/Group/Basic.lean | eq_div_of_mul_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.58698\nβ : Type ?u.58701\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a * c = b\n⊢ a = b / c",
"tactic": "simp [← h]"
}
] | [
770,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofMkLEMk_comp_ofMkLEMk | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nX Y Z : C\nD : Type u₂\ninst✝³ : Category D\nB A₁ A₂ A₃ : C\nf : A₁ ⟶ B\ninst✝² : Mono f\ng : A₂ ⟶ B\ninst✝¹ : Mono g\nh : A₃ ⟶ B\ninst✝ : Mono h\nh₁ : mk f ≤ mk g\nh₂ : mk g ≤ mk h\n⊢ (underlyingIso f).inv ≫ underlying.map (LE.le.hom h₁ ≫ LE.le.hom h₂) ≫ (und... | [
449,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_mono' | [] | [
380,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
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Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.independent_of_dfinsupp_sumAddHom_injective | [
{
"state_after": "ι : Type u_2\nR : Type ?u.535889\nS : Type ?u.535892\nM : ι → Type ?u.535897\nN : Type u_1\ndec_ι : DecidableEq ι\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\np : ι → AddSubmonoid N\nh : Function.Injective ↑(sumAddHom fun i => AddSubmonoid.subtype (p i))\n⊢ Independent (... | [
461,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
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Mathlib/Data/Matrix/Basic.lean | Equiv.mapMatrix_symm | [] | [
1387,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1386,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.im_eq_zero_of_le | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6777307\ninst✝ : IsROrC K\na : K\nh : ‖a‖ ≤ ↑re a\n⊢ ↑im a = 0",
"tactic": "simpa only [mul_self_norm a, normSq_apply, self_eq_add_right, mul_self_eq_zero]\n using congr_arg (fun z => z * z) ((re_le_norm a).antisymm h)"
}
] | [
742,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
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Mathlib/Data/Complex/Exponential.lean | Complex.exp_int_mul | [
{
"state_after": "case ofNat\nx y z : ℂ\na✝ : ℕ\n⊢ exp (↑(Int.ofNat a✝) * z) = exp z ^ Int.ofNat a✝\n\ncase negSucc\nx y z : ℂ\na✝ : ℕ\n⊢ exp (↑(Int.negSucc a✝) * z) = exp z ^ Int.negSucc a✝",
"state_before": "x y z : ℂ\nn : ℤ\n⊢ exp (↑n * z) = exp z ^ n",
"tactic": "cases n"
},
{
"state_after":... | [
560,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieHom.mem_idealRange_iff | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
970,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.toIsometryEquiv_refl | [] | [
509,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
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Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.le_tsub_iff_right | [
{
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"state_bef... | [
116,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
11
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_C_mul_T_ite | [
{
"state_after": "no goals",
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"tactic": "split_ifs with h <;>\n simp only [h, map_zero, MulZeroClass.zero_mul, degree_zero, degree_C_mul_T, Ne.def,\n not_false_iff]"
}
] | [
518,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
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Mathlib/Data/Finmap.lean | Finmap.union_cancel | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.mem_vsub | [] | [
1455,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.colorable_chromaticNumber_of_fintype | [
{
"state_after": "case intro\nV : Type u\nG✝ : SimpleGraph V\nα : Type v\nC : Coloring G✝ α\nG : SimpleGraph V\ninst✝ : Finite V\nval✝ : Fintype V\n⊢ Colorable G (chromaticNumber G)",
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57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.mk' | [
{
"state_after": "G : Type u_2\nH : Type ?u.2056\nα : Type u_1\nβ : Type ?u.2062\nE : Type ?u.2065\ninst✝⁶ : Group G\ninst✝⁵ : Group H\ninst✝⁴ : MulAction G α\ninst✝³ : MeasurableSpace α\ninst✝² : MulAction H β\ninst✝¹ : MeasurableSpace β\ninst✝ : NormedAddCommGroup E\ns t : Set α\nμ : Measure α\nh_meas : NullM... | [
88,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.fixedPoint_unique | [] | [
320,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.codisjoint_coe | [
{
"state_after": "no goals",
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"tactic": "simp [disjoint_iff, codisjoint_iff, SetLike.ext'_iff]"
... | [
624,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackAssoc_hom_snd_fst | [
{
"state_after": "C : Type u\ninst✝⁷ : Category C\nD : Type u₂\ninst✝⁶ : Category D\nW X Y Z X₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝⁵ : HasPullback f₁ f₂\ninst✝⁴ : HasPullback f₃ f₄\ninst✝³ : HasPullback (pullback.snd ≫ sorryAx (sorryAx C true ⟶ Y₂) true) f₄\ninst✝² : H... | [
2423,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2416,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_one | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\n⊢ a * Nat.rawCast 1 = a",
"tactic": "simp [Nat.rawCast]"
}
] | [
356,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_eq_of_subset' | [] | [
989,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
src/lean/Init/Control/Lawful.lean | seqRight_eq_bind | [
{
"state_after": "m : Type u_1 → Type u_2\nα β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\ny : m β\n⊢ (Seq.seq (const α id <$> x) fun x => y) = do\n let _ ← x\n y",
"state_before": "m : Type u_1 → Type u_2\nα β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nx : m α\ny : m β\n⊢ ... | [
82,
50
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
80,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_diff_right | [] | [
1848,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1847,
1
] |
Mathlib/Data/Set/Finite.lean | Finset.finite_toSet | [] | [
534,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Order/Compare.lean | cmp_eq_gt_iff | [] | [
240,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.nonempty | [] | [
178,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotEquivQuotSupₐ | [] | [
760,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Data/Set/Basic.lean | AntitoneOn.union | [] | [
2924,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2922,
1
] |
Mathlib/Order/Monotone/Basic.lean | MonotoneOn.reflect_lt | [] | [
765,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_im | [
{
"state_after": "no goals",
"state_before": "⊢ Continuous fun q => im q",
"tactic": "simpa only [← sub_self_re] using continuous_id.sub (continuous_coe.comp continuous_re)"
}
] | [
229,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.monotone_mem | [] | [
216,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_modEq' | [
{
"state_after": "case nil\nn b b' k : ℕ\nh : b ≡ b' [MOD k]\n⊢ ofDigits b [] ≡ ofDigits b' [] [MOD k]\n\ncase cons\nn b b' k : ℕ\nh : b ≡ b' [MOD k]\nd : ℕ\nL : List ℕ\nih : ofDigits b L ≡ ofDigits b' L [MOD k]\n⊢ ofDigits b (d :: L) ≡ ofDigits b' (d :: L) [MOD k]",
"state_before": "n b b' k : ℕ\nh : b ≡ b... | [
512,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_not | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.397891\nγ : Type ?u.397894\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns : Finset α\na : α\n⊢ a ∈ filter (fun a => ¬p a) s ↔ a ∈ s \\ filter p s",
"tactic": "simp only [Bool.decide_coe... | [
2861,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2858,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_mk' | [] | [
195,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_lt_self | [
{
"state_after": "n : ℕ\nh : 1 < n\nthis : n * 1 < n * n\n⊢ n < n * n",
"state_before": "n : ℕ\nh : 1 < n\n⊢ n < n * n",
"tactic": "have := Nat.mul_lt_mul_of_pos_left h (lt_of_succ_lt h)"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : 1 < n\nthis : n * 1 < n * n\n⊢ n < n * n",
... | [
135,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_inter_not | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ns t : Set α\nH : ∀ (a b : α), ∃ m, ∀ (c : α), r c a ∨ r c b → r c m\na : α\n⊢ Bounded r (s ∩ {b | ¬r b a}) → Bounded r s",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\nH : ∀ (a b : α), ∃ m, ∀ (c : α), r c a ∨ r c b → r c m\na : α\n⊢ Bounded ... | [
308,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_mul_le_Lp_mul_Lq_of_ne_zero_of_ne_top | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np q : ℝ\nhpq : Real.IsConjugateExponent p q\nf g : α → ℝ≥0∞\nhf : AEMeasurable f\nhf_nontop : (∫⁻ (a : α), f a ^ p ∂μ) ≠ ⊤\nhg_nontop : (∫⁻ (a : α), g a ^ q ∂μ) ≠ ⊤\nhf_nonzero : (∫⁻ (a : α), f a ^ p ∂μ) ≠ 0\nhg_nonzero : (∫... | [
128,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_smul | [] | [
889,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.mem_entourage | [
{
"state_after": "α : Type u\nβ✝ : Type v\ninst✝¹ : UniformSpace α\nβ : Type u_1\ninst✝ : SemilatticeSup β\nu : β → α\nh : CauchySeq u\nV : Set (α × α)\nhV : V ∈ 𝓤 α\nthis : Nonempty β\n⊢ ∃ k₀, ∀ (i j : β), k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V",
"state_before": "α : Type u\nβ✝ : Type v\ninst✝¹ : UniformSpace α... | [
185,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_mod | [
{
"state_after": "a n : ℕ\n⊢ ↑(a % n) = ↑(a % n + n * (a / n))",
"state_before": "a n : ℕ\n⊢ ↑(a % n) = ↑a",
"tactic": "conv =>\n rhs\n rw [← Nat.mod_add_div a n]"
},
{
"state_after": "no goals",
"state_before": "a n : ℕ\n⊢ ↑(a % n) = ↑(a % n + n * (a / n))",
"tactic": "simp"
}
] | [
667,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Topology/Connected.lean | IsConnected.isPreconnected | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodal_erase_eq_nodal_div | [
{
"state_after": "case a0\nF : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhi : i ∈ s\n⊢ X - ↑C (v i) ≠ 0",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : Decidabl... | [
533,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.triangle_assoc_comp_left | [] | [
323,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Data/List/Nodup.lean | Option.toList_nodup | [] | [
468,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.182364\nβ : Type ?u.182367\nγ : Type ?u.182370\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\n⊢ card (succ o) = card o + 1",
"tactic": "simp only [← add_one_eq_succ, card_add, card_one]"
}
] | [
1102,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.coe_one | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.unitsEquiv_apply | [] | [
2347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2346,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | measurable_div_const' | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : DivInvMonoid G\ninst✝¹ : MeasurableSpace G\ninst✝ : MeasurableMul G\ng : G\n⊢ Measurable fun h => h / g",
"tactic": "simp_rw [div_eq_mul_inv, measurable_mul_const]"
}
] | [
193,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.coe_subtypeEquivCodomain_symm | [
{
"state_after": "case h\nX : Sort ?u.87976\ninst✝ : DecidableEq X\nx : X\nY : Sort ?u.88012\nf : { x' // x' ≠ x } → Y\ny : Y\nx' : { x' // x' ≠ x }\n⊢ ((fun x' => if h : x' ≠ x then f { val := x', property := h } else y) ∘ Subtype.val) x' = f x'",
"state_before": "X : Sort ?u.87976\ninst✝ : DecidableEq X\n... | [
1379,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1371,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Ioo_left | [] | [
191,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_homOfLe | [] | [
606,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_coe | [] | [
793,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.srange_top_of_surjective | [] | [
896,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.degree_minpoly | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.140709\nS : Type u_2\nT : Type ?u.140715\ninst✝⁹ : CommRing R\ninst✝⁸ : Ring S\ninst✝⁷ : Algebra R S\nA : Type u_1\nB : Type ?u.141021\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing B\ninst✝⁴ : IsDomain B\ninst✝³ : Algebra A B\nK : Type ?u.141443\ninst✝² : ... | [
217,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.171001\nι : Sort x\na : Set α\np : α → Prop\n⊢ (∃ᶠ (x : α) in 𝓟 a, p x) ↔ ∃ x, x ∈ a ∧ p x",
"tactic": "simp [Filter.Frequently, not_forall]"
}
] | [
1395,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1394,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_mk' | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_option | [
{
"state_after": "α : Type u_1\nβ : Type ?u.2024\nγ : Type ?u.2027\ninst✝ : Finite α\nthis : Fintype α\n⊢ Nat.card (Option α) = Nat.card α + 1",
"state_before": "α : Type u_1\nβ : Type ?u.2024\nγ : Type ?u.2027\ninst✝ : Finite α\n⊢ Nat.card (Option α) = Nat.card α + 1",
"tactic": "haveI := Fintype.ofFin... | [
98,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.intDegree_neg | [
{
"state_after": "case pos\nK : Type u\ninst✝ : Field K\nx : RatFunc K\nhx : x = 0\n⊢ intDegree (-x) = intDegree x\n\ncase neg\nK : Type u\ninst✝ : Field K\nx : RatFunc K\nhx : ¬x = 0\n⊢ intDegree (-x) = intDegree x",
"state_before": "K : Type u\ninst✝ : Field K\nx : RatFunc K\n⊢ intDegree (-x) = intDegree ... | [
1620,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1614,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_le_card_mul_right | [] | [
1924,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1923,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.comp_continuous_iff | [] | [
208,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.symm_apply_apply | [] | [
897,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparator_iff_mono | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nG : C\ninst✝ : ∀ (A : C), HasProduct fun x => G\n⊢ (∀ ⦃X Y : C⦄ (f g : X ⟶ Y), (∀ (h : Y ⟶ G), f ≫ h = g ≫ h) → f = g) ↔ ∀ (A : C), Mono (Pi.lift fun f => f)",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂... | [
541,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Std/Data/String/Lemmas.lean | String.Iterator.Valid.validFor | [
{
"state_after": "no goals",
"state_before": "l r : List Char\n⊢ ValidFor (List.reverse l) r { s := { data := l ++ r }, i := { byteIdx := utf8ByteSize.go l } }",
"tactic": "simpa [List.reverseAux_eq] using @ValidFor.mk l.reverse r"
}
] | [
627,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
625,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.pullbackIsoProdSubtype_inv_snd_apply | [] | [
123,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_le_of_subset | [
{
"state_after": "S✝ : Set Ordinal\nS T : Set Ordinal\nhS : Unbounded (fun x x_1 => x < x_1) S\nhST : S ⊆ T\na : Ordinal\n⊢ ∀ (j : Ordinal), (∀ (k : Ordinal), k < j → enumOrd T k ≤ enumOrd S k) → enumOrd T j ≤ enumOrd S j",
"state_before": "S✝ : Set Ordinal\nS T : Set Ordinal\nhS : Unbounded (fun x x_1 => x... | [
2244,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2239,
1
] |
Mathlib/Topology/Basic.lean | Filter.Eventually.eventually_nhds | [] | [
959,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.comp_continuousOn_iff | [] | [
1067,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.continuous_sSup | [
{
"state_after": "case inl\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\ninst✝⁴ : ConditionallyCompleteLinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : γ → β → α\nhf : Continuous ↿f\nhK : IsCompact ∅\n⊢ Continuous fun x => sSup (f x ... | [
404,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
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] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mul_injective | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : Ring A\ninst✝¹ : Algebra R A\ninst✝ : NoZeroDivisors A\nx : A\nhx : x ≠ 0\nthis : Nontrivial A := { exists_pair_ne := Exists.intro x (Exists.intro 0 hx) }\n⊢ Function.Injective ↑(↑(mul R A) x)",
"state_before": "R : Type u_2\nA ... | [
255,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Algebra/Order/SMul.lean | lt_inv_smul_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.118036\n𝕜 : Type u_1\nR : Type ?u.118042\nM : Type u_2\nN : Type ?u.118048\ninst✝⁵ : LinearOrderedSemifield 𝕜\ninst✝⁴ : OrderedAddCommMonoid M\ninst✝³ : OrderedAddCommMonoid N\ninst✝² : MulActionWithZero 𝕜 M\ninst✝¹ : MulActionWithZero 𝕜 N\ninst✝... | [
260,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Ioc_subtype | [] | [
318,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_of_pred_lt | [] | [
612,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_inv_intCast_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1018297\nm : Type u_2\nn : Type u_3\no : Type ?u.1018306\nm' : o → Type ?u.1018311\nn' : o → Type ?u.1018316\nR : Type u_1\nS : Type ?u.1018322\nα : Type v\nβ : Type w\nγ : Type ?u.1018329\ninst✝³ : DivisionRing R\ninst✝² : AddCommGroup α\ninst✝¹ : S... | [
2224,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2222,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Images.lean | CategoryTheory.PreservesImage.hom_comp_map_image_ι | [
{
"state_after": "no goals",
"state_before": "A : Type u₁\nB : Type u₂\ninst✝⁷ : Category A\ninst✝⁶ : Category B\ninst✝⁵ : HasEqualizers A\ninst✝⁴ : HasImages A\ninst✝³ : StrongEpiCategory B\ninst✝² : HasImages B\nL : A ⥤ B\ninst✝¹ : {X Y Z : A} → (f : X ⟶ Z) → (g : Y ⟶ Z) → PreservesLimit (cospan f g) L\ni... | [
66,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.sSup_apply | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y✝ Z : C\nf✝ : Y✝ ⟶ X\nS R : Sieve X\nSs : Set (Sieve X)\nY : C\nf : Y ⟶ X\n⊢ (sSup Ss).arrows f ↔ ∃ S x, S.arrows f",
"tactic": "simp [sSup, Sieve.sup, setOf]"
}
] | [
364,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
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