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/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.isBoundedLinearMap_comp_left | [] | [
459,
55
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457,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.const_smul | [] | [
467,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
11
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.naturality_pf | [
{
"state_after": "case h\nt : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng : α → F β\nh : β → G γ\nf✝ : β → γ\nx : t β\nη : ApplicativeT... | [
149,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_summable_of_mem_ball' | [] | [
225,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_comp_inr | [] | [
156,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.coe_id | [] | [
575,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_subset_closedBall | [] | [
599,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_id_unmop | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Data/Fin/Basic.lean | Fin.add_one_pos | [
{
"state_after": "case zero\nm : ℕ\ni : Fin (zero + 1)\nh : i < last zero\n⊢ 0 < i + 1\n\ncase succ\nm n✝ : ℕ\ni : Fin (Nat.succ n✝ + 1)\nh : i < last (Nat.succ n✝)\n⊢ 0 < i + 1",
"state_before": "n m : ℕ\ni : Fin (n + 1)\nh : i < last n\n⊢ 0 < i + 1",
"tactic": "cases n"
},
{
"state_after": "no... | [
835,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
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Mathlib/LinearAlgebra/Dual.lean | Module.DualBases.lc_coeffs | [
{
"state_after": "R : Type u_2\nM : Type u_1\nι : Type u_3\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ne : ι → M\nε : ι → Dual R M\ninst✝ : DecidableEq ι\nh : DualBases e ε\nm : M\n⊢ ∀ (i : ι), ↑(ε i) (lc e (coeffs h m) - m) = 0",
"state_before": "R : Type u_2\nM : Type u_1\nι : Type... | [
722,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
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Mathlib/Data/List/Rotate.lean | List.rotate_eq_drop_append_take | [
{
"state_after": "α : Type u\nl : List α\nn : ℕ\n⊢ n ≤ length l → rotate' l n = drop n l ++ take n l",
"state_before": "α : Type u\nl : List α\nn : ℕ\n⊢ n ≤ length l → rotate l n = drop n l ++ take n l",
"tactic": "rw [rotate_eq_rotate']"
},
{
"state_after": "no goals",
"state_before": "α : ... | [
144,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_zero | [] | [
593,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
593,
11
] |
Mathlib/Data/List/Sort.lean | List.sorted_mergeSort | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : IsTotal α r\ninst✝ : IsTrans α r\n⊢ Sorted r (mergeSort r [])",
"tactic": "simp [mergeSort]"
},
{
"state_after": "no goals",
"state_before": "α : Type uu\nr : α → α → Prop\ninst✝² :... | [
450,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.coeff_sin_bit1 | [
{
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116,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Data/List/Join.lean | List.join_filter_isEmpty_eq_false | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1507\ninst✝ : DecidablePred fun l => isEmpty l = false\nL : List (List α)\n⊢ join (filter (fun l => decide (isEmpty l = false)) ([] :: L)) = join ([] :: L)",
"tactic": "simp [join_filter_isEmpty_eq_false (L := L), isEmpty_iff_eq_nil... | [
59,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Ici_eq_Ici | [] | [
1339,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1338,
1
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Mathlib/Algebra/Hom/Aut.lean | MulAut.one_def | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Data/Complex/Exponential.lean | Real.abs_exp_sub_one_sub_id_le | [
{
"state_after": "x : ℝ\nhx : abs' x ≤ 1\n⊢ abs' (exp x - 1 - x) ≤ abs' x ^ 2",
"state_before": "x : ℝ\nhx : abs' x ≤ 1\n⊢ abs' (exp x - 1 - x) ≤ x ^ 2",
"tactic": "rw [← _root_.sq_abs]"
},
{
"state_after": "x : ℝ\nhx : abs' x ≤ 1\nthis : ↑Complex.abs ↑x ≤ 1\n⊢ abs' (exp x - 1 - x) ≤ abs' x ^ 2"... | [
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13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1733,
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Mathlib/Data/Prod/Basic.lean | Function.Bijective.Prod_map | [] | [
326,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_sub_sq | [
{
"state_after": "no goals",
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1066,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
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Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.tfst_eq_fst_id | [
{
"state_after": "no goals",
"state_before": "t : Type u → Type u → Type u\ninst✝⁵ : Bitraversable t\nβ✝ : Type u\nF G : Type u → Type u\ninst✝⁴ : Applicative F\ninst✝³ : Applicative G\ninst✝² : IsLawfulBitraversable t\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα α' β : Type u\nf : α → α'\n... | [
118,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Combinatorics/DoubleCounting.lean | Finset.coe_bipartiteAbove | [] | [
70,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | continuousWithinAt_of_locally_uniform_approx_of_continuousWithinAt | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\nhx : x ∈ s\nL : ∀ (u : Set (β × β)), u ∈ 𝓤 β → ∃ t, t ∈ 𝓝[s] x ∧ ∃ F, ContinuousWithinAt F s x ∧ ∀ (y : ... | [
827,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
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Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_le_left | [] | [
138,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Topology/Basic.lean | map_mem_closure | [] | [
1774,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1772,
1
] |
Mathlib/Topology/Instances/Irrational.lean | Irrational.eventually_forall_le_dist_cast_rat_of_den_le | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : Irrational x\nn : ℕ\nε : ℝ\nH : ∀ (k : ℕ), k ≤ n → ∀ (m : ℤ), ε ≤ dist x (↑m / ↑k)\nr : ℚ\nhr : r.den ≤ n\n⊢ ε ≤ dist x ↑r",
"tactic": "simpa only [Rat.cast_def] using H r.den hr r.num"
}
] | [
101,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ite_diff_self | [] | [
2262,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2261,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.disjoint_closure_left | [] | [
143,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_funs | [
{
"state_after": "no goals",
"state_before": "x y f : ZFSet\n⊢ f ∈ funs x y ↔ IsFunc x y f",
"tactic": "simp [funs, IsFunc]"
}
] | [
1364,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
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Mathlib/Algebra/Lie/Basic.lean | lie_lie | [
{
"state_after": "no goals",
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212,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nh : ∀ (a : Pseudoelement P), pseudoApply f a = 0\n⊢ 𝟙 P ≫ f = 0",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nh : ∀ (a : Pseudoelement P), pseudoApply f a = 0\n⊢ f = 0",
... | [
286,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.bind_continuous' | [
{
"state_after": "α : Type u\nα' : Type ?u.58987\nβ✝ : Type v\nβ' : Type ?u.58992\nγ✝ : Type ?u.58995\nφ : Type ?u.58998\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β✝\ninst✝³ : OmegaCompletePartialOrder γ✝\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ : OmegaCompletePartialOrder α... | [
659,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
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Mathlib/Analysis/Normed/Group/Basic.lean | dist_mul_mul_le_of_le | [] | [
1436,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1434,
1
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.properSpace | [
{
"state_after": "α✝ : Type ?u.96684\nβ : Type u_2\nγ : Type ?u.96690\ninst✝³ : PseudoMetricSpace α✝\ninst✝² : PseudoMetricSpace β\nK✝ : ℝ≥0\nf✝ : α✝ → β\nα : Type u_1\ninst✝¹ : MetricSpace α\nK : ℝ≥0\nf : α → β\ninst✝ : ProperSpace α\nhK : AntilipschitzWith K f\nf_cont : Continuous f\nhf : Function.Surjective ... | [
249,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
11
] |
Mathlib/Algebra/Order/Ring/Defs.lean | StrictAnti.const_mul_of_neg | [] | [
746,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.embedding_pullback_to_prod | [] | [
185,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.inv_zero | [
{
"state_after": "⊢ (if h : 0.num < 0 then mk' (-↑0.den) (Int.natAbs 0.num)\n else if h : 0.num > 0 then mk' (↑0.den) (Int.natAbs 0.num) else 0) =\n 0",
"state_before": "⊢ Rat.inv 0 = 0",
"tactic": "unfold Rat.inv"
},
{
"state_after": "no goals",
"state_before": "⊢ (if h : 0.num < 0 th... | [
297,
7
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
295,
19
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_sub_partitions | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nπ₁ π₂ : TaggedPrepartition I\nh₁ : IsPartition π₁\nh₂ : IsParti... | [
125,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMinOn.neg | [] | [
409,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
8
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.isRegular_of_boolean | [] | [
260,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_changeOriginSeries_radius | [] | [
1238,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.id_comp | [] | [
355,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_self_nonneg | [] | [
1097,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Topology/Basic.lean | isOpen_empty | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\n⊢ IsOpen (⋃₀ ∅)",
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"tactic": "rw [← s... | [
160,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
9
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_zero | [
{
"state_after": "𝕜 : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type ?u.403828\nE : Type u_1\nEₗ : Type ?u.403834\nF : Type u_2\nFₗ : Type ?u.403840\nG : Type ?u.403843\nGₗ : Type ?u.403846\n𝓕 : Type ?u.403849\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : SeminormedAddCommGroup F\n... | [
281,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_sub | [] | [
937,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
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] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_one | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuousOn_sub | [
{
"state_after": "α : Type ?u.107946\nβ : Type ?u.107949\nγ : Type ?u.107952\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\n⊢ ∀ (x : ℝ≥0∞ × ℝ≥0∞), x ∈ {p | p ≠ (⊤, ⊤)} → ContinuousWithinAt (fun p => p.fst - p.snd) {p | p ≠ (⊤, ⊤)} x",
"state_before": "α : Type ?u.107946\nβ : Type ?u.10794... | [
445,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_map_nhds_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.31160\nδ : Type ?u.31163\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\nx : α\nhx : x ∈ e.source\n⊢ 𝓝... | [
372,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.differentiableWithinAt_arccos_Iic | [] | [
171,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.diam_image | [] | [
198,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.isUnit_leadingCoeff_mul_left_eq_zero_iff | [
{
"state_after": "case mp\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : IsUnit (leadingCoeff p)\nq : R[X]\n⊢ q * p = 0 → q = 0\n\ncase mpr\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : IsUnit (leadingCoeff p)\nq : R[X]\n⊢ q = ... | [
550,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.prod_coe | [] | [
953,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_monomial_single | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.263576\nr✝ : R\ne✝ : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\ninst✝ : CommSemiring S\nf : R →+* S\ni : σ\ne : ℕ\nr : R\nhe : e ≠ 0\nhr : r ≠ 0\n⊢ vars (↑(monomial (Finsupp.single i... | [
467,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
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Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.subset_compl_right | [] | [
64,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Algebra/Hom/Ring.lean | AddMonoidHom.coe_addMonoidHom_mkRingHomOfMulSelfOfTwoNeZero | [
{
"state_after": "case h\nF : Type ?u.127699\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.127708\ninst✝² : CommRing α\ninst✝¹ : IsDomain α\ninst✝ : CommRing β\nf : β →+ α\nh : ∀ (x : β), ↑f (x * x) = ↑f x * ↑f x\nh_two : 2 ≠ 0\nh_one : ↑f 1 = 1\n⊢ ∀ (x : β), ↑↑(mkRingHomOfMulSelfOfTwoNeZero f h h_two h_one) x = ↑f ... | [
805,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
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Mathlib/Data/ENat/Basic.lean | ENat.sub_top | [] | [
153,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Order/Cover.lean | AntisymmRel.trans_covby | [] | [
314,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_eq_one_of | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\nhs' : Set.Nonempty s\nht : s ⊆ t\nthis : IsProbabilityMeasure (condCount s)\n⊢ ↑↑(condCount s) t = 1",
"state_before": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : Measurab... | [
117,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Data/Finset/Preimage.lean | Finset.sigma_preimage_mk | [
{
"state_after": "case a\nα : Type u\nβ✝ : Type v\nι : Sort w\nγ : Type x\nβ : α → Type u_1\ninst✝ : DecidableEq α\ns : Finset ((a : α) × β a)\nt : Finset α\nx : (i : α) × β i\n⊢ (x ∈ Finset.sigma t fun a => preimage s (Sigma.mk a) (_ : InjOn (Sigma.mk a) (Sigma.mk a ⁻¹' ↑s))) ↔\n x ∈ filter (fun a => a.fst ... | [
127,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_nonneg | [] | [
286,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.sum_le_iSup | [
{
"state_after": "α β ι : Type u\nf : ι → Cardinal\n⊢ sum f ≤ lift (#ι) * iSup f",
"state_before": "α β ι : Type u\nf : ι → Cardinal\n⊢ sum f ≤ (#ι) * iSup f",
"tactic": "rw [← lift_id (#ι)]"
},
{
"state_after": "no goals",
"state_before": "α β ι : Type u\nf : ι → Cardinal\n⊢ sum f ≤ lift (#... | [
999,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_monomial | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nha : a ≠ 0\n⊢ ↑n = ↑n",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nha : a ≠ 0\n⊢ trailingDegree (↑(monomial n) a) = ↑n",
"tactic": "rw [trailingDegree, support_... | [
204,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.ExactFunctor.forget_obj | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.sinh_arsinh | [
{
"state_after": "x✝ y x : ℝ\n⊢ (x + sqrt (1 + x ^ 2) - (-x + sqrt (1 + x ^ 2))) / 2 = x",
"state_before": "x✝ y x : ℝ\n⊢ sinh (arsinh x) = x",
"tactic": "rw [sinh_eq, ← arsinh_neg, exp_arsinh, exp_arsinh, neg_sq]"
},
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\n⊢ (x + sqrt (1 +... | [
82,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Topology/Separation.lean | compl_singleton_mem_nhds_iff | [] | [
618,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.Bounded.ediam_ne_top | [] | [
2653,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2652,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_zero | [
{
"state_after": "no goals",
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"tactic": "rw [count, List.range_zero, List.countp, List.countp.go]"
}
] | [
42,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/Topology/SubsetProperties.lean | isClosed_of_mem_irreducibleComponents | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.184023\nπ : ι → Type ?u.184028\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t s : Set α\nH : s ∈ irreducibleComponents α\n⊢ s = closure s",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.184023\nπ : ι → Type ?u.184028\ninst✝¹ : Topo... | [
1769,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_insert | [
{
"state_after": "case inl\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.177830\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ... | [
401,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
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Mathlib/Analysis/Convex/Between.lean | mem_vadd_const_affineSegment | [
{
"state_after": "no goals",
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127,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.le_induction | [
{
"state_after": "case refl\nm✝ n k m : ℕ\nP : (n : ℕ) → m ≤ n → Prop\nbase : P m (_ : m ≤ m)\nsucc : ∀ (n : ℕ) (hn : m ≤ n), P n hn → P (n + 1) (_ : m ≤ n + 1)\n⊢ P m (_ : Nat.le m m)\n\ncase step\nm✝ n k m : ℕ\nP : (n : ℕ) → m ≤ n → Prop\nbase : P m (_ : m ≤ m)\nsucc : ∀ (n : ℕ) (hn : m ≤ n), P n hn → P (n + ... | [
488,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.eq_iff | [] | [
81,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prod_coe | [] | [
1246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1244,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.restrictScalars_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_3\nι' : Type ?u.1271219\nR : Type u_2\nR₂ : Type ?u.1271225\nK : Type ?u.1271228\nM : Type u_1\nM' : Type ?u.1271234\nM'' : Type ?u.1271237\nV : Type u\nV' : Type ?u.1271242\nS : Type u_4\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring S\ninst✝⁶ : Nontrivial S\ni... | [
1661,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1660,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.hasFDerivWithinAt | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.253209\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.253304\... | [
513,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_map | [] | [
1280,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_rpow_of_exponent_ge | [] | [
185,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.isLittleO_zpow_mul_exp | [
{
"state_after": "no goals",
"state_before": "l : Filter ℂ\nb₁ b₂ : ℝ\nhl : IsExpCmpFilter l\nhb : b₁ < b₂\nm n : ℤ\n⊢ (fun z => z ^ ↑m * exp (↑b₁ * z)) =o[l] fun z => z ^ ↑n * exp (↑b₂ * z)",
"tactic": "simpa only [cpow_int_cast] using hl.isLittleO_cpow_mul_exp hb m n"
}
] | [
225,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_lt | [
{
"state_after": "ι : Type u_1\nκ : Type ?u.38034\nα : Type u_2\ninst✝³ : OrderedAddCommGroup α\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalAddGroup α\ninst✝ : OrderClosedTopology α\nf g : ι → α\na₁ a₂ : α\ni : ι\nh : f ≤ g\nhi : f i < g i\nhf : HasSum f a₁\nhg : HasSum g a₂\nthis : update f i 0 ≤ update ... | [
167,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAtFilter_pi | [] | [
404,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Nat.toAdd_pow | [] | [
1208,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.eq_comp_toLinearMap_symm | [
{
"state_after": "case mp.h\nR : Type ?u.193960\nR₁ : Type u_5\nR₂ : Type u_1\nR₃ : Type u_2\nk : Type ?u.193972\nS : Type ?u.193975\nM : Type ?u.193978\nM₁ : Type u_6\nM₂ : Type u_3\nM₃ : Type u_4\nN₁ : Type ?u.193990\nN₂ : Type ?u.193993\nN₃ : Type ?u.193996\nN₄ : Type ?u.193999\nι : Type ?u.194002\nM₄ : Type... | [
436,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsAtomic.isPrenex | [] | [
764,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | tendsto_of_le_liminf_of_limsup_le | [] | [
227,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Order/Basic.lean | Antitone.map_sSup_of_continuousAt | [] | [
2718,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2715,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_eq_zero_iff | [
{
"state_after": "case refine'_1\nz : ℂ\nh : arg z = 0\n⊢ 0 ≤ z.re ∧ z.im = 0\n\ncase refine'_2\nz : ℂ\n⊢ 0 ≤ z.re ∧ z.im = 0 → arg z = 0",
"state_before": "z : ℂ\n⊢ arg z = 0 ↔ 0 ≤ z.re ∧ z.im = 0",
"tactic": "refine' ⟨fun h => _, _⟩"
},
{
"state_after": "case refine'_1\nz : ℂ\nh : arg z = 0\n⊢... | [
230,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.prod_symm_apply | [] | [
259,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_eq_eval₂Hom | [] | [
1440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1439,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | ContinuousOn.comp_fract | [] | [
220,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasLimitsOfShape_of_hasLimitsOfShape_createsLimitsOfShape | [] | [
171,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Algebra/Support.lean | Function.support_smul_subset_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.86818\nA : Type u_1\nB : Type u_2\nM : Type ?u.86827\nN : Type ?u.86830\nP : Type ?u.86833\nR : Type ?u.86836\nS : Type ?u.86839\nG : Type ?u.86842\nM₀ : Type ?u.86845\nG₀ : Type ?u.86848\nι : Sort ?u.86851\ninst✝² : AddMonoid A\ninst✝¹... | [
371,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/RingTheory/Henselian.lean | isLocalRingHom_of_le_jacobson_bot | [
{
"state_after": "case map_nonunit\nR : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nh : I ≤ Ideal.jacobson ⊥\n⊢ ∀ (a : R), IsUnit (↑(Ideal.Quotient.mk I) a) → IsUnit a",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nh : I ≤ Ideal.jacobson ⊥\n⊢ IsLocalRingHom (Ideal.Quotient.mk I)",
"tac... | [
85,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_div_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.23085\nα : Type u_1\nβ : Type ?u.23091\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhc : 0 < c\n⊢ a ≤ b / c ↔ c * a ≤ b",
"tactic": "rw [mul_comm, le_div_iff hc]"
}
] | [
143,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mul_apply' | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_left | [] | [
120,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_injective | [] | [
165,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
11
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_neg | [] | [
427,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.convex_hypograph | [] | [
259,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.sum_fintype | [
{
"state_after": "case h.h\nα : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ✝ : { x // x ∈ kernel α β }\ninst✝ : Fintype ι\nκ : ι → { x // x ∈ kernel α β }\na : α\ns : Set β\n⊢ MeasurableSet s → ↑↑(↑(kernel.sum κ) a) s = ↑↑(↑(∑ i : ι, κ i) a) s",
"state_before": "α... | [
252,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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