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/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_dist | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np : P\nv : V\n⊢ dist ((-2 * inner v (p -ᵥ s.center) / inner v v) • v +ᵥ p) s.center = dist p s.center",
"state_before": "V : Type u_... | [
52,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.incl_eq_val | [] | [
575,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.infDist | [] | [
1540,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
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Mathlib/Data/Sum/Interval.lean | Finset.inr_mem_sumLift₂ | [
{
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78,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'_lt | [] | [
178,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousWithinAt_iInf | [] | [
1009,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
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Mathlib/Topology/Instances/ENNReal.lean | summable_of_nonneg_of_le | [
{
"state_after": "case intro\nα : Type ?u.339900\nβ : Type u_1\nγ : Type ?u.339906\ng : β → ℝ\nhg : ∀ (b : β), 0 ≤ g b\nf : β → ℝ≥0\nhgf : ∀ (b : β), g b ≤ (fun i => ↑(f i)) b\nhf : Summable fun i => ↑(f i)\n⊢ Summable g",
"state_before": "α : Type ?u.339900\nβ : Type u_1\nγ : Type ?u.339906\nf g : β → ℝ\nh... | [
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72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Lattice.lean | sup_eq_sup_iff_left | [] | [
302,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_mul_sym | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Data/Set/Prod.lean | Set.subset_eval_image_pi | [
{
"state_after": "no goals",
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"tactic": "classical\nobtain ⟨f, hf⟩ := ht\nrefine' fun y hy => ⟨update f i y, fun j... | [
810,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
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Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.eq_zero | [] | [
67,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_zero_right_iff | [] | [
1232,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
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Mathlib/Algebra/Group/Prod.lean | Prod.mk_div_mk | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.leadingCoeff_opRingEquiv | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np : R[X]ᵐᵒᵖ\n⊢ leadingCoeff (↑(opRingEquiv R) p) = op (leadingCoeff (unop p))",
"tactic": "rw [leadingCoeff, coeff_opRingEquiv, natDegree_opRingEquiv, leadingCoeff]"
}
] | [
123,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
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Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | AddMonoidAlgebra.toDirectSum_single | [] | [
84,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.finset_inf_arrow_factors | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nI : Type u_1\nB : C\ns : Finset I\nP : I → Subobject B\n⊢ ∀ (i : I), i ∈ s → Factors (P i) (arrow (Finset.inf s P))",
"state_before": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Typ... | [
460,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.U_of_two_le | [
{
"state_after": "case intro\nR : Type u_1\nS : Type ?u.11533\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\nh : 2 ≤ 2 + n\n⊢ U R (2 + n) = 2 * X * U R (2 + n - 1) - U R (2 + n - 2)",
"state_before": "R : Type u_1\nS : Type ?u.11533\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\nh : 2 ≤ n\n⊢ U R n = 2 *... | [
124,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_pow | [
{
"state_after": "case ofFinsupp\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ ({ toFinsupp := toFinsupp✝ } ^ n).toFinsupp = { toFinsupp := toFinsupp✝ }.toFinsupp ^ n",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q a : ... | [
247,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_singleton | [] | [
658,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Topology/LocalAtTarget.lean | openEmbedding_iff_openEmbedding_of_iSup_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set β\nι : Type ?u.45890\nU : ι → Opens β\nhU : iSup U = ⊤\nh : Continuous f\n⊢ Embedding f ∧ IsOpen (range f) ↔\n ∀ (i : ι), Embedding (restrictPreimage (U i).carrier f) ∧ IsOpen (range (res... | [
158,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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] |
Mathlib/Data/Fintype/Card.lean | Set.toFinset_card | [] | [
245,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_of_not_le | [] | [
683,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
683,
11
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toPmf_eq_iff_toMeasure_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.350230\nγ : Type ?u.350233\ninst✝⁴ : Countable α\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSingletonClass α\np : Pmf α\nμ✝ : MeasureTheory.Measure α\ninst✝¹ : IsProbabilityMeasure μ✝\nμ : MeasureTheory.Measure α\ninst✝ : IsProbabi... | [
396,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.measurable | [] | [
359,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
11
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.isCompl_range_coe_infty | [] | [
117,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_eq_zero | [] | [
358,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
357,
11
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.nonempty_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.562\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Finset.Nonempty (Ioc a b) ↔ a < b",
"tactic": "rw [← coe_nonempty, coe_Ioc, Set.nonempty_Ioc]"
}
] | [
60,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/Logic/Equiv/Set.lean | Set.mem_image_equiv | [] | [
49,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjUnion_eq_union | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
1346,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_smul | [
{
"state_after": "α : Type ?u.828266\nβ : Type ?u.828269\na b c d : ℝ≥0∞\nr✝ p q r : ℝ≥0\ns : ℝ≥0∞\n⊢ ↑r * ENNReal.toReal s = r • ENNReal.toReal s",
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"tacti... | [
2275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2273,
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Mathlib/Data/List/Basic.lean | List.getLast_cons | [
{
"state_after": "case nil\nι : Type ?u.29930\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nh✝ : [] ≠ []\n⊢ getLast [a] (_ : [a] ≠ []) = getLast [] h✝\n\ncase cons\nι : Type ?u.29930\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na head✝ : α\ntail✝ : List α\ntail_ih✝ ... | [
702,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Order/Monotone/Monovary.lean | MonovaryOn.empty | [] | [
70,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.alephIdx_le | [
{
"state_after": "no goals",
"state_before": "a b : Cardinal\n⊢ alephIdx a ≤ alephIdx b ↔ a ≤ b",
"tactic": "rw [← not_lt, ← not_lt, alephIdx_lt]"
}
] | [
111,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.add_pred_div_lt | [
{
"state_after": "b n : ℕ\nhb : 1 < b\nhn : 2 ≤ n\n⊢ n + b ≤ n * b",
"state_before": "b n : ℕ\nhb : 1 < b\nhn : 2 ≤ n\n⊢ (n + b - 1) / b < n",
"tactic": "rw [div_lt_iff_lt_mul (zero_lt_one.trans hb), ← succ_le_iff, ← pred_eq_sub_one,\n succ_pred_eq_of_pos (add_pos (zero_lt_one.trans hn) (zero_lt_one.tr... | [
232,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.left_le_of_le_right'' | [] | [
1112,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Data/Set/Finite.lean | Set.card_range_of_injective | [] | [
1252,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.of_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ℤ\n⊢ ↑↑n = ↑n",
"tactic": "rw [← cast_to_int, to_of_int]"
}
] | [
1565,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1564,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_algHom_injective | [] | [
265,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_true | [] | [
1098,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1098,
9
] |
src/lean/Init/SimpLemmas.lean | of_eq_true | [] | [
12,
53
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
12,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_add_le | [] | [
1980,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.coe_add | [] | [
140,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
11
] |
Mathlib/Computability/Primrec.lean | Primrec.sum_casesOn | [
{
"state_after": "no goals",
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1010,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
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] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.restrict_split | [
{
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"state_before": "ι : Type u_1\nM : Type ?u.38714\nn : ℕ\nI J : Box ι\ni✝ : ι\nx✝ : ℝ\nh : I ≤ J\ni : ι\nx : ℝ\n⊢ restrict (split J i x) I... | [
234,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | archimedean_iff_nat_le | [] | [
341,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mem_inf_iff | [] | [
894,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | map_inv₀ | [
{
"state_after": "case pos\nα : Type ?u.17885\nM₀ : Type ?u.17888\nG₀ : Type u_2\nM₀' : Type ?u.17894\nG₀' : Type u_1\nF : Type u_3\nF' : Type ?u.17903\ninst✝³ : MonoidWithZero M₀\ninst✝² : GroupWithZero G₀\ninst✝¹ : GroupWithZero G₀'\ninst✝ : MonoidWithZeroHomClass F G₀ G₀'\nf : F\na b : G₀\nh : a = 0\n⊢ ↑f a⁻... | [
241,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Std/Logic.lean | forall_eq_or_imp | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ (∀ (a : α), a = a' ∨ q a → p a) ↔ p a' ∧ ∀ (a : α), q a → p a",
"tactic": "simp only [or_imp, forall_and, forall_eq]"
}
] | [
471,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
470,
9
] |
Mathlib/Topology/Basic.lean | dense_univ | [] | [
634,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isTrichotomous | [] | [
383,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
11
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.toNonneg_of_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Zero α\ninst✝ : LinearOrder α\na : α\nh : 0 ≤ a\n⊢ toNonneg a = { val := a, property := h }",
"tactic": "simp [toNonneg, h]"
}
] | [
365,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/RingTheory/IntegrallyClosed.lean | IsIntegrallyClosed.exists_algebraMap_eq_of_pow_mem_subalgebra | [] | [
104,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | Measurable.div_const | [] | [
318,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.unbounded_of_tendsto_atTop | [
{
"state_after": "case intro\nι : Type ?u.350259\nι' : Type ?u.350262\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.350271\ninst✝³ : Nonempty α\ninst✝² : SemilatticeSup α\ninst✝¹ : Preorder β\ninst✝ : NoMaxOrder β\nf : α → β\nh : Tendsto f atTop atTop\nM : β\nhM : M ∈ upperBounds (range f)\n⊢ False",
"state_befo... | [
1698,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.neg_mk | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_forall_le_atBot | [] | [
254,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/RingTheory/Finiteness.lean | AlgHom.Finite.of_comp_finite | [] | [
747,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioc | [
{
"state_after": "case inl.inl\nα : Type u_1\nβ : Type ?u.134545\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab : a ≤ b\nhcd : c ≤ d\nh₁ : a ≤ d\nh₂ : c ≤ b\n⊢ Ioc a b ∪ Ioc c d = Ioc (min a c) (max b d)\n\ncase inl.inr\nα : Type u_1\nβ : Type ?u.134545\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab... | [
1617,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1613,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.CompleteLatticeHom.apply_limsup_iterate | [
{
"state_after": "α : Type u_1\nβ : Type ?u.123164\nγ : Type ?u.123167\nι : Type ?u.123170\ninst✝ : CompleteLattice α\nf : CompleteLatticeHom α α\na : α\n⊢ (⨅ (i : ℕ), ↑f (⨆ (i_1 : ℕ), (↑f^[i_1 + i]) a)) = ⨅ (n : ℕ), ⨆ (i : ℕ), (↑f^[i + n]) a",
"state_before": "α : Type u_1\nβ : Type ?u.123164\nγ : Type ?u.... | [
845,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Topology/Separation.lean | Embedding.t5Space | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T5Space β\ne : α → β\nhe : _root_.Embedding e\nthis : T1Space α\n⊢ T5Space α",
"state_before": "α : Type u\nβ : Type v\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : T5Space β\ne :... | [
1835,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1826,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_zero_left' | [] | [
380,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_preimage_ofDual_iff | [] | [
180,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mem_of_mulIndicator_ne_one | [] | [
161,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_undef | [] | [
382,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_hasSum_exp | [] | [
433,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.inter_iUnion₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.115953\nγ : Type ?u.115956\nι : Sort u_2\nι' : Sort ?u.115962\nι₂ : Sort ?u.115965\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.115975\nκ₂ : ι → Sort ?u.115980\nκ' : ι' → Sort ?u.115985\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ (s ∩ ⋃ (i : ι) (j ... | [
1008,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_update_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.154510\nγ : Type ?u.154513\nι : Type ?u.154516\nM : Type u_2\nM' : Type ?u.154522\nN : Type ?u.154525\nP : Type ?u.154528\nG : Type ?u.154531\nH : Type ?u.154534\nR : Type ?u.154537\nS : Type ?u.154540\ninst✝¹ : Zero M\nf : α →₀ M\na : ... | [
594,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Dynamics/OmegaLimit.lean | eventually_closure_subset_of_isCompact_absorbing_of_isOpen_of_omegaLimit_subset | [] | [
280,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.two_lt_card_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.56033\ns t : Finset α\nf : α → β\nn : ℕ\nh : 2 < card s\n⊢ ∃ a b c, a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.56033\ns t : Finset α\nf : α → β\nn : ℕ\n⊢ (∃ a b c, a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ ... | [
582,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/Set/Image.lean | Set.exists_subtype_range_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.66669\nγ : Type ?u.66672\nι : Sort u_2\nι' : Sort ?u.66678\nf : ι → α\ns t : Set α\np : ↑(range f) → Prop\nx✝ : ∃ a, p a\ni : ι\nha : p { val := f i, property := (_ : ∃ y, f y = f i) }\n⊢ ∃ i, p { val := f i, property := (_ : f i ∈ range f) }",
"state_before": "α ... | [
682,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.FilteredColimit.eqvGen_quot_rel_of_rel | [
{
"state_after": "case refine'_1\nJ : Type v\ninst✝ : SmallCategory J\nF : J ⥤ TypeMax\nx y : (j : J) × F.obj j\nx✝ : FilteredColimit.Rel F x y\nk : J\nf : x.fst ⟶ k\ng : y.fst ⟶ k\nh : F.map f x.snd = F.map g y.snd\n⊢ EqvGen (Quot.Rel F) x { fst := k, snd := F.map f x.snd }\n\ncase refine'_2\nJ : Type v\ninst✝... | [
407,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.univ_mem | [] | [
150,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ne_one | [] | [
383,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Order/WithBot.lean | WithBot.ofDual_apply_coe | [] | [
949,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_iff_exists_wbtw | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.333089\nP : Type u_3\nP' : Type ?u.333095\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y : P\nh :... | [
697,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_le_of_le | [] | [
940,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Topology/SubsetProperties.lean | irreducibleComponent_mem_irreducibleComponents | [] | [
1811,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1809,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_toNNReal | [
{
"state_after": "case intro\nα : Type ?u.26680\nβ : Type ?u.26683\nγ : Type ?u.26686\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\na : ℝ≥0\n⊢ Tendsto ENNReal.toNNReal (𝓝 ↑a) (𝓝 (ENNReal.toNNReal ↑a))",
"state_before": "α : Type ?u.26680\nβ : Type ?u.26683\nγ : Type ?u.26686\na✝ b c d... | [
120,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.Regular.innerRegular_measurable | [] | [
496,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nonneg_of_mem_Icc | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ Icc (-(π / 2)) (π / 2)\n⊢ 0 ≤ x + π / 2",
"tactic": "linarith [hx.1]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ Icc (-(π / 2)) (π / 2)\n⊢ x + π / 2 ≤ π",
"tactic": "linarith [hx.2]"
}
] | [
469,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | ContinuousConstSMul.secondCountableTopology | [] | [
537,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Data/Vector3.lean | exists_vector_zero | [
{
"state_after": "α : Type u_1\nm n : ℕ\nf : Vector3 α 0 → Prop\nx✝ : Exists f\nv : Vector3 α 0\nfv : f v\n⊢ f v",
"state_before": "α : Type u_1\nm n : ℕ\nf : Vector3 α 0 → Prop\nx✝ : Exists f\nv : Vector3 α 0\nfv : f v\n⊢ f []",
"tactic": "rw [← eq_nil v]"
},
{
"state_after": "no goals",
"s... | [
238,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_mul | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np q : R[X]\nh : ∀ (n : ℕ) (p q : R[X]), degree (p * q) < ↑n → content (p * q) = content p * content q\n⊢ content (p * q) = content p * content q\n\ncase h\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomai... | [
408,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Algebra/Module/Basic.lean | smul_right_injective | [] | [
675,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Order/Disjoint.lean | isCompl_toDual_iff | [] | [
613,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/List/MinMax.lean | List.not_of_mem_foldl_argAux | [
{
"state_after": "case H0\nα : Type u_1\nβ : Type ?u.22970\nr : α → α → Prop\ninst✝ : DecidableRel r\nl : List α\no : Option α\na m : α\nhr₀ : Irreflexive r\nhr₁ : Transitive r\n⊢ ∀ {a m : α} {o : Option α}, a ∈ [] → m ∈ foldl (argAux r) o [] → ¬r a m\n\ncase H1\nα : Type u_1\nβ : Type ?u.22970\nr : α → α → Pro... | [
87,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_Ico | [] | [
728,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_bot_of_noZeroDivisors | [] | [
991,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.max_comm | [
{
"state_after": "a b : Nat\n⊢ (if a ≤ b then b else a) = if b ≤ a then a else b",
"state_before": "a b : Nat\n⊢ max a b = max b a",
"tactic": "simp only [Nat.max_def]"
},
{
"state_after": "case pos\na b : Nat\nh₁ : a ≤ b\nh₂ : b ≤ a\n⊢ b = a\n\ncase neg\na b : Nat\nh₁ : ¬a ≤ b\nh₂ : ¬b ≤ a\n⊢ a... | [
200,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
196,
11
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.star_def | [] | [
438,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/GradedMonoid.lean | SetLike.homogeneous_one | [] | [
691,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | subset_tangentCone_prod_left | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\n𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.36135\ninst✝¹ : NormedAddCommGroup G\ninst✝ ... | [
165,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.support_smul | [
{
"state_after": "α : Type u_3\nβ : Type ?u.617480\nγ : Type ?u.617483\nι : Type ?u.617486\nM : Type u_1\nM' : Type ?u.617492\nN : Type ?u.617495\nP : Type ?u.617498\nG : Type ?u.617501\nH : Type ?u.617504\nR : Type u_2\nS : Type ?u.617510\ninst✝¹ : AddMonoid M\ninst✝ : SMulZeroClass R M\nb : R\ng : α →₀ M\na :... | [
1559,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.convergents'Aux_stable_of_terminated | [
{
"state_after": "case refl\nK : Type u_1\ng : GeneralizedContinuedFraction K\nn m : ℕ\ninst✝ : DivisionRing K\ns : Stream'.Seq (Pair K)\nterminated_at_n : Stream'.Seq.TerminatedAt s n\n⊢ convergents'Aux s n = convergents'Aux s n\n\ncase step\nK : Type u_1\ng : GeneralizedContinuedFraction K\nn m✝ : ℕ\ninst✝ : ... | [
69,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.clog_antitone_left | [] | [
354,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.cancel_right | [] | [
615,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Logic/Basic.lean | em' | [] | [
198,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_one | [] | [
489,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | Submodule.mem_graph_toLinearPMap | [] | [
980,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_iSup | [
{
"state_after": "no goals",
"state_before": "ι✝ : Type ?u.17100\nα : Type u_2\nβ : Type ?u.17106\nγ : Type ?u.17109\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nι : Sort u_1\ns : ι → Opens α\n⊢ ↑(⨆ (i : ι), s i) = ⋃ (i : ι), ↑(s i)",
"tactic": "simp [iSup]"
}... | [
232,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
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