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/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.Limits.BinaryFan.assoc_fst | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.nnnorm_le | [] | [
1016,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_lt_of_mul_lt_right | [] | [
244,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.separatingLeft_iff_linear_nontrivial | [
{
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708,
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700,
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Mathlib/Data/Matrix/Basic.lean | Matrix.col_smul | [
{
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2663,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2661,
1
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.sin_pos_of_not_collinear | [] | [
521,
95
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519,
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Mathlib/Analysis/Calculus/Inverse.lean | ContDiffAt.mem_toLocalHomeomorph_source | [] | [
767,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
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Mathlib/Data/Vector/Basic.lean | Vector.scanl_val | [] | [
340,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_sInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.83182\nγ : Type ?u.83185\nι : Sort ?u.83188\nκ : ι → Sort ?u.83193\ninst✝ : LE α\ns t : UpperSet α\na : α\nS : Set (UpperSet α)\n⊢ ↑(compl (sInf S)) = ↑(⨅ (s : UpperSet α) (_ : s ∈ S), compl s)",
"tactic": "simp only [coe_compl, coe... | [
843,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
11
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Mathlib/Data/Set/Lattice.lean | Set.sUnion_subset_iff | [] | [
1058,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
1
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Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_iInf | [] | [
124,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_le' | [] | [
142,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
9
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Mathlib/LinearAlgebra/Dual.lean | Subspace.dualLift_injective | [] | [
1052,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
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Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.exists_monotone_subseq | [] | [
410,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
8
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.exists_root_of_splits | [] | [
295,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.union_div | [] | [
662,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
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Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.isEquivalent_of_tendsto_one | [
{
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217,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.floor_mono | [
{
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192,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Algebra/Support.lean | Function.mulSupport_eq_iff | [
{
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91,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean | CategoryTheory.Pretriangulated.comp_dist_triangle_mor_zero₃₁ | [
{
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160,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_inr | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.sum.of | [] | [
953,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | continuousAt_fract | [] | [
165,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.hasFiniteIntegral_prod_iff | [
{
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255,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/Algebra/Star/SelfAdjoint.lean | IsSelfAdjoint.star_eq | [] | [
75,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_add | [] | [
1277,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1275,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.ι_desc | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nX Y : SimplicialObject C\ns : Splitting X\nZ : C\nΔ : SimplexCategoryᵒᵖ\nF : (A : IndexSet Δ) → N s (len A.fst.unop) ⟶ Z\nA : IndexSet Δ\n⊢ (ιCoprod s.N A ≫ (iso s Δ).hom) ≫ (iso s Δ).inv ≫ Sigma.desc F = F A",
"state_before... | [
331,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Std/Data/List/Lemmas.lean | List.drop_subset | [] | [
1731,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1730,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | pow_eq_mod_card | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Fintype G\nn : ℕ\n⊢ x ^ n = x ^ (n % Fintype.card G)",
"tactic": "rw [pow_eq_mod_orderOf, ← Nat.mod_mod_of_dvd n orderOf_dvd_card_univ, ← pow_eq_mod_orderOf]"
... | [
954,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_monadLift | [] | [
271,
181
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
271,
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] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopicRel.symm | [] | [
691,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_def | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_pos | [
{
"state_after": "no goals",
"state_before": "p q : ℚ\n⊢ 0 < toNNRat q ↔ 0 < q",
"tactic": "simp [toNNRat, ← coe_lt_coe]"
}
] | [
348,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_sdiff_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.261878\nγ : Type ?u.261881\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b : α\ns t : Finset α\na : α\n⊢ erase s a \\ t = erase (s \\ t) a",
"tactic": "simp_rw [erase_eq, sdiff_right_comm]"
}
] | [
2254,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2253,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_zero_X | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\n⊢ ↑(coeff R 0) X = 0",
"tactic": "rw [coeff, Finsupp.single_zero, X, MvPowerSeries.coeff_zero_X]"
}
] | [
1436,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.iUnion_compl | [] | [
370,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.dotProduct_diagonal | [
{
"state_after": "l : Type ?u.153650\nm : Type u_1\nn : Type ?u.153656\no : Type ?u.153659\nm' : o → Type ?u.153664\nn' : o → Type ?u.153669\nR : Type ?u.153672\nS : Type ?u.153675\nα : Type v\nβ : Type w\nγ : Type ?u.153682\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : DecidableEq m\ninst✝ : NonUnitalNonAs... | [
818,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
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Mathlib/Data/Finmap.lean | AList.toFinmap_eq | [
{
"state_after": "case mk\nα : Type u\nβ : α → Type v\ns₂ : AList β\nentries✝ : List (Sigma β)\nnodupKeys✝ : NodupKeys entries✝\n⊢ ⟦{ entries := entries✝, nodupKeys := nodupKeys✝ }⟧ = ⟦s₂⟧ ↔\n { entries := entries✝, nodupKeys := nodupKeys✝ }.entries ~ s₂.entries",
"state_before": "α : Type u\nβ : α → Typ... | [
82,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | MonoidHom.map_dvd | [] | [
107,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.gluedSection_isAmalgamation | [
{
"state_after": "C D : Type u\ninst✝³ : Category C\ninst✝² : Category D\nA : Type w\ninst✝¹ : Category A\ninst✝ : HasLimits A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nG : C ⥤ D\nhu : CoverLifting J K G\nℱ : Sheaf J A\nX : A\nU : D\nS : Sieve U\nhS : S ∈ GrothendieckTopology.sieves K U\nx : Fami... | [
268,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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] |
Mathlib/Analysis/SpecificLimits/Normed.lean | norm_sum_neg_one_pow_le | [
{
"state_after": "α : Type ?u.1626294\nβ : Type ?u.1626297\nι : Type ?u.1626300\nE : Type ?u.1626303\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nb : ℝ\nf : ℕ → ℝ\nz : ℕ → E\nn : ℕ\n⊢ ‖if Even n then 0 else 1‖ ≤ 1",
"state_before": "α : Type ?u.1626294\nβ : Type ?u.1626297\nι : Type ?u.1626300\n... | [
615,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.transpose_transpose | [
{
"state_after": "case cells.a\nμ : YoungDiagram\nx : ℕ × ℕ\n⊢ x ∈ (transpose (transpose μ)).cells ↔ x ∈ μ.cells",
"state_before": "μ : YoungDiagram\n⊢ transpose (transpose μ) = μ",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case cells.a\nμ : YoungDiagram\nx : ℕ × ℕ\n... | [
225,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec.add | [
{
"state_after": "p : ℕ\n⊢ Nat.rec (unpair p).fst (fun y IH => succ IH) (unpair p).snd = (unpair p).fst + (unpair p).snd",
"state_before": "p : ℕ\n⊢ unpaired (fun z n => Nat.rec (id z) (fun y IH => succ (unpair (unpair (Nat.pair z (Nat.pair y IH))).snd).snd) n) p =\n unpaired (fun x x_1 => x + x_1) p",
... | [
135,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.set_lintegral_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.925342\nγ : Type ?u.925345\nδ : Type ?u.925348\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\n⊢ (∫⁻ (x : α) in ∅, f x ∂μ) = 0",
"tactic": "rw [Measure.restrict_empty, lintegral_zero_measure]"
}
] | [
650,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.mk_coordChange | [
{
"state_after": "case h₁\nR : Type u_1\nB : Type u_2\nF : Type u_3\nE : B → Type u_4\ninst✝⁶ : NontriviallyNormedField R\ninst✝⁵ : (x : B) → AddCommMonoid (E x)\ninst✝⁴ : (x : B) → Module R (E x)\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace R F\ninst✝¹ : TopologicalSpace B\ninst✝ : (x : B) → Topologica... | [
906,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.forget_obj_of | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.ker_toLin_eq_bot | [] | [
101,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Std/Data/String/Lemmas.lean | String.utf8Len_cons | [] | [
49,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
49,
9
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_inf | [
{
"state_after": "x y : ℝ\na b : CauSeq ℚ abs\n⊢ { cauchy := Quotient.mk equiv (a ⊓ b) } =\n match { cauchy := Quotient.mk equiv a }, { cauchy := Quotient.mk equiv b } with\n | { cauchy := x }, { cauchy := y } =>\n { cauchy := Quotient.map₂ (fun x x_1 => x ⊓ x_1) Real.definition.proof_2✝ x y }",
... | [
483,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_le_of_injective | [] | [
464,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_iff_forall_closed | [] | [
128,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_2\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.96628\ninst✝¹... | [
139,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/Order/Filter/Basic.lean | Filter.principal_neBot_iff | [] | [
987,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.bit1_eq_one | [
{
"state_after": "case h\nR : Type u_1\nι : Type ?u.3727\ninst✝¹ : Semiring R\ninst✝ : CharP R 2\nx✝ : R\n⊢ bit1 x✝ = OfNat.ofNat 1 x✝",
"state_before": "R : Type u_1\nι : Type ?u.3727\ninst✝¹ : Semiring R\ninst✝ : CharP R 2\n⊢ bit1 = 1",
"tactic": "funext"
},
{
"state_after": "no goals",
"s... | [
53,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/IsLocallyHomeomorph.lean | IsLocallyHomeomorphOn.comp | [
{
"state_after": "X : Type u_3\nY : Type u_1\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ng : Y → Z\nf : X → Y\ns : Set X\nt : Set Y\nhg : IsLocallyHomeomorphOn g t\nhf : IsLocallyHomeomorphOn f s\nh : Set.MapsTo f s t\nx : X\nhx : x ∈ s\n⊢ ∃ e, x ∈ e.sour... | [
80,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
11
] |
Mathlib/Topology/MetricSpace/Isometry.lean | isometry_iff_dist_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.476\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf : α → β\n⊢ Isometry f ↔ ∀ (x y : α), dist (f x) (f y) = dist x y",
"tactic": "simp only [isometry_iff_nndist_eq, ← coe_nndist, NNReal.coe_eq]"
... | [
52,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.union_left | [] | [
118,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | edist_div_left | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝⁶ : PseudoEMetricSpace X\ninst✝⁵ : Group G\ninst✝⁴ : MulAction G X\ninst✝³ : IsometricSMul G X\ninst✝² : PseudoEMetricSpace G\ninst✝¹ : IsometricSMul G G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b c : G\n⊢ edist (a / b) (a / c) =... | [
152,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Complex.inner | [] | [
2235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2234,
11
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Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.isMittagLeffler_iff_eventualRange | [] | [
156,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom | [] | [
1016,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_nonempty | [] | [
715,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.Quotient.mk_smul_out' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : Group α\ninst✝² : Monoid β\ninst✝¹ : MulAction β α\nH : Subgroup α\ninst✝ : QuotientAction β H\nb : β\nq : α ⧸ H\n⊢ ↑(b • Quotient.out' q) = b • q",
"tactic": "rw [← Quotient.smul_mk, QuotientGroup.out_eq']"
}
] | [
113,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Sigma/Basic.lean | Prod.fst_toSigma | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_sub_linear_isLittleO_of_tendsto_ae | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\n𝕜 : Type ?u.1613008\nE : Type u_1\nF : Type ?u.1613014\nA : Type ?u.1613017\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedSpace ℝ E\nf : ℝ → E\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\na b z : ℝ\nu✝ v✝ ... | [
511,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.WF.update | [
{
"state_after": "case refine_1\nα : Type u_1\nβ : Type u_2\ninst✝³ : BEq α\ninst✝² : Hashable α\nbuckets : Bucket α β\ni : USize\nd : AssocList α β\nh : USize.toNat i < Array.size buckets.val\nH : WF buckets\nh₁ :\n ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α],\n List.Pairwise (fun a b => ¬(a.fst... | [
60,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
46,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.ofFunction_eq_sSup | [] | [
731,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_apply_eq_zero' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.291960\nγ : Type ?u.291963\nδ : Type ?u.291966\nι : Type ?u.291969\nR : Type ?u.291972\nR' : Type ?u.291975\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1672,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
] |
Mathlib/Data/Set/Function.lean | Set.injective_iff_injOn_univ | [] | [
651,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.comp_assoc | [] | [
1156,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.compLinearMap_id | [] | [
425,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.leadingCoeff_prod' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type w\ns : Finset ι\ninst✝ : CommSemiring R\nf : ι → R[X]\nt : Multiset R[X]\nh : ∏ i in s, leadingCoeff (f i) ≠ 0\n⊢ leadingCoeff (∏ i in s, f i) = ∏ i in s, leadingCoeff (f i)",
"tactic": "simpa using leadingCoeff_multiset_prod' (s.1.map f... | [
162,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.continuousOn | [] | [
700,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.card_inv | [] | [
279,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Topology/Sequences.lean | Continuous.seqContinuous | [] | [
219,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
11
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAt_apply_mk | [] | [
698,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.LpAddConst_of_one_le | [
{
"state_after": "case hnc\nα : Type ?u.3022017\nE : Type ?u.3022020\nF : Type ?u.3022023\nG : Type ?u.3022026\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np : ℝ≥0∞\nhp : 1 ≤ p\n⊢ ¬p ∈ Set.Ioo 0 1",
... | [
797,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_toMul | [] | [
2203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2202,
1
] |
Mathlib/Control/LawfulFix.lean | Part.Fix.mem_iff | [
{
"state_after": "case pos\nα : Type u_2\nβ : α → Type u_1\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\na : α\nb : β a\nh₀ : ∃ i, (approx (↑f) i a).Dom\n⊢ b ∈ Part.fix (↑f) a ↔ ∃ i, b ∈ approx (↑f) i a\n\ncase neg\nα : Type u_2\nβ : α → Type u_1\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\na : α... | [
94,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Control/Traversable/Lemmas.lean | Traversable.id_sequence | [
{
"state_after": "no goals",
"state_before": "t : 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✝... | [
101,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.independent_iff_dfinsupp_lsum_injective | [] | [
531,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous_trans | [] | [
538,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_rat_le_one | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\nd : ℕ\nhn : d ≠ 0\nhd : coprime (Int.natAbs n) d\nhq : ¬p ∣ d\nhnz : n = 0\nthis : Rat.mk' n d = 0\n⊢ ‖↑(Rat.mk' n d)‖ ≤ 1",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\nd : ℕ\nhn : d ≠ 0\nhd : coprime (Int.natAbs n) d\nhq : ¬p ∣ d\nhnz : n... | [
912,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.cont_withSeminorms_normedSpace | [
{
"state_after": "𝕜 : Type ?u.643524\n𝕜₂ : Type ?u.643527\n𝕝 : Type u_4\n𝕝₂ : Type u_2\nE : Type u_3\nF✝ : Type ?u.643539\nG : Type ?u.643542\nι : Type u_5\nι' : Type ?u.643548\ninst✝¹⁷ : NontriviallyNormedField 𝕜\ninst✝¹⁶ : AddCommGroup E\ninst✝¹⁵ : Module 𝕜 E\ninst✝¹⁴ : NormedField 𝕝\ninst✝¹³ : Module ... | [
653,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Topology/PathConnected.lean | Path.trans_symm | [
{
"state_after": "case a.h\nX : Type u_1\nY : Type ?u.237548\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.237563\nγ✝ γ : Path x y\nγ' : Path y z\nt : ↑I\n⊢ ↑(symm (trans γ γ')) t = ↑(trans (symm γ') (symm γ)) t",
"state_before": "X : Type u_1\nY : Type ?u.237548\ninst✝¹ :... | [
368,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_one | [] | [
401,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.measure_sum_seq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.382317\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ✝ κ : { x // x ∈ kernel α β }\nh : IsSFiniteKernel κ\na : α\n⊢ (Measure.sum fun n => ↑(seq κ n) a) = ↑κ a",
"tactic": "rw [← kernel.sum_apply, kernel_sum_seq κ]"... | [
292,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lsubtypeDomain_apply | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mk_eq_add_mul_I | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\n⊢ { re := a, im := b }.re = (↑a + ↑b * I).re ∧ { re := a, im := b }.im = (↑a + ↑b * I).im",
"tactic": "simp [ofReal']"
}
] | [
329,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Relabelling.ge | [] | [
1115,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_image_eq_source_inter_preimage | [] | [
287,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.OrderTop.atTop_eq | [] | [
284,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.dvd_of_multiplicity_pos | [
{
"state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nh : 0 < multiplicity a b\n⊢ a ^ 1 ∣ b",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nh : 0 < multiplicity a b\n⊢ a ∣ b",
"tactic": "rw [← pow_on... | [
271,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sup_idem | [] | [
902,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
11
] |
Std/Data/Nat/Lemmas.lean | Nat.mod_add_div | [
{
"state_after": "no goals",
"state_before": "m k : Nat\n⊢ m % k + k * (m / k) = m",
"tactic": "induction m, k using mod.inductionOn with rw [div_eq, mod_eq]\n| base x y h => simp [h]\n| ind x y h IH => simp [h]; rw [Nat.mul_succ, ← Nat.add_assoc, IH, Nat.sub_add_cancel h.2]"
},
{
"state_after":... | [
253,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
250,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.sigmaFinsuppLEquivPiFinsupp_symm_apply | [] | [
995,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/CategoryTheory/Sites/Types.lean | CategoryTheory.generate_discretePresieve_mem | [] | [
57,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat_def' | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\nhp : p ≠ 1\nhn : 0 < n\n⊢ ↑(padicValNat p n) = multiplicity p n",
"tactic": "simp [padicValNat, hp, hn]"
}
] | [
230,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.tr_eval_rev | [
{
"state_after": "case intro\nσ₁ : Type u_1\nσ₂ : Type u_2\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂ → Prop\nH : Respects f₁ f₂ tr\na₁ : σ₁\nb₂ a₂ : σ₂\naa : tr a₁ a₂\nab✝ : b₂ ∈ eval f₂ a₂\nab : Reaches f₂ a₂ b₂\nb0 : f₂ b₂ = none\n⊢ ∃ b₁, tr b₁ b₂ ∧ b₁ ∈ eval f₁ a₁",
"state_before": "σ₁ : Ty... | [
946,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eventually_ne_nhdsWithin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.24737\nδ : Type ?u.24740\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne✝ : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ne : LocalHomeomorph α β\nx : ... | [
260,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
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