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 |
|---|---|---|---|---|---|---|
src/lean/Init/Data/Nat/Basic.lean | Nat.eq_of_mul_eq_mul_left | [] | [
466,
71
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
464,
11
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.tsub_lt_tsub_iff_left_of_le | [] | [
463,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
11
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasKernel_of_hasEqualizer | [] | [
362,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_max | [] | [
179,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.lt_left_of_right_lt' | [] | [
781,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/Data/Part.lean | Part.sdiff_mem_sdiff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.95752\nγ : Type ?u.95755\ninst✝ : SDiff α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 \\ a = ma \\ mb",
"state_before": "α : Type u_1\nβ : Type ?u.95752\nγ : Type ?u.95755\ninst✝ : SDiff α\na b : Part α\nma mb : α\nha : ... | [
863,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_map | [] | [
310,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_ne_coe | [] | [
44,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | comp_smul_left | [] | [
496,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/List/Count.lean | List.count_singleton | [
{
"state_after": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\na : α\n⊢ (if a = a then succ (count a []) else count a []) = 1",
"state_before": "α : Type u_1\nl : List α\ninst✝ : DecidableEq α\na : α\n⊢ count a [a] = 1",
"tactic": "rw [count_cons]"
},
{
"state_after": "no goals",
"state_... | [
223,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_apply_lt | [] | [
73,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.deriv_rpow_const | [] | [
364,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.lt_inv_iff_mul_lt | [
{
"state_after": "no goals",
"state_before": "r p : ℝ≥0\nh : p ≠ 0\n⊢ r < p⁻¹ ↔ r * p < 1",
"tactic": "rw [← mul_lt_mul_left (pos_iff_ne_zero.2 h), mul_inv_cancel h, mul_comm]"
}
] | [
796,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_le_sqrt_iff | [] | [
56,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.symm_refl | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_eq_foldr | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1814\nα : Type ?u.1817\nβ : Type ?u.1820\nγ : Type ?u.1823\ninst✝ : CommMonoid α\ns✝ t : Multiset α\na : α\nm : Multiset ι\nf g : ι → α\ns : Multiset α\nx y z : α\n⊢ (fun x x_1 => x * x_1) x ((fun x x_1 => x * x_1) y z) = (fun x x_1 => x * x_1) y ((f... | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Control/Traversable/Instances.lean | List.comp_traverse | [
{
"state_after": "no goals",
"state_before": "F G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα : Type u_1\nβ γ : Type u\nf : β → F γ\ng : α → G β\nx : List α\n⊢ List.traverse (Comp.mk ∘ (fun x x_1 => x <$> x_1) f ∘ g) x = Com... | [
86,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.limRatioMeas_measurable | [] | [
435,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.zero_smul' | [
{
"state_after": "case h\nR : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\ns : { x // x ∈ S }\n⊢ 0 • mk m s = 0",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module ... | [
385,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
9
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_comp_toAlgHom | [] | [
430,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/RingTheory/NonZeroDivisors.lean | map_le_nonZeroDivisors_of_injective | [
{
"state_after": "case inl\nM : Type u_3\nM' : Type u_1\nM₁ : Type ?u.57271\nR : Type ?u.57274\nR' : Type ?u.57277\nF : Type u_2\ninst✝⁶ : MonoidWithZero M\ninst✝⁵ : MonoidWithZero M'\ninst✝⁴ : CommMonoidWithZero M₁\ninst✝³ : Ring R\ninst✝² : CommRing R'\ninst✝¹ : NoZeroDivisors M'\ninst✝ : MonoidWithZeroHomCla... | [
157,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_zero_eq_const | [] | [
78,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | a_soln_is_unique | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nha : Polynomial.eval a F = 0\nz' : ℤ_[p]\nhz' : Polynomial.eval z' F = 0\nhnormz' : ‖z' - a‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖\nh : ℤ_[p] := z' - a\nq : ℤ_[p]\nhq : Polynomial.eval (a + h) F = Polynomial.eval a ... | [
485,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
9
] |
Mathlib/Analysis/NormedSpace/Basic.lean | frontier_closedBall' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.308974\nβ : Type ?u.308977\nγ : Type ?u.308980\nι : Type ?u.308983\ninst✝⁶ : NormedField α\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace α E\nF : Type ?u.309076\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace α F\ninst✝¹ : N... | [
392,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Combinatorics/Quiver/Basic.lean | Prefunctor.comp_assoc | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_const | [] | [
182,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Functor.preimageIso_mapIso | [
{
"state_after": "case w\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nF : C ⥤ D\ninst✝¹ : Full F\ninst✝ : Faithful F\nX Y Z : C\nf : X ≅ Y\n⊢ (preimageIso F (F.mapIso f)).hom = f.hom",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nF : C ⥤ D\nins... | [
157,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_iff_segment_subset | [] | [
65,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.le_smul_iff | [] | [
1055,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_negPart_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15046\ninst✝ : MeasurableSpace α\nj : JordanDecomposition α\nr : ℝ\nhr : r < 0\n⊢ (r • j).negPart = Real.toNNReal (-r) • j.posPart",
"tactic": "rw [real_smul_def, ← smul_posPart, if_neg (not_le.2 hr), neg_negPart]"
}
] | [
168,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.coe_decide | [] | [
46,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.antitone_pair_of_not_sorted | [] | [
183,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/AddTorsor.lean | vsub_eq_sub | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coeSucc_eq_succ | [
{
"state_after": "case zero\nm : ℕ\na : Fin zero\n⊢ ↑castSucc a + 1 = succ a\n\ncase succ\nm n✝ : ℕ\na : Fin (Nat.succ n✝)\n⊢ ↑castSucc a + 1 = succ a",
"state_before": "n m : ℕ\na : Fin n\n⊢ ↑castSucc a + 1 = succ a",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case... | [
1312,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_iff_comap_le | [] | [
214,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.add_eq_zero_iff | [
{
"state_after": "R : Type u\ninst✝ : LinearOrder R\na b : Tropical (WithTop R)\n⊢ a = 0 ∧ a ≤ b ∨ b = 0 ∧ b ≤ a ↔ a = 0 ∧ b = 0",
"state_before": "R : Type u\ninst✝ : LinearOrder R\na b : Tropical (WithTop R)\n⊢ a + b = 0 ↔ a = 0 ∧ b = 0",
"tactic": "rw [add_eq_iff]"
},
{
"state_after": "case m... | [
370,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.image_add_left_Ioo | [
{
"state_after": "ι : Type ?u.242100\nα : Type u_1\ninst✝³ : OrderedCancelAddCommMonoid α\ninst✝² : ExistsAddOfLE α\ninst✝¹ : LocallyFiniteOrder α\ninst✝ : DecidableEq α\na b c : α\n⊢ image ((fun x x_1 => x + x_1) c) (Ioo a b) = image (↑(addLeftEmbedding c)) (Ioo a b)",
"state_before": "ι : Type ?u.242100\n... | [
1119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_le_inter_not_le | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : SemilatticeSup α\na : α\n⊢ Bounded (fun x x_1 => x ≤ x_1) (s ∩ {b | ¬b ≤ a}) ↔ Bounded (fun x x_1 => x ≤ x_1) s",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : SemilatticeSup α\na : α\n⊢ Unbounded (fun x x_1 => x ... | [
327,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.update | [] | [
850,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Algebra/LinearRecurrence.lean | LinearRecurrence.is_sol_iff_mem_solSpace | [] | [
140,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.zero_snd | [] | [
269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisorsAntidiagonal_zero | [
{
"state_after": "case a\nn : ℕ\na✝ : ℕ × ℕ\n⊢ a✝ ∈ divisorsAntidiagonal 0 ↔ a✝ ∈ ∅",
"state_before": "n : ℕ\n⊢ divisorsAntidiagonal 0 = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nn : ℕ\na✝ : ℕ × ℕ\n⊢ a✝ ∈ divisorsAntidiagonal 0 ↔ a✝ ∈ ∅",
"tactic": "sim... | [
204,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.image_inclusion' | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.62091\nγ : Type ?u.62094\nδ : Type ?u.62097\nδ' : Type ?u.62100\nι : Sort uι\ns✝ t✝ u✝ : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\ns t : Set α\nh : s ⊆ t\nhs : MeasurableSet (Subtype.val ⁻¹' s)\nu : Set α\nhu : MeasurableSet u\n⊢ Measurab... | [
588,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Multiset/Sort.lean | Multiset.length_sort | [] | [
58,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | OrthogonalFamily.inner_sum | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_3\nF : Type ?u.3657440\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\ndec_ι : DecidableEq ι\nG : ι → Type u_4\ninst✝¹ : (i : ι) → ... | [
2051,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2039,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_add_measure_compl | [] | [
157,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_mono | [] | [
153,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Matrix/Basic.lean | LinearEquiv.mapMatrix_trans | [] | [
1514,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
1
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Mathlib/Data/List/Perm.lean | List.Perm.pairwise_iff | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁✝¹ l₂✝² : List α\nR : α → α → Prop\nS : Symmetric R\nl₁✝ l₂✝¹ l₁ l₂✝ : List α\np✝ : l₁ ~ l₂✝\nl₂ : List α\np : [] ~ l₂\n⊢ Pairwise R l₂\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁✝² l₂✝² : List α\nR : α → α → Prop\nS : Symmetric R\nl₁✝¹ l₂✝¹ l₁✝ l₂✝ : List ... | [
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33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.nat_div | [] | [
454,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.eq_prod_roots_of_splits | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni✝ : K →+* L\np : K[X]\ni : K →+* L\nhsplit : Splits i p\n⊢ map i p = ↑C (leadingCoeff (map i p)) * Multiset.prod (Multiset.map (fun a => X - ↑C a) (roots (map i p)))",
"state_before": "F : Type u\nK :... | [
355,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | LipschitzOnWith.norm_div_le_of_le | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.186854\n𝕜 : Type ?u.186857\nα : Type ?u.186860\nι : Type ?u.186863\nκ : Type ?u.186866\nE : Type u_1\nF : Type u_2\nG : Type ?u.186875\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : ... | [
815,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_ediv_cancel_of_emod_eq_zero | [
{
"state_after": "a b : Int\nH : a % b = 0\nthis : a % b + b * (a / b) = a\n⊢ b * (a / b) = a",
"state_before": "a b : Int\nH : a % b = 0\n⊢ b * (a / b) = a",
"tactic": "have := emod_add_ediv a b"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nH : a % b = 0\nthis : a % b + b * (... | [
586,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
585,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.mapsTo_sphere | [] | [
262,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Int/Basic.lean | Int.natAbs_surjective | [] | [
200,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_le | [] | [
268,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.add_tprodCoeff' | [] | [
165,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.dist_eq | [] | [
133,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_spec | [] | [
63,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
11
] |
src/lean/Init/Data/List/Basic.lean | List.append_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas bs cs : List α\n⊢ as ++ bs ++ cs = as ++ (bs ++ cs)",
"tactic": "induction as with\n| nil => rfl\n| cons a as ih => simp [ih]"
},
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u\nβ : Type ... | [
106,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
103,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsAddCyclic.card_orderOf_eq_totient | [
{
"state_after": "case mk.intro\nα✝ : Type u\na : α✝\ninst✝³ : Group α✝\nα : Type u_1\ninst✝² : AddGroup α\ninst✝¹ : IsAddCyclic α\ninst✝ : Fintype α\nd : ℕ\nhd : d ∣ Fintype.card α\ng : α\nhg : ∀ (x : α), x ∈ AddSubgroup.zmultiples g\n⊢ card (filter (fun a => addOrderOf a = d) univ) = φ d",
"state_before":... | [
426,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.epi_of_pseudo_surjective | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nh : Function.Surjective (pseudoApply f)\n⊢ Epi f",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\n⊢ Function.Surjective (pseudoApply f) → Epi f",
"tactic": "intro h"
},
... | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_zero | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.955922\nm : Type u_1\nn : Type u_2\no : Type ?u.955931\nm' : o → Type ?u.955936\nn' : o → Type ?u.955941\nR : Type ?u.955944\nS : Type ?u.955947\nα : Type v\nβ : Type w\nγ : Type ?u.955954\ninst✝¹ : AddMonoid α\ninst✝ : StarAddMonoid α\n⊢ ∀ (i : n) (... | [
2140,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2139,
1
] |
Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.isSemisimple_iff_no_solvable_ideals | [] | [
69,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_some | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : DecidableEq (Associates α)\np : Associates α\nhp : Irreducible p\ns : Multiset { a // Irreducible a }\n⊢ dite (Irreducible p) (fun hp => bcount { val := p, property := hp }) (fu... | [
1296,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.isRight_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.8798\nδ : Type ?u.8801\nx y : α ⊕ β\n⊢ isRight x = true ↔ ∃ y, x = inr y",
"tactic": "cases x <;> simp"
}
] | [
150,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.finset_sum_apply' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nI : Finset ι\nκ : ι → { x // x ∈ kernel α β }\na : α\ns : Set β\n⊢ ↑↑(↑(∑ i in I, κ i) a) s = ∑ i in I, ↑↑(↑(κ i) a) s",
"tactic": "rw [finset_sum_apply, Measure.finset... | [
111,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.Finite.mul | [] | [
53,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff | [] | [
1916,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1915,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.nextCoeff_X_add_C | [
{
"state_after": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝² : Nontrivial R\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nc : S\n✝ : Nontrivial S\n⊢ nextCoeff (X + ↑C c) = c",
"state_before": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝² : Nontrivial R\ninst✝¹ : Semiring R\ninst✝ : Semiring ... | [
1375,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.Preorder.wellFounded_lt | [] | [
915,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.powerlt_zero | [] | [
2324,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2321,
1
] |
Mathlib/Algebra/Module/PointwisePi.lean | smul_univ_pi | [
{
"state_after": "case refine'_1\nK : Type u_1\nι : Type u_3\nR : ι → Type u_2\ninst✝ : (i : ι) → SMul K (R i)\nr : K\nt : (i : ι) → Set (R i)\nx : (i : ι) → R i\nh : x ∈ pi univ (r • t)\ni : ι\nx✝ : i ∈ univ\n⊢ (fun i => Classical.choose (_ : x i ∈ (r • t) i)) i ∈ t i\n\ncase refine'_2\nK : Type u_1\nι : Type ... | [
46,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.exists | [] | [
62,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.closure_subset_interior_image_homothety_of_one_lt | [] | [
329,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_empty | [] | [
117,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderiv_zero_of_not_differentiableAt | [
{
"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.41308\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.41403\ni... | [
227,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mul_apply_le | [] | [
1118,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_self_add_left | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ coprime (m + n) m ↔ coprime n m",
"tactic": "rw [coprime, coprime, gcd_self_add_left]"
}
] | [
149,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_inter | [] | [
948,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.lt_succ | [] | [
171,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_iInf_left | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.11121\nδ : Type ?u.11124\nι : Sort u_1\ns : Set α\nt : Set β\nf✝ : Filter α\ng✝ : Filter β\ninst✝ : Nonempty ι\nf : ι → Filter α\ng : Filter β\n⊢ Filter.prod (⨅ (i : ι), f i) g = ⨅ (i : ι), Filter.prod (f i) g",
"state_before": "α : Type u_2\nβ : Typ... | [
220,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.mapRange.linearMap_id | [
{
"state_after": "case h.h.h\nι : Type u_1\nR : Type u_3\nS : Type ?u.140242\nM : ι → Type ?u.140247\nN : Type ?u.140250\ndec_ι : DecidableEq ι\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : ι) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → Module R (M i)\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module R N\nβ : ι → Type ?u.140337\... | [
211,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_module' | [] | [
522,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
src/lean/Init/Data/String/Basic.lean | String.utf8PrevAux_lt_of_pos | [
{
"state_after": "c : Char\ncs : List Char\ni p : Pos\nh : p ≠ 0\n⊢ (ite (i + c = p) i (utf8PrevAux cs (i + c) p)).byteIdx < p.byteIdx",
"state_before": "c : Char\ncs : List Char\ni p : Pos\nh : p ≠ 0\n⊢ (utf8PrevAux (c :: cs) i p).byteIdx < p.byteIdx",
"tactic": "simp [utf8PrevAux]"
},
{
"state... | [
149,
48
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
140,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.sum_apply | [
{
"state_after": "no goals",
"state_before": "R₁ : Type u_2\nR₂ : Type u_3\nR₃ : Type ?u.493091\ninst✝¹⁷ : Semiring R₁\ninst✝¹⁶ : Semiring R₂\ninst✝¹⁵ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_4\ninst✝¹⁴ : TopologicalSpace M₁\ninst✝¹³ : AddCommMonoid M₁\nM'₁ : Type ?u.493... | [
763,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.map_sub | [] | [
360,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
11
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_sublist_of_dvd | [
{
"state_after": "case intro\nn a : ℕ\nh' : n * a ≠ 0\n⊢ factors n <+ factors (n * a)",
"state_before": "n k : ℕ\nh : n ∣ k\nh' : k ≠ 0\n⊢ factors n <+ factors k",
"tactic": "obtain ⟨a, rfl⟩ := h"
},
{
"state_after": "no goals",
"state_before": "case intro\nn a : ℕ\nh' : n * a ≠ 0\n⊢ factors... | [
230,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.PreEnvelGroupRel'.rel | [] | [
640,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
1
] |
Mathlib/Data/Int/Interval.lean | Int.card_Ioo | [
{
"state_after": "a b : ℤ\n⊢ card (map (Function.Embedding.trans Nat.castEmbedding (addLeftEmbedding (a + 1))) (range (toNat (b - a - 1)))) =\n toNat (b - a - 1)",
"state_before": "a b : ℤ\n⊢ card (Ioo a b) = toNat (b - a - 1)",
"tactic": "change (Finset.map _ _).card = _"
},
{
"state_after":... | [
127,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.sub_re | [] | [
927,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
9
] |
Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.coe_top | [] | [
344,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Topology/Maps.lean | closedEmbedding_of_embedding_closed | [] | [
677,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_Ico | [] | [
732,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.ramificationIdx_spec | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nn : ℕ\nhle : map f p ≤ P ^ n\nhgt : ¬map f p ≤ P ^ (n + 1)\nQ : ℕ → Prop := fun m => ∀ (k : ℕ), map f p ≤ P ^ k → k ≤ m\n⊢ ramificationIdx f p P = n",
"state_before": "R : Type u\ninst✝¹... | [
98,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneEquiv.le_congr_left | [] | [
245,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/CategoryTheory/Skeletal.lean | CategoryTheory.Functor.eq_of_iso | [] | [
66,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.C_one | [] | [
973,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.congr | [] | [
412,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_zero | [
{
"state_after": "no goals",
"state_before": "⊢ bernoulli 0 = 1",
"tactic": "simp [bernoulli]"
}
] | [
76,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
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