file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_eq_norm_vsub | [] | [
77,
36
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76,
1
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_pow | [] | [
323,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
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Mathlib/Topology/ContinuousFunction/T0Sierpinski.lean | TopologicalSpace.eq_induced_by_maps_to_sierpinski | [
{
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"state_before": "X : Type u_1\nt : TopologicalSpace X\n⊢ t = ⨅ ... | [
40,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_triple | [
{
"state_after": "no goals",
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"tactic": "simp_rw [einfsep_insert, iInf_insert, iInf_singleton, einfsep_s... | [
238,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/Data/List/Nodup.lean | List.Nodup.of_map | [] | [
241,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.prod_fst_snd | [] | [
641,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.infty_not_mem_image_coe | [] | [
164,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Data/Bool/Basic.lean | Bool.and_le_right | [
{
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}
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358,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.add_val | [
{
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418,
6
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411,
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Mathlib/Data/Real/EReal.lean | EReal.exists_rat_btwn_of_lt | [
{
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},
{
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"tactic": "simpa using hab... | [
609,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
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Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | Measurable.re | [] | [
46,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_eval_one | [
{
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"state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\n⊢ eval 1 (mirror p) = eval 1 p",
... | [
123,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Topology/UniformSpace/Cauchy.lean | SequentiallyComplete.le_nhds_of_seq_tendsto_nhds | [
{
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706,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
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Mathlib/Data/Nat/ModEq.lean | Nat.add_mod_of_add_mod_lt | [
{
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"tactic": "rw [← add_mod_add_ite, if_neg (not_le_of_lt hc), add_zero]"
}
] | [
440,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.symm_symm | [
{
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838,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
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Mathlib/Topology/Order/Basic.lean | le_on_closure | [] | [
235,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Order/Closure.lean | ClosureOperator.top_mem_closed | [] | [
238,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/Heyting/Basic.lean | LE.le.disjoint_compl_right | [] | [
856,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
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Mathlib/Analysis/Complex/Basic.lean | IsROrC.hasSum_im | [] | [
531,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
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Mathlib/Topology/UrysohnsLemma.lean | Urysohns.CU.lim_eq_midpoint | [
{
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"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : NormalSpace X\nc : CU X\nx : X\n... | [
238,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_sub | [
{
"state_after": "R : Type u_1\ninst✝¹⁰ : CommSemiring R\nM : Type u_4\nN : Type u_2\nP : Type u_3\nQ : Type ?u.1448279\nS : Type ?u.1448282\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : AddCommGroup N\ninst✝⁷ : AddCommGroup P\ninst✝⁶ : AddCommGroup Q\ninst✝⁵ : AddCommGroup S\ninst✝⁴ : Module R M\ninst✝³ : Module R N\nins... | [
1285,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1283,
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Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.pentagon_inv_hom | [
{
"state_after": "no goals",
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"tactic": "coherence"
}
] | [
90,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.add_add | [
{
"state_after": "no goals",
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1083,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.nat_ne_bot | [] | [
544,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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Mathlib/Algebra/CharP/Quotient.lean | Ideal.Quotient.index_eq_zero | [
{
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"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ↑(AddSubgroup.index (Submodule.toAddSubgroup I)) = 0",
"tac... | [
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12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.absolutelyContinuous_map_div_left | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulLeftInvariant μ\ng : G\n⊢ μ ≪ map (fun h => g * h⁻¹) μ",
"state_before": "G : Type u_1\n... | [
241,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/Algebra/GeomSum.lean | geom_sum₂_succ_eq | [] | [
309,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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Mathlib/Analysis/Normed/Field/Basic.lean | Finset.nnnorm_prod_le | [
{
"state_after": "no goals",
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"tactic": ... | [
356,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iSup_ennreal | [] | [
453,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
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] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_prodMap' | [] | [
1131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.le_sup_right_iff_inf_left_le | [] | [
518,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.map_bot | [] | [
933,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.finrank_prime_pow_ramificationIdx | [
{
"state_after": "R : Type u\ninst✝⁵ : CommRing R\nS : Type v\ninst✝⁴ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\nhfp : NeZero e\ninst✝³ : IsDomain S\ninst✝² : IsDedekindDomain S\nhP0 : P ≠ ⊥\ninst✝¹ : IsMaximal p\ninst✝ : IsPrime P\nhe : e ≠ 0\nthis : NeZero e := { out := he }\n⊢ finrank (R ⧸ p) (S ⧸ ... | [
685,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_zpow | [
{
"state_after": "case h.e'_2.h.e'_3\nι : Type u_2\nα : Type u_1\nβ : Type ?u.99606\nγ : Type ?u.99609\ninst✝ : DivisionCommMonoid α\nm : Multiset ι\nf g : ι → α\nn : ℤ\n⊢ map (fun i => f i ^ n) m = map (↑(zpowGroupHom n)) (map f m)",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.99606\nγ : Type ... | [
328,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
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Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometryEquiv.norm_iteratedFDerivWithin_comp_left | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
313,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.isTopologicalBasis_Ioo_rat | [
{
"state_after": "no goals",
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"tactic": "simp (config := { contextual := true }) [isOpen_Ioo]"
},
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : ℝ\nv : Se... | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
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Mathlib/Computability/Partrec.lean | Computable.list_reverse | [] | [
350,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Std/Logic.lean | forall₄_congr | [] | [
400,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
398,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_int_mem | [] | [
205,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.affineSpan_parallel_iff_vectorSpan_eq_and_eq_empty_iff_eq_empty | [
{
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... | [
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56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.gc | [] | [
68,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/FDerivAnalytic.lean | AnalyticOn.fderiv | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\ninst✝ : CompleteSpace F... | [
126,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.ne_zero_of_d_ne_zero | [] | [
199,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.isBigO' | [] | [
385,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
11
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | MonoidWithZero.coe_inverse | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_hom' | [
{
"state_after": "case h.e'_2.h.e'_3\nι : Type u_2\nα : Type u_4\nβ : Type u_1\nγ : Type ?u.42625\ninst✝² : CommMonoid α\ns✝ t : Multiset α\na : α\nm : Multiset ι\nf✝ g✝ : ι → α\ninst✝¹ : CommMonoid β\ns : Multiset ι\nF : Type u_3\ninst✝ : MonoidHomClass F α β\nf : F\ng : ι → α\n⊢ map (fun i => ↑f (g i)) s = ma... | [
169,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAtFilter.comp | [
{
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166,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/Data/Fintype/Basic.lean | Finset.compl_union | [] | [
213,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.fst_mem_support_of_mem_edges | [
{
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804,
49
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798,
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.div_tendsto_atBot_of_degree_gt | [] | [
218,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.lintegral_edist_triangle | [
{
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84,
29
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Mathlib/Data/Real/ENNReal.lean | ENNReal.smul_top | [
{
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"... | [
570,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
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Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.disjoint_iff_left | [
{
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"tact... | [
729,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
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Mathlib/Data/Sum/Order.lean | Sum.not_inr_le_inl | [] | [
163,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | eventually_le_limsup | [
{
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274,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.smul_le_self_of_tower | [
{
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262,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | StrictOrder.cof_nonempty | [] | [
131,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translation_number₀ | [
{
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"tactic": "exact_mod_cast f.tendsto_translation_number₀'"
}
] | [
789,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
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Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.seq1_fst_eq_of | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/Analysis/Calculus/Deriv/Star.lean | HasDerivWithinAt.star | [] | [
45,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
18
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Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.isVanKampenColimit_of_evaluation | [
{
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564,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_map_le | [
{
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1287,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | IsCompact.measure_lt_top_of_nhdsWithin | [
{
"state_after": "no goals",
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4487,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4484,
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Filter.Tendsto.exp | [] | [
141,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableAt_snd | [] | [
278,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_le_of_le_left | [
{
"state_after": "no goals",
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"tactic": "rw [Ico, ← Finset.filter_val, Finset.Ico_filter_le_of_le_le... | [
172,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Data/Set/Countable.lean | Set.Finite.countable | [] | [
236,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
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Mathlib/Analysis/Convex/Join.lean | convexJoin_mono | [] | [
50,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.constr_pow_gen | [
{
"state_after": "no goals",
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273,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.map_range | [
{
"state_after": "no goals",
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"tactic": "simpa only [range_eq_map] using (⊤ : Subring R).map_map g f"
}
] | [
672,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Std/Data/Int/Lemmas.lean | Int.min_comm | [
{
"state_after": "a b : Int\n⊢ (if a ≤ b then a else b) = if b ≤ a then b else a",
"state_before": "a b : Int\n⊢ min a b = min b a",
"tactic": "simp [Int.min_def]"
},
{
"state_after": "case pos\na b : Int\nh₁ : a ≤ b\nh₂ : b ≤ a\n⊢ a = b\n\ncase neg\na b : Int\nh₁ : ¬a ≤ b\nh₂ : ¬b ≤ a\n⊢ b = a"... | [
693,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
689,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.C_neg | [] | [
1222,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_prime_pow_succ | [
{
"state_after": "p : ℕ\nhp : Prime p\nn : ℕ\n⊢ filter (coprime (p ^ (n + 1))) (range (p ^ (n + 1))) =\n filter (fun x => ¬x ∈ image (fun x => x * p) (range (p ^ n))) (range (p ^ (n + 1)))",
"state_before": "p : ℕ\nhp : Prime p\nn : ℕ\n⊢ filter (coprime (p ^ (n + 1))) (range (p ^ (n + 1))) = range (p ^ (... | [
218,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.mem_iff_one_sub_mem | [] | [
172,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.rightUnitor_inv_naturality | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf g : a ⟶ b\nη : f ⟶ g\n⊢ η ≫ (ρ_ g).inv = (ρ_ f).inv ≫ η ▷ 𝟙 b",
"tactic": "simp"
}
] | [
410,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | ofReal_norm_eq_coe_nnnorm' | [] | [
977,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.smul_of_top_right | [
{
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1040,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivWithinAt.mul_const | [
{
"state_after": "case h.e'_7\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Typ... | [
205,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.pred_succ | [
{
"state_after": "case mk\nn m val✝ : ℕ\nisLt✝ : val✝ < n\nh : succ { val := val✝, isLt := isLt✝ } ≠ 0\n⊢ pred (succ { val := val✝, isLt := isLt✝ }) h = { val := val✝, isLt := isLt✝ }",
"state_before": "n m : ℕ\ni : Fin n\nh : succ i ≠ 0\n⊢ pred (succ i) h = i",
"tactic": "cases i"
},
{
"state_a... | [
1512,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | diam_smul | [] | [
353,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_option' | [
{
"state_after": "ι : Type u'\nι' : Type ?u.1214502\nR : Type ?u.1214505\nK : Type u_1\nM : Type ?u.1214511\nM' : Type ?u.1214514\nM'' : Type ?u.1214517\nV : Type u\nV' : Type ?u.1214522\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module K V\ninst✝ : Module K V'\nv : ι ... | [
1192,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.Equiv.prod_comp_finset | [
{
"state_after": "ι : Type u_2\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝¹ : CommMonoid β\nι' : Type u_1\ninst✝ : DecidableEq ι\ne : ι ≃ ι'\nf : ι' → β\ns' : Finset ι'\ns : Finset ι\nh : s = image (↑e.symm) s'\n⊢ ∏ i' in s', f i' = ∏ i in image (↑e.symm) s', f (↑e i)",
... | [
594,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.ord_card_unbounded' | [] | [
380,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_mul_cycle | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.28957\nm : Type u_2\nn : Type u_3\np : Type u_4\nα : Type ?u.28969\nR : Type u_1\nS : Type ?u.28975\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : Fintype p\ninst✝ : NonUnitalCommSemiring R\nA : Matrix m n R\nB : Matrix n p R\nC : Matrix p m R\n⊢ ... | [
157,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Data/Rat/Defs.lean | Rat.den_neg_eq_den | [] | [
398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.measure_eq_zero_or_one_or_top_of_indepSet_self | [
{
"state_after": "Ω : Type u_1\nι : Type ?u.53841\nm m0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nt : Set Ω\nh_indep : ↑↑μ (t ∩ t) = ↑↑μ t * ↑↑μ t\n⊢ ↑↑μ t = 0 ∨ ↑↑μ t = 1 ∨ ↑↑μ t = ⊤",
"state_before": "Ω : Type u_1\nι : Type ?u.53841\nm m0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nt : Set Ω... | [
44,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_lt_iff_succ_le | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ni : Fin n\nj : Fin (n + 1)\n⊢ ↑castSucc i < j ↔ succ i ≤ j",
"tactic": "simpa only [lt_iff_val_lt_val, le_iff_val_le_val, val_succ, Fin.coe_castSucc] using\n Nat.lt_iff_add_one_le"
}
] | [
1234,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.div_right | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace α\ninst✝¹ : Group α\ninst✝ : TopologicalGroup α\ns t : Set α\nhs : IsOpen s\n⊢ IsOpen (⋃ (a : α) (_ : a ∈ t), (fun x => x / a) '' s)",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : Topolog... | [
1344,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_mem_smul_set | [] | [
328,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_mul_aleph0 | [] | [
596,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vectorSpan_mono | [] | [
75,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_ciSup_set | [] | [
803,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_inter_distrib | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.373972\nγ : Type ?u.373975\np q : α → Prop\ninst✝² : DecidablePred p\ninst✝¹ : DecidablePred q\ninst✝ : DecidableEq α\ns t : Finset α\na✝ : α\n⊢ a✝ ∈ filter p (s ∩ t) ↔ a✝ ∈ filter p s ∩ filter p t",
"state_before": "α : Type u_1\nβ : Type ?u.373972\nγ : T... | [
2827,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2825,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_tmul | [] | [
995,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.splittings_comm | [
{
"state_after": "𝒜 : Type u_1\ninst✝² : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝¹ : Preadditive 𝒜\ninst✝ : HasBinaryBiproducts 𝒜\nh✝ h h' : Splitting f g\nthis : Mono f\n⊢ section h' ≫ retraction h = -section h ≫ retraction h'",
"state_before": "𝒜 : Type... | [
297,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.symm_mulLeft₀ | [] | [
186,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.splits_iff_card_roots | [
{
"state_after": "R : Type ?u.689546\nS : Type ?u.689549\nF : Type u_1\nK : Type u_2\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nφ : F →+* K\nx y z : K\nha : (map φ P).a ≠ 0\n⊢ Splits φ (toPoly P) ↔ ↑card (roots (map φ P)) = 3",
"state_before": "R : Type ?u.689546\nS : Type ?u.689549\nF : Type u_1\nK :... | [
516,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.sum.map_one | [] | [
965,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Order/PropInstances.lean | sup_Prop_eq | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin.symm_sign | [
{
"state_after": "no goals",
"state_before": "n : ℕ\np : Fin (n + 1)\ne : Perm (Fin n)\n⊢ ↑sign (↑decomposeFin.symm (p, e)) = (if p = 0 then 1 else -1) * ↑sign e",
"tactic": "refine' Fin.cases _ _ p <;> simp [Equiv.Perm.decomposeFin, Fin.succ_ne_zero]"
}
] | [
69,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
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