file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Data/Seq/Computation.lean | Computation.results_of_terminates | [] | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_involution | [
{
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftAlgHom_apply_div | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | DenseRange.exists_dist_lt | [] | [
1140,
46
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Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.continuous_of_bound | [
{
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Mathlib/Data/Set/Countable.lean | Set.subset_range_enumerate | [
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Mathlib/Data/Finset/Sups.lean | Finset.Nonempty.infs | [] | [
297,
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Mathlib/Data/Finset/Sort.lean | Finset.sort_toFinset | [] | [
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toBasicOpen_injective | [
{
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{
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678,
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrable.indicator | [
{
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222,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coe_LpSubmodule | [] | [
488,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.unique_single | [] | [
456,
49
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455,
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Mathlib/Order/Ideal.lean | Order.sequenceOfCofinals.encode_mem | [
{
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577,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.add_smul_subset | [
{
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_apply' | [
{
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78,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_induction | [] | [
683,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.add_left_inj | [] | [
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Mathlib/Order/Cover.lean | Wcovby.image | [
{
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124,
20
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Mathlib/CategoryTheory/Preadditive/Projective.lean | CategoryTheory.Adjunction.projective_of_map_projective | [
{
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224,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.SatelliteConfig.exists_normalized_aux2 | [
{
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443,
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390,
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Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measurePreserving_smul | [
{
"state_after": "case h\nG : Type ?u.6308\nM : Type u_2\nα : Type u_1\ns✝ : Set α\nm : MeasurableSpace α\ninst✝³ : MeasurableSpace M\ninst✝² : SMul M α\ninst✝¹ : MeasurableSMul M α\nc : M\nμ : Measure α\ninst✝ : SMulInvariantMeasure M α μ\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(map (fun x => c • x) μ) s = ↑↑μ s... | [
95,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_const_pure | [] | [
3061,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3060,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_eq_sInf | [
{
"state_after": "R : Type u\nι : Type ?u.327198\ninst✝ : CommSemiring R\nI✝ J K L I : Ideal R\nr : R\nhr : r ∈ sInf {J | I ≤ J ∧ IsPrime J}\nhri : ¬r ∈ radical I\nhrm : ¬r ∈ radical ⊤\nhim : I ≤ ⊤\nhm : ∀ (z : Ideal R), z ∈ {K | ¬r ∈ radical K} → ⊤ ≤ z → z = ⊤\nthis : ∀ (x : R), ¬x ∈ ⊤ → r ∈ radical (⊤ ⊔ span ... | [
981,
98
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Mathlib/Analysis/Convex/Basic.lean | Convex.smul_preimage | [] | [
429,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/GroupTheory/Coset.lean | QuotientGroup.preimage_image_mk | [
{
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570,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.bUnion | [
{
"state_after": "Ω : Type u_1\nι : Type u_2\ninst✝ : MeasurableSpace Ω\ns : ι → Set (Set Ω)\ns' : Set (Set Ω)\nμ : MeasureTheory.Measure Ω\nu : Set ι\nhyp : ∀ (n : ι), n ∈ u → IndepSets (s n) s'\nt1 t2 : Set Ω\nht1 : t1 ∈ ⋃ (n : ι) (_ : n ∈ u), s n\nht2 : t2 ∈ s'\n⊢ ↑↑μ (t1 ∩ t2) = ↑↑μ t1 * ↑↑μ t2",
"state... | [
233,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.toSemiring_of | [] | [
634,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
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Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.inf_apply | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.coe_hom | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
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] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesOnBall.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... | [
118,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/CategoryTheory/Functor/Functorial.lean | CategoryTheory.map_functorial_obj | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/Computability/Partrec.lean | Computable₂.comp | [] | [
549,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
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Mathlib/Order/Grade.lean | grade_bot | [] | [
213,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
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Std/Logic.lean | or_congr_right | [] | [
259,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
259,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.extend_apply_of_le_zero | [
{
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"state_b... | [
177,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/MeasureTheory/Integral/PeakFunction.lean | tendsto_set_integral_peak_smul_of_integrableOn_of_continuousWithinAt_aux | [
{
"state_after": "α : Type u_1\nE : Type u_3\nι : Type u_2\nhm : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : BorelSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ng : α → E\nl : Filter ι\nx₀ : α\ns : Set α\nφ : ι → α → ℝ\ninst✝ : CompleteSpace E\nhs : M... | [
158,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup_set_eq_biUnion | [] | [
300,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_ball | [] | [
980,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
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Mathlib/Data/List/Zip.lean | List.zipWith3_same_right | [] | [
336,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
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Mathlib/Data/Multiset/Interval.lean | Multiset.card_Iic | [
{
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}
] | [
78,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Array/Init/Lemmas.lean | Array.get_push_lt | [
{
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{
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88
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126,
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.self_comp_symm | [] | [
447,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
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Mathlib/Algebra/Periodic.lean | Function.Periodic.div_const | [
{
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"tactic": "simpa only [div_eq_mul_inv] using h.mul_const_inv a"
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] | [
158,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.add_moveLeft_inr | [
{
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"state_before": "x y : PGame\ni : LeftMoves y\n⊢ moveLeft (x + y) (↑toLeftMovesAdd (Sum.inr i)) = x + ... | [
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Mathlib/Data/Finset/Basic.lean | Finset.inter_congr_right | [] | [
1807,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.zero_mul | [
{
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997,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
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Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_l_inv | [] | [
231,
6
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230,
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Mathlib/Data/Seq/Computation.lean | Computation.results_thinkN_pure | [
{
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600,
73
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599,
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Mathlib/Algebra/Module/Zlattice.lean | Zspan.coe_fract_self | [
{
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195,
97
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194,
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Mathlib/Analysis/Calculus/Deriv/Star.lean | deriv.star' | [] | [
68,
29
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67,
11
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_sub_pi | [] | [
249,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_eq_torsionBySet_span | [
{
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289,
31
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281,
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc | [
{
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683,
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678,
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Mathlib/Data/Set/Lattice.lean | Set.Iic_iInf₂ | [
{
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2139,
21
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2138,
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_sup | [] | [
133,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Topology/Constructions.lean | Continuous.subtype_map | [] | [
1049,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
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Mathlib/Analysis/Convex/Jensen.lean | ConvexOn.map_centerMass_le | [
{
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55,
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49,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_mul_const_Iic_of_neg | [] | [
569,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
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src/lean/Init/Core.lean | Quotient.exact | [] | [
1500,
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1499,
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Mathlib/Data/Sym/Sym2.lean | Sym2.forall | [] | [
139,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
11
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Mathlib/Data/List/Basic.lean | List.cons_head?_tail | [
{
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},
{
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915,
13
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911,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.subtypeEquivCodomain_symm_apply_eq | [] | [
1390,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1388,
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Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_mulHom_mk | [
{
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227,
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225,
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Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.mono_iff_exact_zero_left | [
{
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... | [
333,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/Topology/Algebra/Order/Compact.lean | Continuous.exists_forall_le' | [
{
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311,
34
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307,
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Mathlib/Algebra/Homology/Single.lean | CochainComplex.single₀_map_f_succ | [] | [
386,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
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Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_sup | [] | [
840,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_tower_bot_of_isIntegral_field | [] | [
1059,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
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Mathlib/Data/List/Basic.lean | List.drop_append_of_le_length | [
{
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"tactic": "simp [drop_append_eq_append_drop, tsub_eq_zero_iff_le.mpr h]"
}
] | [
2183,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2181,
1
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Mathlib/Data/Finset/Basic.lean | Finset.eq_of_veq | [
{
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155,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Algebra/Quaternion.lean | Cardinal.mk_univ_quaternionAlgebra | [
{
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}
] | [
1441,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1440,
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.mk_coe | [
{
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_apply_of_lt_aleph0 | [] | [
1678,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1676,
1
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Mathlib/Data/Complex/Basic.lean | Complex.abs_cast_nat | [
{
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}
] | [
1109,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/Order/OrderIsoNat.lean | RelEmbedding.exists_not_acc_lt_of_not_acc | [
{
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64,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_one_le | [
{
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"tactic": "rw [← C_1]"
},
{
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"st... | [
265,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lift_nat_cast | [
{
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ lift ↑(n + 1) = ↑(n + 1)",
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}
] | [
2364,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2362,
1
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Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.zmod_congr_of_sub_mem_max_ideal | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr : ℚ\nx : ℤ_[p]\nm n : ℕ\nhm : x - ↑m ∈ Ideal.span {↑p}\nhn : x - ↑n ∈ Ideal.span {↑p}\n⊢ ↑m = ↑n",
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169,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.card_multiples | [
{
"state_after": "case zero\np : ℕ\n⊢ card (Finset.filter (fun e => p ∣ e + 1) (Finset.range zero)) = zero / p\n\ncase succ\np n : ℕ\nhn : card (Finset.filter (fun e => p ∣ e + 1) (Finset.range n)) = n / p\n⊢ card (Finset.filter (fun e => p ∣ e + 1) (Finset.range (succ n))) = succ n / p",
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951,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mul_sub_mul_mem | [
{
"state_after": "α : Type u\nβ : Type v\nR : Type u_1\ninst✝ : CommRing R\nI : Ideal R\na b c d : R\nh1 : a - b ∈ I\nh2 : c - d ∈ I\n⊢ (a - b) * c + b * (c - d) ∈ I",
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730,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
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Mathlib/Algebra/AddTorsor.lean | vadd_eq_vadd_iff_neg_add_eq_vsub | [
{
"state_after": "no goals",
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"tactic": "rw [eq_vadd_iff_vsub_eq, vadd_vsub_assoc, ← add_right_inj (-v₁), neg_add_cancel_left, eq_comm]"
}
] | [
188,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsSubgroup.mul_mem_cancel_left | [
{
"state_after": "no goals",
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"tactic": "simpa using hs.mul_mem (hs.inv_mem h) hab"
}
] | [
157,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/LinearAlgebra/Prod.lean | Submodule.map_inl | [
{
"state_after": "case h.mk\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.292947\nM₆ : Type ?u.292950\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R M\ninst✝ : Module R ... | [
554,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
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Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_bot | [] | [
845,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Data/Set/Function.lean | Set.InvOn.mono | [] | [
1186,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.div | [
{
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1723,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1720,
1
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Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.coe_tsub | [
{
"state_after": "case h\nι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → CanonicallyOrderedAddMonoid (α i)\ninst✝¹ : (i : ι) → Sub (α i)\ninst✝ : ∀ (i : ι), OrderedSub (α i)\nf✝ g✝ : Π₀ (i : ι), α i\ni✝ : ι\na b : α i✝\nf g : Π₀ (i : ι), α i\ni : ι\n⊢ ↑(f - g) i = (↑f - ↑g) i",
"state_before": "ι : Type... | [
208,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/RingTheory/Nilpotent.lean | nilradical_eq_sInf | [
{
"state_after": "no goals",
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"tactic": "simp_rw [and_iff_right bot_le]"
}
] | [
201,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.eq_top_iff_isIso | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpresheaf F\n⊢ G = ⊤ → IsIso (ι G)\n\ncase mpr\nC : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpresheaf F\n⊢ IsIso (ι G) → G = ⊤",
"state_b... | [
132,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Std/Logic.lean | Eq.to_iff | [] | [
45,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
45,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_refl | [
{
"state_after": "case h.mk\nα : Type ?u.12863\nX : Type u_1\nY : Type ?u.12869\nZ : Type ?u.12872\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nS A B C : DiscreteQuotient X\nx✝ : Quotient A.toSetoid\na✝ : X\n⊢ ofLE (_ : A ≤ A) (Quot.mk Setoid.r a✝) = id (Quot.mk Setoid.... | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | mk_eq_mk_of_basis | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.266192\nR : Type u\ninst✝³ : Ring R\ninst✝² : InvariantBasisNumber R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nv : Basis ι R M\nv' : Basis ι' R M\nthis : N... | [
562,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetAux'_cons | [
{
"state_after": "α : Type u_1\na : α\nl : List α\n⊢ List.map (ofList ∘ List.cons a) (sublists' l) = List.map (cons a ∘ ofList) (sublists' l)",
"state_before": "α : Type u_1\na : α\nl : List α\n⊢ powersetAux' (a :: l) = powersetAux' l ++ List.map (cons a) (powersetAux' l)",
"tactic": "simp [powersetAux'... | [
61,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_def | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Involutive.eq_iff | [] | [
912,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
11
] |
Mathlib/Data/Multiset/Lattice.lean | Multiset.sup_zero | [] | [
43,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSet.indep_generateFrom_lt | [
{
"state_after": "case h.e'_2.h.e'_2\nΩ : Type u_2\nι : Type u_1\nm0 : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ninst✝¹ : Preorder ι\ninst✝ : IsProbabilityMeasure μ\ns : ι → Set Ω\nhsm : ∀ (n : ι), MeasurableSet (s n)\nhs : iIndepSet s\ni : ι\n⊢ {s i} = {t | ∃ n, n ∈ {i} ∧ s n = t}",
"state_before": "... | [
485,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.map_ofDual_max | [
{
"state_after": "F : Type ?u.347556\nα : Type u_1\nβ : Type ?u.347562\nγ : Type ?u.347565\nι : Type ?u.347568\nκ : Type ?u.347571\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset αᵒᵈ\n⊢ WithBot.map (↑ofDual) (Finset.max s) = inf s (WithTop.some ∘ ↑ofDual)",
"state_before": "... | [
1416,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/CategoryTheory/Idempotents/Basic.lean | CategoryTheory.Idempotents.isIdempotentComplete_of_isIdempotentComplete_opposite | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nh : IsIdempotentComplete Cᵒᵖ\n⊢ ∀ (X : C) (p : X ⟶ X), p ≫ p = p → ∃ Y i e, i ≫ e = 𝟙 Y ∧ e ≫ i = p",
"state_before": "C : Type u_1\ninst✝ : Category C\nh : IsIdempotentComplete Cᵒᵖ\n⊢ IsIdempotentComplete C",
"tactic": "refine' ⟨_⟩"
},
{
"sta... | [
197,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_const | [
{
"state_after": "case h\nα : Type u_2\nβ : Type ?u.9120\nA : Type ?u.9123\nB : Type ?u.9126\nM : Type u_1\nN : Type ?u.9132\nP : Type ?u.9135\nR : Type ?u.9138\nS : Type ?u.9141\nG : Type ?u.9144\nM₀ : Type ?u.9147\nG₀ : Type ?u.9150\nι : Sort ?u.9153\ninst✝² : One M\ninst✝¹ : One N\ninst✝ : One P\nc : M\nhc :... | [
145,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
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