file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/CompleteLattice.lean | sSup_eq_top | [] | [
602,
42
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597,
1
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Mathlib/Computability/Primrec.lean | Primrec.vector_get' | [] | [
1329,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
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Mathlib/Topology/Algebra/Order/Compact.lean | ContinuousOn.image_uIcc | [
{
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438,
38
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434,
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Mathlib/Data/List/Zip.lean | List.sum_zipWith_distrib_left | [
{
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464,
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458,
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.mul_apply | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.hasInitial_of_unique | [] | [
336,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.coe_mul | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.dist_smul_vadd_eq_dist | [
{
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... | [
156,
11
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144,
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Mathlib/Deprecated/Subring.lean | Ring.closure_subset_iff | [] | [
201,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/Analysis/Normed/Field/Basic.lean | Filter.isBoundedUnder_le_mul_tendsto_zero | [] | [
223,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.const_add | [] | [
374,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Analysis/Seminorm.lean | Seminorm.smul_ball_zero | [
{
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951,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Std/Logic.lean | not_iff_self | [] | [
92,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
92,
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Mathlib/Data/Finset/Sups.lean | Finset.disjSups_subset_sups | [
{
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"state_before": "α : Type ... | [
443,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_swap | [] | [
711,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_smul_le_mul_snorm' | [] | [
1497,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1493,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.inv | [
{
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"tacti... | [
576,
47
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571,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Measurable.stronglyMeasurable | [
{
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632,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
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Mathlib/Data/Matrix/Basic.lean | Matrix.add_mul | [
{
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1009,
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Mathlib/Data/List/Basic.lean | List.nthLe_map' | [] | [
1308,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.mem_vars | [
{
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"tactic": "classical simp only [vars_def, Multiset.mem_toFinset, mem_deg... | [
309,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_restrict' | [] | [
1655,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1653,
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.eq_of_true | [] | [
759,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
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Mathlib/Data/Set/Basic.lean | Set.monotone_powerset | [] | [
2154,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2154,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_pi_lambda | [] | [
859,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.Commute.zpow_left | [] | [
225,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.Rat.invOf_denom_swap | [
{
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"tactic": "rw [mul_invOf_eq_iff_eq_mul_right, ← Int.commute_cast, mul_assoc,\n ← mul_left_eq_iff_eq_invOf_mul... | [
717,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_lt_span_singleton | [
{
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"tactic": "rw [lt_iff_le_not_le, span_singleton_le_span_singleton, span_singleton_le_span_single... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
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Mathlib/Algebra/Lie/SkewAdjoint.lean | skewAdjointLieSubalgebraEquiv_symm_apply | [
{
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.conj | [
{
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320,
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Mathlib/Topology/Connected.lean | Continuous.connectedComponentsLift_apply_coe | [] | [
1509,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
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Mathlib/Order/CompleteLattice.lean | iInf_eq_if | [] | [
1132,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
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Mathlib/Data/Fin/Basic.lean | Fin.castLT_castAdd | [
{
"state_after": "case h\nn m✝ m : ℕ\ni : Fin n\n⊢ ↑(castLT (↑(castAdd m) i) (_ : ↑(↑(castAdd m) i) < n)) = ↑i",
"state_before": "n m✝ m : ℕ\ni : Fin n\n⊢ castLT (↑(castAdd m) i) (_ : ↑(↑(castAdd m) i) < n) = i",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\nn m✝ m... | [
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1158,
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Mathlib/Data/Setoid/Basic.lean | Setoid.eq_iff_rel_eq | [] | [
70,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Order/CompleteLattice.lean | iSup_emptyset | [
{
"state_after": "no goals",
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... | [
1402,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
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Mathlib/Dynamics/PeriodicPts.lean | Function.iterate_mod_minimalPeriod_eq | [] | [
298,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
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Mathlib/Data/Set/Image.lean | Set.preimage_inter | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_zero | [] | [
1514,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
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Mathlib/Order/Hom/Basic.lean | OrderIso.toFun_eq_coe | [] | [
794,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
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Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.mem_map_C_iff | [
{
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546,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_periodic | [] | [
750,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Basic.lean | Complex.equiv_limAux | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/ClassGroup.lean | FractionalIdeal.map_canonicalEquiv_mk0 | [] | [
256,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.baseChange_obj | [] | [
217,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.ae | [] | [
2501,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2499,
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Mathlib/Data/Finsupp/Multiset.lean | Finsupp.coe_orderIsoMultiset | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.addHaar_parallelepiped | [
{
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555,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
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] |
Mathlib/LinearAlgebra/Span.lean | Submodule.comap_map_eq_self | [
{
"state_after": "no goals",
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864,
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.toEquiv_injective | [] | [
312,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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Mathlib/Data/Sum/Basic.lean | Sum.not_isRight | [
{
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"tactic": "cases x <;> rfl"
}
] | [
137,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_restrictScalarsₗ | [] | [
1735,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1734,
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Mathlib/RingTheory/Ideal/AssociatedPrime.lean | not_isAssociatedPrime_of_subsingleton | [
{
"state_after": "case intro.intro\nR : Type u_2\ninst✝⁵ : CommRing R\nI J : Ideal R\nM : Type u_1\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nM' : Type ?u.27644\ninst✝² : AddCommGroup M'\ninst✝¹ : Module R M'\nf : M →ₗ[R] M'\ninst✝ : Subsingleton M\nhI : Ideal.IsPrime I\nx : M\nhx : I = Submodule.annihilato... | [
82,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.map_sup | [] | [
748,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.SeparatingLeft.congr | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.476585\nR₂ : Type ?u.476588\nR₃ : Type ?u.476591\nM : Type ?u.476594\nM₁ : Type ?u.476597\nM₂ : Type ?u.476600\nMₗ₁ : Type u_2\nMₗ₁' : Type u_4\nMₗ₂ : Type u_3\nMₗ₂' : Type u_5\nK : Type ?u.476615\nK₁ : Type ?u.476618\nK₂ : Type ?u.476621\nV : Type ?u.476624\nV₁ : Ty... | [
657,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.monotone | [] | [
151,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
11
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.hasStrictFDerivAt | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nr : ℝ≥0∞\nf : E → F\nx : E\ns : Set E\nh : HasFPowerSeriesAt f ... | [
44,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_inv | [
{
"state_after": "a b : ℝ\nn : ℕ\nh : ¬0 ∈ [[a, b]]\nh' : ∀ (x : ℝ), x ∈ [[a, b]] → x ≠ 0\n⊢ (∫ (x : ℝ) in a..b, x⁻¹) = Real.log (b / a)",
"state_before": "a b : ℝ\nn : ℕ\nh : ¬0 ∈ [[a, b]]\n⊢ (∫ (x : ℝ) in a..b, x⁻¹) = Real.log (b / a)",
"tactic": "have h' := fun x (hx : x ∈ [[a, b]]) => ne_of_mem_of_n... | [
430,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.lintegral_lt_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.918859\nγ : Type ?u.918862\nδ : Type ?u.918865\nm : MeasurableSpace α\ninst✝¹ : Zero β\ninst✝ : Zero γ\nμ : Measure α\nf✝ : α →ₛ β\nf : α →ₛ ℝ≥0∞\nhm : SimpleFunc.FinMeasSupp f μ\nhf : ∀ᵐ (a : α) ∂μ, ↑f a ≠ ⊤\na : ℝ≥0∞\nha : a ∈ SimpleFunc.range f\n⊢ a * ↑↑μ (↑f ⁻¹' {... | [
1257,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.map_neg₂ | [] | [
163,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.injective | [] | [
244,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
11
] |
Mathlib/CategoryTheory/Monoidal/NaturalTransformation.lean | CategoryTheory.MonoidalNatTrans.comp_toNatTrans | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Deprecated/Submonoid.lean | IsSubmonoid.power_subset | [] | [
225,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.mergeIdem_head2 | [
{
"state_after": "no goals",
"state_before": "x y : Nat\nys : List Nat\nh : x ≠ y\n⊢ mergeIdem (x :: y :: ys) = x :: mergeIdem (y :: ys)",
"tactic": "simp [mergeIdem, mergeIdem.loop, h]"
}
] | [
128,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
127,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.mul_integral_comp_mul_left | [] | [
256,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.equivCongr_trans | [
{
"state_after": "case H.H\nα : Sort u\nβ : Sort v\nγ : Sort w\nδ : Sort u_1\nε : Sort u_2\nζ : Sort u_3\nab : α ≃ β\nde : δ ≃ ε\nbc : β ≃ γ\nef : ε ≃ ζ\nx✝¹ : α ≃ δ\nx✝ : γ\n⊢ ↑(↑((equivCongr ab de).trans (equivCongr bc ef)) x✝¹) x✝ = ↑(↑(equivCongr (ab.trans bc) (de.trans ef)) x✝¹) x✝",
"state_before": "α... | [
409,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
9
] |
Mathlib/Data/PNat/Basic.lean | PNat.coe_inj | [] | [
120,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.circulant_isSymm_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.64028\nm : Type ?u.64031\nn : Type u_1\nR : Type ?u.64037\ninst✝ : AddGroup n\nv : n → α\n⊢ IsSymm (circulant v) ↔ ∀ (i : n), v (-i) = v i",
"tactic": "rw [IsSymm, transpose_circulant, circulant_inj, funext_iff]"
}
] | [
194,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementarySubstructure.theory_model_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\nN : Type ?u.401025\nP : Type ?u.401028\nQ : Type ?u.401031\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\ninst✝ : Structure L Q\nS : ElementarySubstructure L M\nT : Theory L\n⊢ { x // x ∈ S } ⊨ T ↔ M ⊨ T",
... | [
455,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_pullback | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nX Y : C\ng : X ⟶ Y\nf₂ : Subobject Y\n⊢ ∀ (f₁ : Subobject Y), (pullback g).obj (f₁ ⊓ f₂) = (pullback g).obj f₁ ⊓ (pullback g).obj f₂",
"state_before": "C : Type u₁\ninst✝² : Category C\... | [
496,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.single_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.579469\nγ : Type ?u.579472\nι : Type ?u.579475\nM : Type u_1\nM' : Type ?u.579481\nN : Type ?u.579484\nP : Type ?u.579487\nG : Type ?u.579490\nH : Type ?u.579493\nR : Type u_2\nS : Type ?u.579499\ninst✝² : Zero M\ninst✝¹ : MonoidWithZer... | [
1414,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1413,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_imJ | [] | [
1099,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
9
] |
Mathlib/Algebra/Divisibility/Units.lean | IsUnit.mul_right_dvd | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : Monoid α\na b : α\nu : αˣ\n⊢ a * ↑u ∣ b ↔ a ∣ b",
"state_before": "α : Type u_1\ninst✝ : Monoid α\na b u : α\nhu : IsUnit u\n⊢ a * u ∣ b ↔ a ∣ b",
"tactic": "rcases hu with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "case int... | [
94,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Icc_subtype | [] | [
310,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.coe_neg | [] | [
1228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.equalizerSubobject_factors_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf g : X ⟶ Y\ninst✝ : HasEqualizer f g\nW : C\nh : W ⟶ X\nw : Factors (equalizerSubobject f g) h\n⊢ h ≫ f = h ≫ g",
"tactic": "rw [← Subobject.factorThru_arrow _ _ w, Category.assoc, equalizerSubobject_arrow_comp,\n... | [
80,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.degree_cyclotomic' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R\nn : ℕ\nh : IsPrimitiveRoot ζ n\n⊢ degree (cyclotomic' n R) = ↑(Nat.totient n)",
"tactic": "simp only [degree_eq_natDegree (cyclotomic'_ne_zero n R), natDegree_cyclotomic' h]"
}
] | [
125,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.map_comp_map | [] | [
236,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapDomain_apply | [] | [
707,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.zero_divInt | [
{
"state_after": "no goals",
"state_before": "n : Int\n⊢ 0 /. n = 0",
"tactic": "cases n <;> simp [divInt]"
}
] | [
124,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
124,
9
] |
Mathlib/Algebra/Algebra/Basic.lean | algebraMap.coe_inv | [] | [
231,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.C_dvd_iff_zmod | [] | [
30,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.add_rat | [
{
"state_after": "case intro.intro\np q x y : ℝ\nr✝ : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p x\nr : ℚ\nC : ℝ\n_hC₀ : 0 < C\nhC : ∃ᶠ (n : ℕ) in atTop, 1 ≤ n ∧ ∃ m, x ≠ ↑m / ↑n ∧ abs (x - ↑m / ↑n) < C / ↑n ^ p\n⊢ LiouvilleWith p (x + ↑r)",
"state_before": "p q x y : ℝ\nr✝ : ℚ\nm : ℤ\nn : ℕ\nh : LiouvilleWith p ... | [
198,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.symm_refl | [] | [
1249,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.exists_gcd_eq_one_of_isOfFinAddOrder | [] | [
450,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_subset_of_subset | [] | [
353,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Finset/Image.lean | Function.Injective.mem_finset_image | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.69600\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\nhf : Injective f\nh : f a ∈ image f s\n⊢ a ∈ s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.69600\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\n... | [
368,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Topology/Maps.lean | IsOpenMap.preimage_interior_eq_interior_preimage | [] | [
416,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpTo.differentiable | [] | [
1294,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.continuousOn_ball | [
{
"state_after": "case inl\n𝕜 : Type u_2\nE : Type u_1\nF : Type u_3\nG : Type ?u.8350\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedSpace 𝕜 F\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf g : E → F\... | [
72,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/Complex/OperatorNorm.lean | Complex.ofRealClm_nnnorm | [] | [
83,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.preimage_Iio | [
{
"state_after": "case h\nF : Type ?u.246936\nα : Type u_1\nβ : Type ?u.246942\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\nx✝ : ℤ\n⊢ x✝ ∈ Int.cast ⁻¹' Iio a ↔ x✝ ∈ Iio ⌈a⌉",
"state_before": "F : Type ?u.246936\nα : Type u_1\nβ : Type ?u.246942\ninst✝¹ : LinearOrderedRing α\ninst✝ : Flo... | [
1310,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1308,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.bijective_stableUnderComposition | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type ?u.90042\ninst✝¹ : Category D\ninst✝ : ConcreteCategory C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nhf : MorphismProperty.bijective C f\nhg : MorphismProperty.bijective C g\n⊢ Bijective ((forget C).map (f ≫ g))",
"state_before": "C : Type u\ninst✝² : Categ... | [
657,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.nsmul_zero' | [] | [
203,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
9
] |
Std/Data/List/Lemmas.lean | List.disjoint_cons_left | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : α✝\nl₁ l₂ : List α✝\n⊢ Disjoint [a] l₂ ∧ Disjoint l₁ l₂ ↔ ¬a ∈ l₂ ∧ Disjoint l₁ l₂",
"tactic": "simp [singleton_disjoint]"
}
] | [
1390,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1389,
9
] |
Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_inf_le | [] | [
89,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/Linear/Yoneda.lean | CategoryTheory.whiskering_linearCoyoneda₂ | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.rangeSRestrict_surjective | [] | [
1177,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_neg_neg | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1738883\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ inner (-x) (-y) = inner x y",
... | [
644,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_map | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type ?u.691562\nR : Type u_4\nS : Type u_1\nT : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : S →+* MvPolynomial σ T\ng : R →+* S\nφ : MvPolynomial σ R\n⊢ ↑(bind₂ f) (↑(map g)... | [
277,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/GroupTheory/Archimedean.lean | AddSubgroup.cyclic_of_isolated_zero | [
{
"state_after": "case inl\nG : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : Archimedean G\na : G\nh₀ : 0 < a\nhd : Disjoint (↑⊥) (Ioo 0 a)\n⊢ ∃ b, ⊥ = closure {b}\n\ncase inr\nG : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : Archimedean G\nH : AddSubgroup G\na : G\nh₀ : 0 < a\nhd : Disjoi... | [
97,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
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