file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.multispan_map_snd | [] | [
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285,
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Mathlib/Logic/Relation.lean | Relation.TransGen.tail' | [
{
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382,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_pi | [] | [
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58
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1042,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.pair_obj_left | [] | [
140,
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Mathlib/Topology/MetricSpace/Infsep.lean | Finset.coe_infsep | [
{
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506,
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Mathlib/Computability/Ackermann.lean | ack_pair_lt | [] | [
311,
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src/lean/Init/Data/Nat/Basic.lean | Nat.le_of_eq | [] | [
278,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_mul_cancel | [
{
"state_after": "case intro\nα : Type ?u.6577\nM₀ : Type u_1\nG₀ : Type ?u.6583\nM₀' : Type ?u.6586\nG₀' : Type ?u.6589\nF : Type ?u.6592\nF' : Type ?u.6595\ninst✝ : MonoidWithZero M₀\nu : M₀ˣ\n⊢ inverse ↑u * ↑u = 1",
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Mathlib/Order/LiminfLimsup.lean | Filter.liminf_congr | [] | [
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28
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594,
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Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.induction_with_natDegree_le | [
{
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"state_b... | [
248,
31
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Mathlib/Computability/Partrec.lean | Nat.rfind_dom' | [] | [
101,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Algebra/Group/Pi.lean | Pi.mulSingle_mul | [] | [
493,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
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Mathlib/Combinatorics/Composition.lean | Composition.eq_ones_iff | [
{
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536,
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Mathlib/Algebra/Hom/Units.lean | IsUnit.map | [
{
"state_after": "case intro\nF : Type u_1\nG : Type ?u.37609\nα : Type ?u.37612\nM : Type u_2\nN : Type u_3\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : MonoidHomClass F M N\nf : F\ny : Mˣ\n⊢ IsUnit (↑f ↑y)",
"state_before": "F : Type u_1\nG : Type ?u.37609\nα : Type ?u.37612\nM : Type u_2\nN : Type u_3\... | [
224,
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_set_subset_iff | [] | [
364,
19
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363,
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Mathlib/CategoryTheory/Comma.lean | CategoryTheory.Comma.eqToHom_right | [
{
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177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_units_map_submonoid | [
{
"state_after": "R : Type u_1\ninst✝¹² : CommRing R\nM : Submonoid R\nS : Type ?u.3235887\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Algebra R S\nP : Type ?u.3236124\ninst✝⁹ : CommRing P\nRₘ : Type ?u.3236130\nSₘ : Type u_2\ninst✝⁸ : CommRing Rₘ\ninst✝⁷ : CommRing Sₘ\ninst✝⁶ : Algebra R Rₘ\ninst✝⁵ : IsLocalization M Rₘ\... | [
1329,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
1
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Mathlib/Topology/Separation.lean | continuousWithinAt_update_of_ne | [] | [
566,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_range_eq_iSup | [
{
"state_after": "no goals",
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271,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.eq_re_of_eq_coe | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.318178\nT : Type ?u.318181\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x✝ y z : R\na✝ b c a : ℍ[R,c₁,c₂]\nx : R\nh : a = ↑x\n⊢ a = ↑a.re",
"tactic": "rw [h, coe_re]"
}
] | [
683,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
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Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_sum_fiber_lt_of_maps_to_of_sum_lt_nsmul | [] | [
131,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_bound | [] | [
163,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_eq_zero | [] | [
142,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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Mathlib/Probability/ConditionalProbability.lean | ProbabilityTheory.cond_eq_inv_mul_cond_mul | [
{
"state_after": "case pos\nΩ : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\ns t : Set Ω\ninst✝ : IsFiniteMeasure μ\nhms : MeasurableSet s\nhmt : MeasurableSet t\nht : ↑↑μ t = 0\n⊢ ↑↑(μ[|s]) t = (↑↑μ s)⁻¹ * ↑↑(μ[|t]) s * ↑↑μ t\n\ncase neg\nΩ : Type u_1\nm : MeasurableSpace Ω\nμ : MeasureTheory.... | [
167,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.one_le_rpow | [
{
"state_after": "x✝ y z✝ x z : ℝ\nhx : 1 ≤ x\nhz : 0 ≤ z\n⊢ 1 ^ z ≤ x ^ z",
"state_before": "x✝ y z✝ x z : ℝ\nhx : 1 ≤ x\nhz : 0 ≤ z\n⊢ 1 ≤ x ^ z",
"tactic": "rw [← one_rpow z]"
},
{
"state_after": "no goals",
"state_before": "x✝ y z✝ x z : ℝ\nhx : 1 ≤ x\nhz : 0 ≤ z\n⊢ 1 ^ z ≤ x ^ z",
"... | [
541,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.aecover_Ico_of_Ioc | [] | [
249,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.IndepFun.integral_mul_of_integrable | [
{
"state_after": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf g : Ω → ℝ≥0∞\nX Y : Ω → ℝ\nhXY : IndepFun X Y\nhX : Integrable X\nhY : Integrable Y\npos : ℝ → ℝ := fun x => max x 0\n⊢ integral μ (X * Y) = integral μ X * integral μ Y",
"state_before": "Ω : Type u_1\nmΩ : MeasurableSpac... | [
267,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_eq_one_iff_of_le_one' | [] | [
200,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Algebra/Lie/Basic.lean | neg_lie | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L N\ninst... | [
174,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwise_union | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8026\nγ : Type ?u.8029\nι : Type ?u.8032\nι' : Type ?u.8035\nr p q : α → α → Prop\nf g : ι → α\ns t u : Set α\na b : α\n⊢ (((∀ (x : α), x ∈ s → ∀ (x_1 : α), x_1 ∈ s → x ≠ x_1 → r x x_1) ∧\n ∀ (x : α), x ∈ t → ∀ (x_1 : α), x_1 ∈ s → x ≠ x_1 → r x x_1) ∧\n (... | [
146,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_b_ne_zero' | [] | [
409,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Order/SymmDiff.lean | sup_inf_bihimp | [] | [
317,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.insert | [] | [
530,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
11
] |
src/lean/Init/Data/List/BasicAux.lean | List.append_cancel_left_eq | [
{
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"state_before": "α : Type u_1\nas bs cs : List α\n⊢ (as ++ bs = as ++ cs) = (bs = cs)",
"tactic": "apply propext"
},
{
"state_after": "case a.mp\nα : Type u_1\nas bs cs : List α\n⊢ as ++ bs = as ++ cs → ... | [
153,
28
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
150,
9
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.parts_nonempty_iff | [
{
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"tactic": "rw [nonempty_iff_ne_empty, not_iff_not, parts_eq_empty_iff]"
}
] | [
184,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.coe_sumElim | [] | [
1314,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.right_not_mem | [] | [
174,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.NoetherianSpace.isCompact | [
{
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"state_before": "α : Type u_1\nβ ... | [
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25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.norm_of_fun_eq_integral_norm | [
{
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1270,
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.coe_single | [] | [
271,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
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Mathlib/Algebra/Quandle.lean | Quandle.conj_act_eq_conj | [] | [
456,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.setOf_subset_eq_univ_iff | [
{
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Std/Data/List/Lemmas.lean | List.disjoint_of_disjoint_cons_left | [] | [
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42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Logic/Equiv/Defs.lean | Equiv.forall_congr | [
{
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873,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_rw₂ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type ?u.948646\nm : MeasurableSpace α\nμ ν : Measure α\nf₁ f₁' : α → β\nf₂ f₂' : α → γ\nh₁✝ : f₁ =ᵐ[μ] f₁'\nh₂✝ : f₂ =ᵐ[μ] f₂'\ng : β → γ → ℝ≥0∞\nx✝ : α\nh₂ : f₂ x✝ = f₂' x✝\nh₁ : f₁ x✝ = f₁' x✝\n⊢ g (f₁ x✝) (f₂ x✝) = g (f₁' x✝) (f₂' x✝)",
"sta... | [
766,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | isLUB_hasSum' | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousAt.rpow | [] | [
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Mathlib/Algebra/Homology/QuasiIso.lean | CategoryTheory.Functor.quasiIso_of_map_quasiIso | [
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Mathlib/Data/Finite/Card.lean | Finite.card_pos_iff | [
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_mul_row | [
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Mathlib/Analysis/Normed/Group/Basic.lean | nndist_nnnorm_nnnorm_le' | [] | [
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Mathlib/Data/List/Count.lean | List.countp_false | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isPath_copy | [
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.coe_mk | [] | [
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Mathlib/Topology/MetricSpace/Polish.lean | IsClosed.polishSpace | [] | [
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Mathlib/Data/List/Func.lean | List.Func.equiv_symm | [] | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_concat | [
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_neg | [] | [
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.find?_some_mem | [
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Mathlib/Data/Set/Image.lean | Set.image_union | [
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Mathlib/Order/Filter/NAry.lean | Filter.map₂_right | [
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Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.pentagon | [
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | affineIndependent_iff_not_collinear | [
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.curryFinFinset_symm_apply_piecewise_const | [
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Mathlib/Data/Set/Function.lean | Set.injOn_singleton | [] | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_self_apply | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasStrictFDerivAt.comp | [
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.toList_formPerm_nil | [
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Mathlib/RingTheory/IntegralClosure.lean | isIntegral_ofSubring | [] | [
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Mathlib/Topology/Order/Basic.lean | isLUB_of_mem_closure | [
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Mathlib/Data/Matrix/DMatrix.lean | DMatrix.map_apply | [] | [
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Mathlib/Data/Finset/Prod.lean | Finset.diag_card | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add | [] | [
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Mathlib/Data/Finset/Lattice.lean | Finset.le_sup | [] | [
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Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_biInf_of_ul_eq_self | [
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_iff_finrank_le_one | [
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Mathlib/Combinatorics/SimpleGraph/Triangle/Basic.lean | SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty | [] | [
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Mathlib/Data/Set/Ncard.lean | Set.ncard_le_of_subset | [] | [
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq_mk'_iff_mul_eq | [] | [
286,
44
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Mathlib/Data/Num/Lemmas.lean | Num.add_zero | [
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Mathlib/Data/List/Count.lean | List.prod_eq_pow_single | [
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Mathlib/RingTheory/WittVector/Basic.lean | WittVector.ghostFun_sub | [
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | HasStrictDerivAt.arsinh | [] | [
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40
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_sdiff | [] | [
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Mathlib/Topology/Bases.lean | TopologicalSpace.secondCountableTopology_of_countable_cover | [] | [
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.span_mul_span | [] | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.single_mul_single | [] | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_zero_eq_comp | [] | [
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Mathlib/Data/Real/EReal.lean | EReal.bot_mul_bot | [] | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_eq_eval_map | [
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Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.of'_divOf | [
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Mathlib/RingTheory/Subsemiring/Basic.lean | RingHom.sclosure_preimage_le | [] | [
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.le_of_add_le_add_left | [
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineMap.isOpenMap_linear_iff | [
{
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873,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.subset_cl | [
{
"state_after": "no goals",
"state_before": "X : Compactum\nA : Set X.A\na : X.A\nha : a ∈ A\n⊢ str X (incl X a) = a",
"tactic": "simp"
}
] | [
221,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
9
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.mono_left | [] | [
193,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.one_lt_index_of_ne_top | [] | [
526,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
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Mathlib/Logic/Basic.lean | bex_or_left | [
{
"state_after": "α : Sort u_1\nr p q : α → Prop\nP Q : (x : α) → p x → Prop\nb : Prop\n⊢ (∃ x, (p x ∨ q x) ∧ r x) ↔ (∃ x, p x ∧ r x) ∨ ∃ x, q x ∧ r x",
"state_before": "α : Sort u_1\nr p q : α → Prop\nP Q : (x : α) → p x → Prop\nb : Prop\n⊢ (∃ x x_1, r x) ↔ (∃ x x_1, r x) ∨ ∃ x x_1, r x",
"tactic": "si... | [
1115,
64
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1112,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_eq_norm_sq_to_K | [
{
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"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1651405\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 : E\n⊢ inner x x = ↑‖x‖ ^ 2",
"tactic... | [
592,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
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Mathlib/Algebra/Field/Basic.lean | div_add_one | [] | [
51,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
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