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/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_sub | [] | [
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6
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1558,
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Mathlib/LinearAlgebra/Basis.lean | Basis.mapCoeffs_apply | [
{
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Mathlib/CategoryTheory/Category/Bipointed.lean | Bipointed.coe_of | [] | [
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6
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.count_edges_takeUntil_le_one | [
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Mathlib/Algebra/GCDMonoid/Div.lean | Finset.Polynomial.gcd_div_eq_one | [
{
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Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Monad.algebra_epi_of_epi | [] | [
229,
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228,
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Mathlib/Data/Int/Basic.lean | Int.coe_nat_div | [] | [
231,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
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Mathlib/Data/Nat/Totient.lean | Nat.Ico_filter_coprime_le | [
{
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"tactic": "conv_lhs => rw [← Nat.mod_add_div n a]"
},
{
"... | [
110,
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Mathlib/RepresentationTheory/Action.lean | Action.leftUnitor_inv_hom | [
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536,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOn_singleton_iff_tendsto | [
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Mathlib/GroupTheory/Congruence.lean | Con.coe_smul | [] | [
1353,
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lie_sup | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.isUnit_iff_isUnit_val | [
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Mathlib/Order/Filter/Lift.lean | Filter.lift_iInf | [
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.sub_mem | [] | [
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Mathlib/Data/List/Perm.lean | List.Perm.append_left | [] | [
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Mathlib/LinearAlgebra/Dimension.lean | Basis.mk_eq_rank | [
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_apply | [] | [
548,
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_modEq_x2n_sub_lem | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn j : ℕ\nh : j ≤ n\nh1 : xz a1 n ∣ ↑(Pell.d a1) * yz a1 n * yz a1 (n - j) + xz a1 j\n⊢ xn a1 (2 * n - j) + xn a1 j ≡ 0 [MOD xn a1 n]",
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"tactic": "have h1 : xz a1... | [
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Mathlib/Data/Fin/Basic.lean | Fin.castLE_comp_castLE | [] | [
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31
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Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.IsQuadratic.sq_eq_one | [
{
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"tactic": "rw [← mul_left_inv χ, pow_two, hχ.inv]"
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Hom.mapEdgeSet.injective | [
{
"state_after": "case mk.mk\nι : Sort ?u.403479\n𝕜 : Type ?u.403482\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nf : G →g G'\nhinj : Injective ↑f\ne₁ : Sym2 V\nh₁ : e₁ ∈ edgeSet G\ne₂ : Sym2 V\nh₂ : e₂ ∈ edgeSet G\n⊢ mapEdgeSet f { val := e₁, propert... | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.mul_subset_mul | [] | [
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Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.two_div_one_sub_two_div_e_le_eight | [
{
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_constVAdd | [] | [
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.restr_source' | [
{
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src/lean/Init/Core.lean | Ne.elim | [] | [
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Mathlib/CategoryTheory/Sites/Grothendieck.lean | CategoryTheory.GrothendieckTopology.discrete_eq_top | [] | [
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.IndepSets.indep' | [] | [
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_apply_eq_one | [] | [
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19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.absorbs_self | [
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.image_uIcc | [
{
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | IsLeast.csInf_mem | [] | [
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Mathlib/Computability/TuringMachine.lean | Turing.Tape.map_mk₂ | [
{
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"tactic": "simp only [Tape.mk₂, Tape.map_mk', ListBlank.map_mk]"
}
] | [
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Mathlib/Algebra/Quaternion.lean | Quaternion.coe_re | [] | [
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Mathlib/Control/Traversable/Instances.lean | Sum.id_traverse | [
{
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.map_Ioi | [
{
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Mathlib/Data/List/OfFn.lean | List.length_ofFn | [
{
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_injective_of_surjective | [] | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_eq_of_weightedVSub_eq_zero_of_eq_neg_one | [
{
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasDerivAt.const_cpow | [] | [
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56
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Mathlib/Algebra/Order/Ring/Defs.lean | Antitone.const_mul | [] | [
290,
52
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289,
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Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.divOf_add | [
{
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_inf_comap_of_surjective | [] | [
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | EuclideanSpace.inner_piLp_equiv_symm | [] | [
178,
6
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176,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.eq | [] | [
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Mathlib/Topology/Algebra/Module/LocallyConvex.lean | locallyConvexSpace_iff_exists_convex_subset | [] | [
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_cons | [
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_map_submodule | [] | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | orthonormal_subtype_iff_ite | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_id | [] | [
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Mathlib/RingTheory/Localization/AtPrime.lean | IsLocalization.AtPrime.localRing | [
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Mathlib/Analysis/NormedSpace/Banach.lean | LinearEquiv.continuous_symm | [
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Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.mem_shadow_iff_exists_mem_card_add_one | [
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Mathlib/Order/Disjoint.lean | Codisjoint.inf_right | [] | [
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Mathlib/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Functor.IsLocalization.mk' | [
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Mathlib/Analysis/Seminorm.lean | Seminorm.smul_inf | [
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Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.ord_eq | [] | [
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Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Faithful.div_faithful | [] | [
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.nondegenerate_toMatrix₂'_iff | [] | [
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Mathlib/Topology/UniformSpace/Basic.lean | eventually_uniformity_comp_subset | [] | [
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Mathlib/Order/Max.lean | IsMin.snd | [] | [
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Mathlib/Algebra/Hom/Group.lean | map_mul | [] | [
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Mathlib/GroupTheory/Congruence.lean | Con.sup_def | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_eq_mul_right | [] | [
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Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.apply_eq_pow_smul_coeff | [
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Mathlib/Control/Applicative.lean | Functor.Comp.pure_seq_eq_map | [
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Mathlib/Data/TypeVec.lean | TypeVec.lastFun_splitFun | [] | [
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Mathlib/RingTheory/Noetherian.lean | isNoetherian_of_surjective | [] | [
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_add | [
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Std/Data/Option/Lemmas.lean | Option.map_eq_some | [] | [
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Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | AffineSubspace.pointwise_vadd_direction | [
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inr_map | [
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.isCompl_range_inl_inr | [
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Mathlib/LinearAlgebra/FreeModule/Finite/Matrix.lean | Matrix.rank_vecMulVec | [
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Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.mul_comp | [] | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.iSup | [
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Mathlib/Data/List/Basic.lean | List.indexOf_cons_self | [
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.Functor.map_isPullback | [
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.exists_of_mem_map | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.ker_restrict | [] | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_ofMul | [] | [
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Mathlib/Data/Option/Basic.lean | Option.casesOn'_none_coe | [
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.add_lt_add_iff_left | [] | [
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_eq_sum | [] | [
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Mathlib/Data/Fintype/Card.lean | Fintype.card_subtype_compl | [
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.degree_eq_one_of_irreducible | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.comp_bfamilyOfFamily | [] | [
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Mathlib/Algebra/Algebra/Basic.lean | Module.End_algebraMap_isUnit_inv_apply_eq_iff | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_bot | [] | [
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Mathlib/LinearAlgebra/Projection.lean | LinearMap.ofIsCompl_smul | [
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasCokernel_of_hasCoequalizer | [] | [
431,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_compl_iff_disjoint_left | [] | [
824,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_neg | [] | [
234,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.left_lt_of_lt_right | [] | [
811,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.consCases_cons | [
{
"state_after": "m n : ℕ\nα : Fin (n + 1) → Type u\nx✝ : α 0\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (succ i)\ni : Fin n\ny : α (succ i)\nz : α 0\nP : ((i : Fin (Nat.succ n)) → α i) → Sort v\nh : (x₀ : α 0) → (x : (i : Fin n) → α (succ i)) → P (cons x₀ x)\nx₀ : α 0\nx : (i : Fin n) → α (succ i)\n⊢ h ... | [
160,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.sq_lt | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ x ^ 2 < y ↔ -sqrt y < x ∧ x < sqrt y",
"tactic": "rw [← abs_lt, ← sq_abs, lt_sqrt (abs_nonneg _)]"
}
] | [
437,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/List/Basic.lean | List.enumFrom_nil | [] | [
3872,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3871,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.Iio_add_bij | [] | [
419,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.frequently_filterAt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nx : α\nP : Set α → Prop\n⊢ (∃ᶠ (a : Set α) in filterAt v x, P a) ↔ ∀ (ε : ℝ), ε > 0 → ∃ a, a ∈ setsAt v x ∧ a ⊆ closedBall x ε ∧ P a",
"tactic": "si... | [
281,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
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