file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_C_mul_X_pow | [
{
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"state_before": "R : Type u\nS : Type v\na✝ b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\na : R\n⊢ ↑n ≤ trailingDegree (↑C a * X ^ n)",
"tac... | [
261,
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258,
1
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Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.of_nat | [] | [
303,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.rootMultiplicity_sub_one_le_derivative_rootMultiplicity | [
{
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Mathlib/Algebra/Order/WithZero.lean | le_of_le_mul_right | [
{
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}
] | [
137,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Logic/Equiv/Defs.lean | Equiv.symm_comp_eq | [] | [
602,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_prod_mk_left | [] | [
1639,
34
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1638,
1
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.length_toList_pos_of_mem_support | [] | [
246,
68
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245,
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Mathlib/Data/Set/Ncard.lean | Set.ncard_insert_eq_ite | [
{
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170,
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.comap_comap | [] | [
387,
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385,
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | hasSum_mul_left_iff | [
{
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"tactic":... | [
93,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Seminorm.lean | Seminorm.ball_bot | [] | [
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18
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Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_gcd_of_dvd_left | [] | [
126,
67
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
125,
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Mathlib/Data/List/Basic.lean | List.subset_append_of_subset_right' | [] | [
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34
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320,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_eq_zero | [] | [
764,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
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Mathlib/Data/Num/Lemmas.lean | PosNum.add_to_nat | [
{
"state_after": "α : Type ?u.30847\nb : PosNum\n⊢ 1 + ↑b = ↑1 + ↑b",
"state_before": "α : Type ?u.30847\nb : PosNum\n⊢ ↑(1 + b) = ↑1 + ↑b",
"tactic": "rw [one_add b, succ_to_nat, add_comm]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.30847\nb : PosNum\n⊢ 1 + ↑b = ↑1 + ↑b",
... | [
102,
61
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90,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.eq_zero_or_pos | [] | [
413,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
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Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.linearMapAt_apply | [
{
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136,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/Data/Set/Basic.lean | Set.union_congr_right | [] | [
859,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.hom_isIso | [] | [
654,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
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Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_factors | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nA B : C\nf : A ⟶ B\n⊢ ∀ {X Y : Subobject B}, Factors X f ∧ Factors Y f → Factors (X ⊓ Y) f",
"state_before": "C : Type u₁\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category... | [
425,
50
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419,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.dvd_add_iff | [
{
"state_after": "no goals",
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"tactic": "rw [mul_sub, ← e, add_sub_cancel]"
},
... | [
995,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
991,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.eq | [] | [
1096,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
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Mathlib/Analysis/SpecialFunctions/Exp.lean | ContinuousAt.exp | [] | [
154,
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153,
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Mathlib/Data/Set/Image.lean | Set.mem_image_elim | [] | [
244,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/Data/Complex/Basic.lean | Complex.sq_abs | [] | [
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33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/TypeTags.lean | ofMul_toMul | [] | [
118,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Computability/Primrec.lean | Primrec₂.of_eq | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst... | [
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40
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417,
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Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.iIndepSets.iIndep | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
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Mathlib/Algebra/Field/Defs.lean | uniq_inv_of_isField | [
{
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242,
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Mathlib/Order/Filter/Ultrafilter.lean | Filter.iSup_ultrafilter_le_eq | [
{
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"tactic": "simp only [iSup_le_iff, ← le_iff_ultrafilter]"
}
] | [
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_has_biproduct | [] | [
568,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
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Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_addEquiv_lpPiLp | [] | [
92,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.ext | [] | [
143,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.mkContinuous_apply | [] | [
109,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_mk' | [] | [
1697,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
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Mathlib/Data/PNat/Basic.lean | PNat.recOn_one | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/Order/CompleteLattice.lean | Equiv.iSup_congr | [] | [
656,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_lift | [
{
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"state_before": "α β : Type u\nc : Cardinal\n⊢ ↑toNat (lift c) = ↑toNat c",
"tactic": "apply natCast_injective"
},
{
"state_after": "case a.inl\nα β : Type u\nc : Cardinal\nhc : c < ℵ₀\n⊢ ↑(↑toNat (lift c)... | [
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Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_comm | [
{
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_piecewise | [
{
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Mathlib/Data/Seq/Computation.lean | Computation.Equiv.trans | [] | [
997,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
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Mathlib/Algebra/Order/Sub/Defs.lean | tsub_eq_of_eq_add | [] | [
346,
53
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Mathlib/Data/Sum/Order.lean | OrderIso.sumLexDualAntidistrib_symm_inl | [] | [
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6
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722,
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Mathlib/Data/Fin/Basic.lean | Fin.addNat_one | [
{
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{
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.EqOnSource.symm_eqOn | [] | [
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857,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.isOpen_extend_preimage | [
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Mathlib/Algebra/Order/Group/Abs.lean | abs_le_max_abs_abs | [
{
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{
"state_after": "no goals",
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Mathlib/Analysis/Calculus/MeanValue.lean | Monotone.convexOn_univ_of_deriv | [] | [
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24
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.spanSingleton_pow | [
{
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enum_succ_eq_top | [
{
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354,
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.leftAssocTensor_map | [] | [
428,
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.comap_bracket_eq | [
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Mathlib/Data/PNat/Xgcd.lean | PNat.gcd_props | [
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Mathlib/Order/Filter/Partial.lean | Filter.mem_rcomap' | [] | [
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_pow | [] | [
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Mathlib/Data/Set/Image.lean | Set.range_nonempty | [] | [
744,
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Mathlib/Analysis/SpecificLimits/Normed.lean | summable_norm_pow_mul_geometric_of_norm_lt_1 | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.tendsto_cofinite_zero | [
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.eq_padic_norm' | [] | [
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Mathlib/Order/WithBot.lean | WithBot.ofDual_map | [] | [
969,
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Mathlib/Data/List/Basic.lean | List.zipLeft'_nil_right | [
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_zero | [
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Cofix.bisim' | [
{
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Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.subset_one_iff | [] | [
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kronecker_zero | [] | [
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_le_iff_le_comap | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.neg_zero | [
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.pow_zero_eq_zeta | [
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Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.comp_assoc | [] | [
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Mathlib/FieldTheory/Separable.lean | Polynomial.card_rootSet_eq_natDegree | [
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Mathlib/Data/Set/Sups.lean | Set.mem_infs | [] | [
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Mathlib/Algebra/Order/LatticeGroup.lean | inv_sup_eq_inv_inf_inv | [] | [
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31
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101,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.add | [
{
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Mathlib/Data/Matrix/Basic.lean | Matrix.smul_apply | [] | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_pow_sub_sub | [
{
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Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_symm_zero | [] | [
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6
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730,
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Mathlib/Data/Int/ModEq.lean | Int.neg_modEq_neg | [
{
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67
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Mathlib/Analysis/Convex/Integral.lean | ConvexOn.map_integral_le | [
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.inl_injective | [
{
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Mathlib/Order/Max.lean | Prod.isTop_iff | [] | [
452,
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Mathlib/Data/MvPolynomial/Division.lean | MvPolynomial.monomial_one_dvd_monomial_one | [
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Mathlib/Logic/Function/Basic.lean | Function.rightInverse_surjInv | [] | [
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Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.subset_bipolar | [
{
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Mathlib/Data/List/Cycle.lean | Cycle.chain_coe_cons | [] | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_le_of_le | [] | [
762,
36
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.symm_symm | [] | [
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471,
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Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.mem_sup_right | [
{
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Mathlib/Order/WithBot.lean | WithBot.unbot'_lt_iff | [
{
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.image_isVonNBounded_iff_finset_seminorm_bounded | [
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_zero | [
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Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.quotEquivOfEq_symm | [
{
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327,
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Mathlib/Algebra/GroupPower/Lemmas.lean | MonoidHom.apply_mnat | [
{
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896,
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Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Ioc_iff_left | [] | [
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48
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Mathlib/RingTheory/IntegralClosure.lean | IsIntegralClosure.mk'_algebraMap | [
{
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89
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1
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Mathlib/Order/Filter/Bases.lean | Filter.disjoint_principal_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.56617\nγ : Type ?u.56620\nι : Sort ?u.56623\nι' : Sort ?u.56626\nl l' : Filter α\np : ι → Prop\ns✝ : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nf : Filter α\ns : Set α\n⊢ Disjoint (𝓟 s) f ↔ sᶜ ∈ f",
"tac... | [
704,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_differentiableAt_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_4\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
188,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/RingTheory/DedekindDomain/PID.lean | IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime | [
{
"state_after": "R : Type u_2\ninst✝¹⁶ : CommRing R\ninst✝¹⁵ : IsDomain R\ninst✝¹⁴ : IsDedekindDomain R\nS : Type ?u.233823\ninst✝¹³ : CommRing S\ninst✝¹² : IsDomain S\ninst✝¹¹ : Algebra R S\ninst✝¹⁰ : Module.Free R S\ninst✝⁹ : Module.Finite R S\np : Ideal R\nhp0 : p ≠ ⊥\ninst✝⁸ : IsPrime p\nSₚ : Type u_1\nins... | [
254,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.exists_minimalPrimes_comap_eq | [
{
"state_after": "case intro.intro.intro\nR : Type u_2\nS : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nI✝ J : Ideal R\nI : Ideal S\nf : R →+* S\np : Ideal R\nH : p ∈ Ideal.minimalPrimes (comap f I)\np' : Ideal S\nh₁ : IsPrime p'\nh₂ : I ≤ p'\nh₃ : comap f p' = p\n⊢ ∃ p', p' ∈ Ideal.minimalPrimes I ∧ com... | [
166,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasStrictDerivAt.const_mul | [
{
"state_after": "case h.e'_7\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Typ... | [
264,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.isUnit_iff_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.120690\nα : Type u_1\nβ : Type ?u.120696\nγ : Type ?u.120699\ninst✝ : Group α\ns t : Set α\na b : α\n⊢ IsUnit s ↔ ∃ a, s = {a}",
"tactic": "simp only [isUnit_iff, Group.isUnit, and_true_iff]"
}
] | [
1194,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1193,
1
] |
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