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/Algebra/GroupPower/Order.lean | pow_le_pow_of_le_one' | [] | [
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.localInverse_continuousAt | [] | [
648,
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Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousOn_sum | [] | [
536,
59
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533,
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.piecewise_empty | [
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Mathlib/Analysis/Analytic/Basic.lean | Asymptotics.IsBigO.continuousMultilinearMap_apply_eq_zero | [
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Mathlib/Order/Disjoint.lean | Disjoint.of_disjoint_inf_of_le | [] | [
173,
60
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Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.Cocones.cocone_iso_of_hom_iso | [
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534,
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Hom.cast_eq_cast | [
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44,
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Mathlib/Analysis/Calculus/Dslope.lean | differentiableAt_dslope_of_ne | [
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"tactic": "simp only [← d... | [
162,
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160,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.infty_equiv_isometry | [
{
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.lift_mk | [] | [
286,
31
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Mathlib/Algebra/DirectSum/Module.lean | DirectSum.component.lof_self | [] | [
225,
18
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224,
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Mathlib/Data/Part.lean | Part.inv_mem_inv | [
{
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"tactic": "simp [inv... | [
746,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
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Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.norm_fst | [
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... | [
643,
93
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642,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.contDiffAt_arcsin_iff | [] | [
133,
35
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129,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_subset_coe | [] | [
170,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
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Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_idem | [
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114,
24
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112,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_singleton_eq_span_singleton | [
{
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"state_before": "α✝ : Type u\nβ : Type v\na b : α✝\ninst✝² : CommSemiring α✝\nI : Ideal α✝\... | [
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511,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.mul_invOfUnit | [] | [
1933,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.coe_comp | [] | [
166,
6
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165,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.smul | [
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1759,
36
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Ici | [
{
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"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun ... | [
323,
40
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321,
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Mathlib/Order/UpperLower/LocallyFinite.lean | Set.Finite.upperClosure | [
{
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Mathlib/Data/Prod/PProd.lean | PProd.forall' | [] | [
40,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_inter_null_of_null_left | [] | [
348,
46
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.aeval_eq_bind₁ | [] | [
110,
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109,
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Mathlib/Data/List/Rotate.lean | List.isRotated_reverse_comm_iff | [
{
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"tactic": "intro h"
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523,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi | [
{
"state_after": "θ : Angle\n⊢ toReal (2 • ↑(toReal θ)) = 2 * toReal θ + 2 * π ↔ toReal θ ≤ -π / 2",
"state_before": "θ : Angle\n⊢ toReal (2 • θ) = 2 * toReal θ + 2 * π ↔ toReal θ ≤ -π / 2",
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},
{
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712,
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Mathlib/Order/Filter/Basic.lean | Filter.comap_sSup | [
{
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2240,
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Mathlib/Topology/PartitionOfUnity.lean | PartitionOfUnity.locallyFinite | [] | [
144,
20
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143,
11
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_injective | [] | [
1120,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.card_support_eq_zero | [
{
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229,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_zero | [] | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
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Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.map_neg | [] | [
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24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/Data/Finset/Fold.lean | Finset.fold_cons | [
{
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Mathlib/GroupTheory/Complement.lean | Subgroup.smul_toFun | [] | [
466,
99
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461,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_mul_X_ne | [
{
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"tactic": "classical\nrepeat' rw [d... | [
563,
87
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554,
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Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.henstock_le_mcShane | [
{
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"tactic": "trivial"
}
] | [
282,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/PFun.lean | PFun.preimage_inter | [] | [
447,
27
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Mathlib/Algebra/Homology/ImageToKernel.lean | image_le_kernel | [
{
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] | [
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Mathlib/Data/List/Basic.lean | List.getLast_cons_cons | [] | [
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Mathlib/RingTheory/PowerBasis.lean | PowerBasis.finiteDimensional | [] | [
85,
46
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_lsub_or_sup_succ_eq_lsub | [
{
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Mathlib/Analysis/InnerProductSpace/Calculus.lean | contDiff_inner | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Covering.lean | IsCoveringMap.continuous | [] | [
165,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.deg_add | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
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Mathlib/Topology/Instances/Real.lean | Function.Periodic.compact_of_continuous | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α\nf : ℝ → α\nc : ℝ\nhp : Periodic f c\nhc : c ≠ 0\nhf : Continuous f\n⊢ IsCompact (f '' [[0, 0 + c]])",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : TopologicalSpace α\nf : ℝ → α\nc : ℝ\nhp : Periodic f c\nhc : c... | [
207,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Int.mem_zmultiples_iff | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.32208\ninst✝² : Group G\nA : Type ?u.32214\ninst✝¹ : AddGroup A\nN : Type ?u.32220\ninst✝ : Group N\na b k : ℤ\n⊢ (fun x => x • a) k = b ↔ b = a * k",
"tactic": "rw [mul_comm, eq_comm, ← smul_eq_mul]"
}
] | [
162,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_sum | [
{
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574,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.FinMeasAdditive.zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.12375\nF : Type ?u.12378\nF' : Type ?u.12381\nG : Type ?u.12384\n𝕜 : Type ?u.12387\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup... | [
106,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Ring/Semiconj.lean | SemiconjBy.sub_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝ : NonUnitalNonAssocRing R\na b x y x' y' : R\nh : SemiconjBy a x y\nh' : SemiconjBy a x' y'\n⊢ SemiconjBy a (x - x') (y - y')",
"tactic": "simpa only [sub_eq_add_neg] using h.add_right h'.neg_right"
}
] | [
94,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_le_lintegral_abs_det_fderiv_aux2 | [
{
"state_after": "E : Type u_1\nF : Type ?u.785438\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
903,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_pow | [
{
"state_after": "n : ℕ+\nm : ℕ\nu : PrimeMultiset := factorMultiset n\n⊢ factorMultiset (Pow.pow n m) = m • factorMultiset n",
"state_before": "n : ℕ+\nm : ℕ\n⊢ factorMultiset (Pow.pow n m) = m • factorMultiset n",
"tactic": "let u := factorMultiset n"
},
{
"state_after": "n : ℕ+\nm : ℕ\nu : Pr... | [
314,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.congr_arg | [] | [
203,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Topology/Constructions.lean | Continuous.fst | [] | [
332,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_iInf_comap | [
{
"state_after": "α : Type u_3\nι : Sort u_1\nβ : Type u_2\ninst✝ : Nonempty ι\nf : α → β\nm : ι → OuterMeasure β\ns : Set β\n⊢ ↑(⨅ (i : ι), ↑(map f) (↑(comap f) (m i))) s ≤ ↑(↑(map f) (⨅ (i : ι), ↑(comap f) (m i))) s",
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1253,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
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Mathlib/Order/Ideal.lean | Order.Ideal.coe_ssubset_coe | [] | [
159,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.Prime.multiplicity_choose_prime_pow_add_multiplicity | [
{
"state_after": "p n k : ℕ\nhp : Prime p\nhkn : k ≤ p ^ n\nhk0 : k ≠ 0\nhdisj :\n Disjoint (filter (fun i => p ^ i ≤ k % p ^ i + (p ^ n - k) % p ^ i) (Ico 1 (succ n)))\n (filter (fun i => p ^ i ∣ k) (Ico 1 (succ n)))\n⊢ multiplicity p (choose (p ^ n) k) + multiplicity p k ≤ ↑n",
"state_before": "p n k ... | [
240,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.multiplicative_of_coprime | [
{
"state_after": "α : Type u_2\nR : Type ?u.1916855\ninst✝⁴ : CancelCommMonoidWithZero R\ninst✝³ : UniqueFactorizationMonoid R\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : UniqueFactorizationMonoid α\nβ : Type u_1\ninst✝ : CancelCommMonoidWithZero β\nf : α → β\na b : α\nh0 : f 0 = 0\nh1 : ∀ {x y : α}, IsUnit ... | [
1189,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.lt_top_of_mem_eraseTop | [] | [
441,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_or_eq_of_le | [] | [
389,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
388,
11
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.lift_symm_apply | [] | [
1985,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1983,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.base_mul_mem_lifts | [
{
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119,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Dfinsupp/NeLocus.lean | Dfinsupp.subset_mapRange_neLocus | [
{
"state_after": "no goals",
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94,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
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] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero | [
{
"state_after": "𝕜 : Type ?u.3103380\nE : Type ?u.3103383\nF : Type u_1\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 : F\n⊢ 2 = 0 ∨ ↑re (inner x y) = 0 ↔ inner x y = 0",
"state_... | [
1463,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | hasSum_le_inj | [
{
"state_after": "ι : Type u_1\nκ : Type u_2\nα : Type u_3\ninst✝² : OrderedAddCommMonoid α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nf g✝ : ι → α\na a₁ a₂ : α\ng : κ → α\ne : ι → κ\nhe : Injective e\nhs : ∀ (c : κ), ¬c ∈ Set.range e → 0 ≤ g c\nh : ∀ (i : ι), f i ≤ g (e i)\nhf : HasSum (exten... | [
72,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Invertible.lean | Commute.invOf_left | [
{
"state_after": "no goals",
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"tactic": "simp [mul_assoc]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : Monoid α\na b : α\ninst✝ : Invertible... | [
336,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.HasSeparableContraction.dvd_degree | [] | [
90,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublistsLenAux_zero | [
{
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"tactic": "cases l <;> rfl"
}
] | [
259,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.mem_prod | [] | [
860,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsMatching.even_card | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\ninst✝ : Fintype ↑M.verts\nh : IsMatching M\n⊢ Even (Finset.card (Set.toFinset M.verts))",
"tactic": "classical\nrw [isMatching_iff_forall_degree] at h\nuse M.coe.edgeFinset.card\nrw [← two_mul, ← M.coe.sum_de... | [
114,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Topology/Constructions.lean | comap_sigmaMk_nhds | [] | [
1511,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1510,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.uniformContinuous_neg | [
{
"state_after": "ε : ℝ\nε0 : ε > 0\na✝ b✝ : ℚ\nh : dist b✝ a✝ < ε\n⊢ dist (-a✝) (-b✝) < ε",
"state_before": "ε : ℝ\nε0 : ε > 0\na✝ b✝ : ℚ\nh : dist a✝ b✝ < ε\n⊢ dist (-a✝) (-b✝) < ε",
"tactic": "rw [dist_comm] at h"
},
{
"state_after": "no goals",
"state_before": "ε : ℝ\nε0 : ε > 0\na✝ b✝ :... | [
100,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualCoannihilator_bot | [] | [
866,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.condition_ι | [
{
"state_after": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\n⊢ ((homologyIsoKernelDesc f g w).hom ≫ kernel.ι (cokernel.desc f g w)) ≫ cokernel.desc f g w = 0",
"state_before": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\n... | [
162,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.mk_preimage_sigma | [] | [
183,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.range_comp_incl_top | [
{
"state_after": "V : Type ?u.494024\nW : Type ?u.494027\nV₁ : Type u_2\nV₂ : Type u_1\nV₃ : Type ?u.494036\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : SeminormedAddCommGroup W\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf : NormedAddGroupHom V₁ V... | [
814,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
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] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.nonempty | [] | [
233,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
11
] |
Mathlib/Order/Antichain.lean | IsAntichain.eq | [] | [
64,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
11
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.Parallel.trans | [
{
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"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3... | [
1744,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1739,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_left | [] | [
915,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_of_eqOn_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.222676\nι : Type ?u.222679\nG : Type ?u.222682\nM : Type u_2\nN : Type ?u.222688\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t : Set α\nhf : EqOn f 1 s\n⊢ (∏ᶠ (i : α) (_ : i ∈ s), f i) = ∏ᶠ (i : α) (_ : i ∈ s), 1",
"state_before": "α : Ty... | [
654,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.add_mod_eq_add_mod_right | [
{
"state_after": "no goals",
"state_before": "m✝ n✝ k✝ m n k i : ℕ\nH : m % n = k % n\n⊢ (m + i) % n = (k + i) % n",
"tactic": "rw [← mod_add_mod, ← mod_add_mod k, H]"
}
] | [
758,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Algebra/Category/GroupCat/Colimits.lean | AddCommGroupCat.Colimits.quot_add | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_le_bot_iff | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.1255386\nR₂ : Type u_2\nR₃ : Type ?u.1255392\nR₄ : Type ?u.1255395\nS : Type ?u.1255398\nK : Type ?u.1255401\nK₂ : Type ?u.1255404\nM : Type u_3\nM' : Type ?u.1255410\nM₁ : Type ?u.1255413\nM₂ : Type u_4\nM₃ : Type ?u.1255419\nM₄ : Type ?u.1255422\nN : Type ?u.125542... | [
1416,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuous_iff_isOpen_preimage | [] | [
786,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_set_mk | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | summable_one_div_pow_of_le | [
{
"state_after": "α : Type ?u.462750\nβ : Type ?u.462753\nι : Type ?u.462756\nm : ℝ\nf : ℕ → ℕ\nhm : 1 < m\nfi : ∀ (i : ℕ), i ≤ f i\na : ℕ\n⊢ 1 / m ^ f a ≤ (1 / m) ^ a",
"state_before": "α : Type ?u.462750\nβ : Type ?u.462753\nι : Type ?u.462756\nm : ℝ\nf : ℕ → ℕ\nhm : 1 < m\nfi : ∀ (i : ℕ), i ≤ f i\n⊢ Summ... | [
445,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_add_rat_iff | [] | [
548,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_inj | [] | [
182,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_comp | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.size_pop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\n⊢ size (pop a) = size a - 1",
"tactic": "match a with\n| ⟨[]⟩ => rfl\n| ⟨a::as⟩ => simp [pop, Nat.succ_sub_succ_eq_sub, size]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\n⊢ size (pop { da... | [
630,
58
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
627,
9
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_range_zero | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.450036\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\n⊢ ∏ k in range 0, f k = 1",
"tactic": "rw [range_zero, prod_empty]"
}
] | [
1261,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1261,
1
] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.sdiff_compl_neighborFinset_inter_eq | [
{
"state_after": "case a\nV : Type u\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nn k ℓ μ : ℕ\nv w : V\nh : Adj G v w\na✝ : V\n⊢ a✝ ∈ (neighborFinset G vᶜ ∩ neighborFinset G wᶜ) \\ ({w} ∪ {v}) ↔ a✝ ∈ neighborFinset G vᶜ ∩ neighborFinset G wᶜ",
"state_before": "... | [
134,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/List/Basic.lean | List.length_le_length_insertNth | [
{
"state_after": "case inl\nι : Type ?u.123956\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : List α\nx : α\nn : ℕ\nhn : n ≤ length l\n⊢ length l ≤ length (insertNth n x l)\n\ncase inr\nι : Type ?u.123956\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : Li... | [
1685,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_subtype'' | [] | [
1216,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/CategoryTheory/Functor/Const.lean | CategoryTheory.Functor.const.opObjUnop_hom_app | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Topology/Sheaves/PUnit.lean | TopCat.Presheaf.isSheaf_on_pUnit_iff_isTerminal | [] | [
62,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.coe_matrix_coe | [] | [
254,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coordChangeL_apply' | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁹ : Semiring R\ninst✝⁸ : TopologicalSpace F\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F TotalSpace.proj\nx : TotalSpace E\nb✝ : B\ny✝ : E b✝\ninst✝... | [
359,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
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