file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Algebra/Order/Kleene.lean | kstar_eq_one | [
{
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252,
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Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.coe_pointwise_smul | [] | [
281,
6
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280,
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Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.uniformEquiv_mk_coe | [] | [
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66,
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Mathlib/Logic/Function/Basic.lean | Function.Surjective.exists₃ | [] | [
223,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.continuousWithinAt_iff' | [
{
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_induction_on | [
{
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Mathlib/Data/Finset/Fold.lean | Finset.fold_ite | [] | [
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161,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_neg_iff | [] | [
685,
47
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684,
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Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.congr_map | [
{
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"tactic": "rw [h]"
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222,
99
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Terminal.lean | CategoryTheory.Limits.hasTerminal_of_hasTerminal_of_preservesLimit | [
{
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"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u... | [
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86,
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Mathlib/Order/Concept.lean | Concept.swap_lt_swap_iff | [] | [
394,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
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Mathlib/Data/List/Permutation.lean | List.permutations_append | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.33481\nis ts : List α\n⊢ permutations (is ++ ts) = map (fun x => x ++ ts) (permutations is) ++ permutationsAux ts (reverse is)",
"tactic": "simp [permutations, permutationsAux_append]"
}
] | [
267,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/Data/ZMod/Basic.lean | ZMod.cast_neg | [] | [
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26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.inf | [] | [
1361,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_singleton | [
{
"state_after": "no goals",
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"tactic": "simp [volume_val]"
}
] | [
99,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Ncard.lean | Set.map_eq_of_subset | [] | [
334,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
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Std/Data/List/Lemmas.lean | List.mem_of_mem_erase | [] | [
1082,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1082,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_congr | [] | [
1348,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_self | [
{
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"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf : R[X]\n⊢ f ∣ -f + 0",
"tactic": "simp"
}
] | [
202,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_infNndist | [] | [
1545,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1544,
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Mathlib/Analysis/SpecialFunctions/Bernstein.lean | bernsteinApproximation.lt_of_mem_S | [
{
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"state_before": "f : C(↑I, ℝ)\nε : ℝ\nh : 0 < ε\nn : ℕ\nx : ↑I\nk : Fin (n + 1)\nm : k ∈ S f ε h n x\n⊢ abs (↑f k/ₙ - ↑f x) < ε / 2",
"t... | [
200,
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_sum | [] | [
2287,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsDetecting.mono | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_add | [] | [
156,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.inv_smul_integral_comp_sub_div | [
{
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847,
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Mathlib/Logic/Basic.lean | not_and_or | [] | [
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Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.stalkSpecializes_refl | [
{
"state_after": "C✝ : Type u\ninst✝³ : Category C✝\ninst✝² : HasColimits C✝\nX✝ Y Z : TopCat\nC : Type u_1\ninst✝¹ : Category C\ninst✝ : HasColimits C\nX : TopCat\nF : Presheaf C X\nx : ↑X\nx✝¹ : Opens ↑X\nx✝ : x ∈ x✝¹\n⊢ germ F { val := x, property := x✝ } ≫ stalkSpecializes F (_ : x ⤳ x) =\n germ F { val ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.natCast_add | [
{
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"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na₁ : ℕ\nb₁ : R\na₂ : ℕ\nb₂ : R\nx✝¹ : ↑a₁ =... | [
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Mathlib/Data/Multiset/Dedup.lean | Multiset.dedup_eq_zero | [] | [
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Mathlib/Algebra/Order/Field/Basic.lean | inv_le_one_iff | [
{
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.center_le_centralizer | [] | [
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Mathlib/Topology/MetricSpace/ShrinkingLemma.lean | exists_subset_iUnion_ball_radius_lt | [
{
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Mathlib/GroupTheory/Transfer.lean | Subgroup.leftTransversals.smul_diff_smul | [
{
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Mathlib/Data/Finset/Basic.lean | Finset.range_zero | [] | [
2995,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2994,
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Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_eq_right_iff | [
{
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"tactic": "simpa only [lcm_comm b a] using lcm_eq_left_iff b a h"
}
] | [
845,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.le_mulRothNumber | [] | [
355,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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Mathlib/Analysis/Complex/AbsMax.lean | Complex.eventually_eq_of_isLocalMax_norm | [
{
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336,
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Mathlib/Analysis/NormedSpace/Exponential.lean | Prod.fst_exp | [] | [
541,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.jacobson_eq_maximalIdeal | [
{
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194,
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Mathlib/Order/Heyting/Basic.lean | PUnit.sup_eq | [] | [
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1344,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.coe_mkNormedAddGroupHom | [] | [
139,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Analysis/Complex/Liouville.lean | Complex.liouville_theorem_aux | [
{
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94,
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_restrict_of_monotoneOn | [] | [
1178,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
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Mathlib/Order/MinMax.lean | max_lt_max_right_iff | [] | [
198,
36
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197,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulMono_iff_posMulStrictMono | [] | [
991,
79
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990,
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Mathlib/LinearAlgebra/Ray.lean | SameRay.sameRay_nonneg_smul_right | [
{
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121,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.eq_pow_find_of_dvd_irreducible_pow | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na p : Associates α\nhp : Irreducible p\ninst✝ : (n : ℕ) → Decidable (a ∣ p ^ n)\nn : ℕ\nh :... | [
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1889,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.fst_colimit_cocone | [] | [
1151,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
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Mathlib/Data/Finset/Card.lean | Finset.card_insert_of_mem | [
{
"state_after": "no goals",
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"tactic": "rw [insert_eq_of_mem h]"
}
] | [
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98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.induction_on | [
{
"state_after": "case mk.mk\nR : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nβ : LocalizedModule S M → Prop\nh : ∀ (m : M) (s : { x // x ∈ S }), β (mk m s)\nx✝ : LocalizedModule S M\nm : M\ns : { x // x ∈ S }\n⊢ β (Quot.mk Setoid.r (m, s))",
"... | [
106,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousAt.comp_div_cases | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nG₀ : Type u_2\ninst✝⁵ : GroupWithZero G₀\ninst✝⁴ : TopologicalSpace G₀\ninst✝³ : HasContinuousInv₀ G₀\ninst✝² : ContinuousMul G₀\nf✝ g✝ : α → G₀\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns : Set α\na : α\nf g : α → G₀\nh : α → G₀ → β\nhf : Continuous... | [
219,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.toDual_total_right | [
{
"state_after": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : DecidableEq ι\nb : Basis ι R M\nf : ι →₀ R\ni : ι\n⊢ ∑ i_1 in f.support, ↑(↑(toDual b) (↑b i)) (↑f i_1 • ↑b i_1) = ↑f i",
"state_before": "R : Type ... | [
320,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_eq_self | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ ∃ z, b = b + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ toIcoMod hp a b = b ↔ b ∈ Set.Ic... | [
721,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_iff_right | [] | [
277,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasStrictDerivAt.cpow_const | [] | [
174,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_add_le | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.793099\nβ : Type ?u.793102\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nha : a = ⊤\n⊢ ENNReal.toReal (a + b) ≤ ENNReal.toReal a + ENNReal.toReal b",
"tactic": "simp only [ha, top_add, top_toReal, zero_add, toReal_nonneg]"
},
{
"state_after": "no goals",... | [
1970,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1966,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | Differentiable.comp_differentiableOn | [] | [
193,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_le | [] | [
937,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_add_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ (fun x => x + a) '' [[b, c]] = [[b + a, c + a]]",
"tactic": "simp"
}
] | [
460,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.prod_cyclotomic_eq_geom_sum | [
{
"state_after": "n : ℕ\nh : 0 < n\nR : Type u_1\ninst✝ : CommRing R\n⊢ ∏ i in Finset.erase (Nat.divisors n) 1, cyclotomic i ℤ = ∑ i in range n, X ^ i",
"state_before": "n : ℕ\nh : 0 < n\nR : Type u_1\ninst✝ : CommRing R\n⊢ ∏ i in Finset.erase (Nat.divisors n) 1, cyclotomic i R = ∑ i in range n, X ^ i",
... | [
395,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.edist_toL1_zero | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1329799\nδ : Type ?u.1329802\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\nhf : Integrable f\n⊢ (∫⁻ (a : α), ↑‖f a‖₊ ∂μ) = ∫⁻ (a : α), edist (f a) 0 ∂μ",
"... | [
1415,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1412,
1
] |
Mathlib/FieldTheory/Tower.lean | FiniteDimensional.left | [] | [
114,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_radius_eq_top | [
{
"state_after": "𝕂 : Type u_1\n𝔸 : Type u_2\n𝔹 : Type ?u.329102\ninst✝⁴ : IsROrC 𝕂\ninst✝³ : NormedRing 𝔸\ninst✝² : NormedAlgebra 𝕂 𝔸\ninst✝¹ : NormedRing 𝔹\ninst✝ : NormedAlgebra 𝕂 𝔹\nr : NNReal\n⊢ Summable fun n => ‖expSeries 𝕂 𝔸 n‖ * ↑r ^ n",
"state_before": "𝕂 : Type u_1\n𝔸 : Type u_2\n𝔹... | [
402,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_union | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.451772\nγ : Type ?u.451775\ninst✝ : DecidableEq α\ns✝ t✝ s t : Multiset α\na✝ : α\n⊢ a✝ ∈ toFinset (s ∪ t) ↔ a✝ ∈ toFinset s ∪ toFinset t",
"state_before": "α : Type u_1\nβ : Type ?u.451772\nγ : Type ?u.451775\ninst✝ : DecidableEq α\ns✝ t✝ s t : Multiset α... | [
3177,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3176,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.next | [] | [
153,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Order/Zorn.lean | zorn_preorder₀ | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.3853\nr : α → α → Prop\nc✝ : Set α\ninst✝ : Preorder α\ns : Set α\nih : ∀ (c : Set α), c ⊆ s → IsChain (fun x x_1 => x ≤ x_1) c → ∃ ub, ub ∈ s ∧ ∀ (z : α), z ∈ c → z ≤ ub\nc : Set ↑s\nhc : IsChain (fun x x_1 => x ≤ x_1) c\np : { x // x ∈ ... | [
129,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofDual_pow | [] | [
150,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_id | [] | [
1226,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1225,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.eq_of_le_of_finrank_le | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\nS₁ S₂ : Submodule K V\ninst✝ : FiniteDimensional K { x // x ∈ S₂ }\nhle : S₁ ≤ S₂\nhd : finrank K { x // x ∈ S₂ } ≤ finrank K { x // x ∈ ... | [
848,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.symm_constVSub | [
{
"state_after": "case h\n𝕜 : Type u_3\nV : Type u_1\nV₁ : Type ?u.1896593\nV₂ : Type ?u.1896596\nV₃ : Type ?u.1896599\nV₄ : Type ?u.1896602\nP₁ : Type ?u.1896605\nP : Type u_2\nP₂ : Type ?u.1896611\nP₃ : Type ?u.1896614\nP₄ : Type ?u.1896617\ninst✝²¹ : NormedField 𝕜\ninst✝²⁰ : SeminormedAddCommGroup V\ninst✝... | [
739,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_neg | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.equiv_symm | [] | [
173,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.infty_pow | [] | [
888,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_fintype | [] | [
515,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_univ_card | [] | [
947,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_eval_one | [
{
"state_after": "n : ℕ\n⊢ ∑ i in range (n + 1), eval 1 (↑(monomial (n - i)) (_root_.bernoulli i * ↑(Nat.choose n i))) = bernoulli' n",
"state_before": "n : ℕ\n⊢ eval 1 (bernoulli n) = bernoulli' n",
"tactic": "simp only [bernoulli, eval_finset_sum]"
},
{
"state_after": "n : ℕ\n⊢ (if n = 1 then ... | [
99,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.div_eq_zero | [] | [
90,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
11
] |
Mathlib/Topology/Basic.lean | nhds_basis_closeds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na✝ : α\ns s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\na : α\nt : Set α\n⊢ (∃ x, (a ∈ xᶜ ∧ IsOpen (xᶜ)) ∧ xᶜ ⊆ t) ↔ ∃ i, (¬a ∈ i ∧ IsClosed i) ∧ iᶜ ⊆ t",
"tactic": "simp only [isOpen_compl_iff, mem_com... | [
871,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.union | [] | [
723,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Topology/Category/TopCat/EpiMono.lean | TopCat.mono_iff_injective | [
{
"state_after": "X Y : TopCat\nf : X ⟶ Y\n⊢ Mono f ↔ Mono ((forget TopCat).map f)",
"state_before": "X Y : TopCat\nf : X ⟶ Y\n⊢ Mono f ↔ Function.Injective ((forget TopCat).map f)",
"tactic": "suffices Mono f ↔ Mono ((forget TopCat).map f) by\n rw [this, CategoryTheory.mono_iff_injective]"
},
{
... | [
46,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Topology/SubsetProperties.lean | Filter.Tendsto.isCompact_insert_range_of_cofinite | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type u_1\nπ : ι → Type ?u.50005\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nf : ι → α\na : α\nhf : Tendsto f cofinite (𝓝 a)\nthis : TopologicalSpace ι := ⊥\n⊢ IsCompact (insert a (range f))",
"state_before": "α : Type u\nβ : Type v\nι... | [
575,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/List/Basic.lean | List.insertNth_removeNth_of_ge | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.113338\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na head✝ : α\nas : List α\nx✝¹ : 0 < length (head✝ :: as)\nx✝ : 0 ≤ 0\n⊢ insertNth 0 a (removeNth (head✝ :: as) 0) = removeNth (insertNth (0 + 1) a (head✝ :: as)) 0",
"tactic"... | [
1629,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1621,
1
] |
Mathlib/Init/Logic.lean | eq_rec_compose | [] | [
83,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Quaternion.lean | Cardinal.mk_univ_quaternionAlgebra_of_infinite | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nc₁ c₂ : R\ninst✝ : Infinite R\n⊢ (#↑Set.univ) = (#R)",
"tactic": "rw [mk_univ_quaternionAlgebra, pow_four]"
}
] | [
1446,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.exists_unique_congr | [
{
"state_after": "case mp\nα : Sort u\nβ : Sort v\nγ : Sort w\np : α → Prop\nq : β → Prop\nf : α ≃ β\nh : ∀ {x : α}, p x ↔ q (↑f x)\n⊢ (∃! x, p x) → ∃! y, q y\n\ncase mpr\nα : Sort u\nβ : Sort v\nγ : Sort w\np : α → Prop\nq : β → Prop\nf : α ≃ β\nh : ∀ {x : α}, p x ↔ q (↑f x)\n⊢ (∃! y, q y) → ∃! x, p x",
"s... | [
858,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
11
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.sigma_eq_of_eq_comp_cast | [
{
"state_after": "m n : ℕ\nα : Type u_1\nai : ℕ\na : Fin ai → α\nbi : ℕ\nb : Fin bi → α\nhi : ai = bi\nh : { fst := ai, snd := a }.snd = { fst := bi, snd := b }.snd ∘ ↑(cast hi)\n⊢ { fst := ai, snd := a } = { fst := bi, snd := b }",
"state_before": "m n : ℕ\nα : Type u_1\nai : ℕ\na : Fin ai → α\nbi : ℕ\nb :... | [
997,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparating_op_iff | [
{
"state_after": "case refine'_1\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\n𝒢 : Set C\nh𝒢 : IsCoseparating (Set.op 𝒢)\nX Y : C\nf g : X ⟶ Y\nhfg : ∀ (G : C), G ∈ 𝒢 → ∀ (h : G ⟶ X), h ≫ f = h ≫ g\n⊢ f = g\n\ncase refine'_2\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Categ... | [
108,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_det_transpose | [
{
"state_after": "l : Type ?u.97236\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nh : IsUnit (det A)\n⊢ IsUnit (det A)",
"state_before": "l : Type ?u.97236\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : Decidable... | [
246,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_le_self | [
{
"state_after": "a b : Int\nHa : 0 ≤ a\nthis : a / b ≤ ↑(natAbs a)\n⊢ a / b ≤ a",
"state_before": "a b : Int\nHa : 0 ≤ a\n⊢ a / b ≤ a",
"tactic": "have := Int.le_trans le_natAbs (ofNat_le.2 <| natAbs_div_le_natAbs a b)"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nHa : 0 ≤ a\... | [
577,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
575,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | Differentiable.div_const | [] | [
325,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Algebra/Bounds.lean | BddAbove.mul | [] | [
131,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.MemBaseSet.filter | [
{
"state_after": "ι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I\nl l₁ l₂ : IntegrationParams\nhπ : MemBaseSet l I c r π\np : Box ι → Prop\nhD : l.bDistortion = true\n⊢ ∃ π',\n Prepartition.iUnion π' = ↑I \\ TaggedPrepartition.iUn... | [
418,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
11
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.commute_X | [] | [
425,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.id_mem | [] | [
192,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_natCast_of_le_half | [
{
"state_after": "case zero\na : ℕ\nha : a ≤ Nat.zero / 2\n⊢ valMinAbs ↑a = ↑a\n\ncase succ\na n✝ : ℕ\nha : a ≤ Nat.succ n✝ / 2\n⊢ valMinAbs ↑a = ↑a",
"state_before": "n a : ℕ\nha : a ≤ n / 2\n⊢ valMinAbs ↑a = ↑a",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zer... | [
1072,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.extend_iUnion | [
{
"state_after": "case intro\nα : Type u_2\nP : Set α → Prop\nm : (s : Set α) → P s → ℝ≥0∞\nP0 : P ∅\nm0 : m ∅ P0 = 0\nPU : ∀ ⦃f : ℕ → Set α⦄, (∀ (i : ℕ), P (f i)) → P (⋃ (i : ℕ), f i)\nmU :\n ∀ ⦃f : ℕ → Set α⦄ (hm : ∀ (i : ℕ), P (f i)),\n Pairwise (Disjoint on f) → m (⋃ (i : ℕ), f i) (_ : P (⋃ (i : ℕ), f i... | [
1426,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1418,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_map_polarization | [
{
"state_after": "𝕜 : Type ?u.2712404\nE : Type ?u.2712407\nF : Type ?u.2712410\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerPr... | [
1226,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.tendsto_pow_log_div_mul_add_atTop | [
{
"state_after": "no goals",
"state_before": "x y a b : ℝ\nn : ℕ\nha : a ≠ 0\n⊢ (fun x => x ^ n / (a * exp x + b)) ∘ log =ᶠ[atTop] fun x => log x ^ n / (a * x + b)",
"tactic": "filter_upwards [eventually_gt_atTop (0 : ℝ)] with x hx using by simp [exp_log hx]"
},
{
"state_after": "no goals",
... | [
360,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleMap_mem_sphere' | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.9896\ninst✝ : NormedAddCommGroup E\nc : ℂ\nR θ : ℝ\n⊢ circleMap c R θ ∈ sphere c (Abs.abs R)",
"tactic": "simp"
}
] | [
122,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/NumberTheory/ModularForms/CongruenceSubgroups.lean | Gamma0_mem | [] | [
118,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
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