file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/Data/Set/Pointwise/SMul.lean | Set.op_smul_set_subset_mul | [] | [
420,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
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Mathlib/Analysis/SpecificLimits/Normed.lean | summable_geometric_iff_norm_lt_1 | [
{
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326,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measurable_spanningSets | [] | [
3473,
97
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3471,
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Mathlib/Data/List/Card.lean | List.card_eq_of_equiv | [] | [
173,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | coeff_charpoly_mem_ideal_pow | [
{
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... | [
261,
28
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.L1.dist_def | [
{
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1305,
33
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1303,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.smul_apply | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.exists_eq_const | [
{
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400,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | isOpen_extChartAt_preimage' | [] | [
1150,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Basic.lean | dite_eq_right_iff | [
{
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"tactic": "by_cases P <;> simp [*, forall_prop_of_t... | [
1151,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_isEmpty | [
{
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"state_before": "m : Type ?u.172043\nn : Type u_1\ninst✝⁵ : DecidableEq n\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq m\ninst✝² : Fintype m\nR : Type v\ninst✝¹ : CommRing R\ninst✝ : IsEmpty n\nA : Matrix n n R\n⊢ det A = 1",
"tactic": "simp [det_apply]"
}
] | [
103,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.centralizer_eq_top_iff_subset | [] | [
136,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/Topology/UniformSpace/Basic.lean | symmetrizeRel_subset_self | [] | [
222,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
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Mathlib/Data/TypeVec.lean | TypeVec.Arrow.ext | [
{
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"tactic": "intro h"
},
{
"state_after": "case h\nn : ℕ\nα : TypeVec n\nβ : TypeV... | [
65,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Logic/Function/Iterate.lean | Function.Commute.iterate_iterate_self | [] | [
163,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.IsAmalgamation.compPresheafMap | [
{
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388,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.neg | [] | [
174,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Analysis/Convex/Between.lean | Sbtw.affineCombination_of_mem_affineSpan_pair | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.333838\nP : Type u_4\nP' : Type ?u.333844\ninst✝⁸ : OrderedRing R\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module R V\ninst✝⁵ : AddTorsor V P\ninst✝⁴ : AddCommGroup V'\ninst✝³ : Module R V'\ninst✝² : AddTorsor V' P'\ninst✝¹ : NoZeroDivisors R\ninst✝ : NoZeroS... | [
550,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.sum_apply | [
{
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... | [
777,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
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Mathlib/Topology/UniformSpace/Equicontinuity.lean | equicontinuous_iff_range | [] | [
229,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.eq_X_add_C_of_degree_eq_one | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : degree p = 1\n⊢ ↑C (coeff p 1) * X + ↑C (coeff p 0) = ↑C (coeff p One.one) * X + ↑C (coeff p 0)",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : degree ... | [
455,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_iUnion | [] | [
2169,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2167,
1
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Mathlib/Algebra/Ring/Prod.lean | NonUnitalRingHom.prod_unique | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.22238\nβ : Type ?u.22241\nR : Type u_1\nR' : Type ?u.22247\nS : Type u_3\nS' : Type ?u.22253\nT : Type u_2\nT' : Type ?u.22259\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring T\nf✝ : R →ₙ... | [
154,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.val_list_prod | [] | [
94,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Data/SetLike/Basic.lean | SetLike.coe_set_eq | [] | [
142,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Data/Num/Lemmas.lean | PosNum.cast_bit1 | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.range_cons | [
{
"state_after": "no goals",
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"tactic": "simp [Fin.exists_fin_succ, eq_comm]"
}
] | [
170,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Data/Multiset/Dedup.lean | Multiset.mem_dedup | [] | [
44,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
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Mathlib/Data/Multiset/Sum.lean | Multiset.card_disjSum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ns : Multiset α\nt : Multiset β\n⊢ ↑card (disjSum s t) = ↑card s + ↑card t",
"tactic": "rw [disjSum, card_add, card_map, card_map]"
}
] | [
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45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.coe_toContinuousMap | [] | [
465,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
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] |
Mathlib/Algebra/Group/Units.lean | divp_inv | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isBounded_sUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.8797\nα : Type u_1\nβ : Type ?u.8803\ns : Set α\ninst✝ : Bornology α\nS : Set (Set α)\nhs : Set.Finite S\n⊢ IsBounded (⋃₀ S) ↔ ∀ (s : Set α), s ∈ S → IsBounded s",
"tactic": "rw [sUnion_eq_biUnion, isBounded_biUnion hs]"
}
] | [
295,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.Flat.mono | [] | [
392,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.contDiff | [
{
"state_after": "no goals",
"state_before": "n : ℕ∞\n⊢ ContDiff ℝ n expNegInvGlue",
"tactic": "simpa using contDiff_polynomial_eval_inv_mul 1"
}
] | [
160,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
11
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.add_seq | [] | [
278,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.eq_zero_of_forall_not_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.16742\nγ : Type ?u.16745\ns : Multiset α\nl : List α\nH : ∀ (x : α), ¬x ∈ Quot.mk Setoid.r l\n⊢ Quot.mk Setoid.r [] = 0",
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266,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.prod_eq_iff_prod_pow_moebius_eq_of_nonzero | [
{
"state_after": "case refine'_1\nR : Type u_1\ninst✝ : CommGroupWithZero R\nf g : ℕ → R\nhf : ∀ (n : ℕ), 0 < n → f n ≠ 0\nhg : ∀ (n : ℕ), 0 < n → g n ≠ 0\nn : ℕ\nhn : 0 < n\n⊢ ∏ i in divisors n, f i = g n ↔\n (∏ i in divisors n, if h : 0 < i then Units.mk0 (f i) (_ : f i ≠ 0) else 1) =\n if h : 0 < n t... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
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Mathlib/Topology/Separation.lean | disjoint_nhds_pure | [] | [
528,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_ne_zero | [] | [
204,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indep_iff_forall_indepSet | [] | [
642,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.sub_one_mul_conj | [] | [
84,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
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] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.sub_apply | [] | [
493,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
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] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | summable_iff_vanishing_norm | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type ?u.2223\nE : Type u_1\nF : Type ?u.2229\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : CompleteSpace E\nf : ι → E\n⊢ Summable f ↔ ∀ (ε : ℝ), ε > 0 → ∃ s, ∀ (t : Finset ι), Disjoint t s → ‖∑ i in t, f i‖ < ε"... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.hasBasis_nhds | [] | [
340,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
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Mathlib/Data/Set/NAry.lean | Set.image2_image_right | [
{
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297,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
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Mathlib/Data/List/Rdrop.lean | List.rdropWhile_concat_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\nh : ¬p x = true\n⊢ rdropWhile p (l ++ [x]) = l ++ [x]",
"tactic": "rw [rdropWhile_concat, if_neg h]"
}
] | [
120,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
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Mathlib/Data/Seq/Computation.lean | Computation.liftRel_think_left | [] | [
1205,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
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Std/Data/Int/DivMod.lean | Int.natAbs_dvd_natAbs | [
{
"state_after": "a b : Int\nx✝ : natAbs a ∣ natAbs b\nk : Nat\nhk : natAbs b = natAbs a * k\n⊢ a ∣ b",
"state_before": "a b : Int\n⊢ natAbs a ∣ natAbs b ↔ a ∣ b",
"tactic": "refine ⟨fun ⟨k, hk⟩ => ?_, fun ⟨k, hk⟩ => ⟨natAbs k, hk.symm ▸ natAbs_mul a k⟩⟩"
},
{
"state_after": "a b : Int\nx✝ : nat... | [
649,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
644,
9
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Mathlib/Data/Real/NNReal.lean | NNReal.inv_le_of_le_mul | [
{
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"tactic": "by_cases r = 0 <;> simp [*, inv_le]"
}
] | [
786,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_ite_eq | [
{
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116,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.extend_agrees | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR : Presieve X\nJ J₂ : GrothendieckTopology C\nx : FamilyOfElements P R\nt : FamilyOfElements.Compatible x\nf : Y ⟶ X\nhf : R f\nh : ∃ h g, R g ∧ h ≫ g = f\n⊢ FamilyOfElements.sieveExtend x f (_ : f ∈ (generate R).arr... | [
206,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.order_eq_find | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝¹¹ : CommRing 𝕜\nn : ℕ\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : Module 𝕜 E\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : TopologicalAddGroup E\ninst✝⁶ : ContinuousConstSMul 𝕜 E\ninst✝⁵ : AddCommGroup F\... | [
230,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithTop.succ_coe_top | [] | [
1059,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.eventually | [] | [
1437,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineIndependent.vectorSpan_eq_of_le_of_card_eq_finrank_add_one | [] | [
229,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.smul | [
{
"state_after": "no goals",
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"tactic": "simp_all"
}
] | [
107,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
11
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.nsmul_apply | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_iff_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a * b⁻¹ < c ↔ a < b * c",
"tactic": "rw [← inv_mul_lt_iff_lt_mul, mul_comm]"
}
] | [
560,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_prime_order | [
{
"state_after": "case refine_1\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : Nat.Prime (orderOf σ)\n⊢ ↑card (cycleType σ) = ↑card (cycleType σ) - 1 + 1\n\ncase refine_2\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ : Nat.Prime (orderOf σ)\nn : ℕ\nhn : n ∈... | [
213,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.radical_pow | [
{
"state_after": "no goals",
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"tactic": "decide"
},
{
"state_after": "R : Type u\nι : Type ?u.339982\ninst✝ : CommSemiring R\nI J K L : Ideal R\nn✝ : ℕ\nH✝¹ : n✝ > 0\nn ... | [
1020,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prod_factorization_eq_prod_factors | [
{
"state_after": "n : ℕ\nβ : Type u_1\ninst✝ : CommMonoid β\nf : ℕ → β\n⊢ ∀ (x : ℕ), x ∈ toFinset (factors n) → (fun p x => f p) x (↑(factorization n) x) = f x",
"state_before": "n : ℕ\nβ : Type u_1\ninst✝ : CommMonoid β\nf : ℕ → β\n⊢ (Finsupp.prod (factorization n) fun p x => f p) = ∏ p in toFinset (factor... | [
241,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardFactors_multiset_prod | [
{
"state_after": "R : Type ?u.554754\ns : Multiset ℕ\n⊢ Multiset.prod s ≠ 0 → ↑Ω (Multiset.prod s) = Multiset.sum (Multiset.map (↑Ω) s)",
"state_before": "R : Type ?u.554754\ns : Multiset ℕ\nh0 : Multiset.prod s ≠ 0\n⊢ ↑Ω (Multiset.prod s) = Multiset.sum (Multiset.map (↑Ω) s)",
"tactic": "revert h0"
}... | [
887,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/Finite/Basic.lean | Finite.prod_right | [] | [
81,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_singleton | [] | [
58,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegrable_iff | [
{
"state_after": "case pos\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nc : ℂ\nR : ℝ\nh₀ : R = 0\n⊢ CircleIntegrable f c R ↔ IntervalIntegrable (fun θ => deriv (circleMap c R) θ • f (circleMap c R θ)) volume 0 (2 * π)\n\ncase neg\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\... | [
288,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.one_def | [] | [
730,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | Filter.Tendsto.inv₀ | [] | [
119,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ 0 ≤ ‖x‖ / ‖x + y‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\n⊢ angle x (x + y) ≤ π / 2",
"tactic": "... | [
126,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.toFun_eq_coe | [] | [
100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_sub' | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Odd (m - n) ↔ (Odd n ↔ Even m)",
"tactic": "rw [odd_iff_not_even, even_sub, not_iff, not_iff_comm, odd_iff_not_even]"
}
] | [
193,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_insert_iff_of_not_mem | [] | [
1169,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.π'_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⊢ (cokernel.π (kernel.lift g f w) ≫ (homologyIsoCokernelLift f g w).inv) ≫\n ((homologyIsoCokernelLift f g w).hom ≫ Abelian.homologyCToK f g w) ≫ kernel.ι (cokernel.desc f g w) =\n kerne... | [
193,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_one | [
{
"state_after": "no goals",
"state_before": "⊢ factorization 1 = 0",
"tactic": "simp [factorization]"
}
] | [
127,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_nat | [] | [
427,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.lt_on_open_segment' | [
{
"state_after": "case h₁.h₁\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.484521\nα : Type ?u.484524\nβ : Type u_3\nι : Type ?u.484530\ninst✝⁶ : OrderedSemiring 𝕜\ninst✝⁵ : AddCommMonoid E\ninst✝⁴ : AddCommMonoid F\ninst✝³ : LinearOrderedAddCommMonoid β\ninst✝² : SMul 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSM... | [
675,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_positive | [
{
"state_after": "α : Type u_1\nβ : Type ?u.53280\ninst✝² : MeasurableSpace α\ns : SignedMeasure α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nu v w : Set α\nhu : MeasurableSet u\nhv : MeasurableSet v\nhsu : ∀ ⦃j : Set α⦄, MeasurableSet j → j ⊆ u → ↑0 j ≤ ↑s j\nhsv : ∀ ⦃j : Set α⦄, ... | [
317,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_preimage_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.52437\nι : Sort ?u.52440\nι' : Sort ?u.52443\nf✝ : α → β\ns✝ t✝ : Set α\nf : α → β\ns : Set α\nt : Set β\n⊢ f '' (f ⁻¹' t ∩ s) = t ∩ f '' s",
"tactic": "simp only [inter_comm, image_inter_preimage]"
}
] | [
516,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.terminatedAt_iff_part_denom_none | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ng : GeneralizedContinuedFraction α\nn : ℕ\n⊢ TerminatedAt g n ↔ Stream'.Seq.get? (partialDenominators g) n = none",
"tactic": "rw [terminatedAt_iff_s_none, part_denom_none_iff_s_none]"
}
] | [
56,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Limit.lift_π_apply | [] | [
197,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.classifier_isSheaf | [
{
"state_after": "C : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\nX : C\nS : Sieve X\nhS : S ∈ GrothendieckTopology.sieves J₁ X\n⊢ Presieve.IsSheafFor (Functor.closedSieves J₁) S.arrows",
"state_before": "C : Type u\ninst✝ : Category C\nJ₁ J₂ : GrothendieckTopology C\n⊢ Presieve.IsSheaf J₁ (... | [
247,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.conGen_mono | [] | [
539,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.maybeNormalize_eq_normalize | [
{
"state_after": "num : Int\nden g : Nat\nden_nz : den / g ≠ 0\nreduced : Nat.coprime (Int.natAbs (Int.div num ↑g)) (den / g)\nhn : ↑g ∣ num\nhd : g ∣ den\n⊢ normalize (num / ↑g) (den / g) = normalize num den",
"state_before": "num : Int\nden g : Nat\nden_nz : den / g ≠ 0\nreduced : Nat.coprime (Int.natAbs ... | [
66,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
60,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.coe_inf | [] | [
527,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.IsColimit.π_desc | [] | [
437,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Topology/Basic.lean | mem_closure_iff_nhds_basis' | [
{
"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\np : ι → Prop\ns : ι → Set α\nh : HasBasis (𝓝 a) p s\nt : Set α\n⊢ (∀ ⦃i : ι⦄, p i → ∀ ⦃j : Unit⦄, True → Set.Nonempty (s i ∩ t)) ↔ ∀ (i : ι)... | [
1349,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_lt | [] | [
242,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
236,
1
] |
Mathlib/Data/Complex/Module.lean | finrank_real_of_complex | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℂ E\n⊢ FiniteDimensional.finrank ℝ E = 2 * FiniteDimensional.finrank ℂ E",
"tactic": "rw [← FiniteDimensional.finrank_mul_finrank ℝ ℂ E, Complex.finrank_real_complex]"
}
] | [
245,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Std/Data/List/Lemmas.lean | List.diff_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ : List α\na : α\n⊢ List.erase (List.diff l₁ l₂) a = List.diff (List.erase l₁ a) l₂",
"tactic": "rw [← diff_cons_right, diff_cons]"
}
] | [
1501,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1500,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_insert | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.7176\nα : Type u_1\nβ : Type ?u.7182\nγ : Type ?u.7185\ninst✝ : InvolutiveInv α\ns✝ t : Set α\na✝ a : α\ns : Set α\n⊢ (insert a s)⁻¹ = insert a⁻¹ s⁻¹",
"tactic": "rw [insert_eq, union_inv, inv_singleton, insert_eq]"
}
] | [
286,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_X | [] | [
703,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/LinearAlgebra/AffineSpace/MidpointZero.lean | homothety_one_half | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Field k\ninst✝³ : CharZero k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AddTorsor V P\na b : P\n⊢ ↑(homothety a (1 / 2)) b = midpoint k a b",
"tactic": "rw [one_div, homothety_inv_two]"
}
] | [
50,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.zero_not_mem_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA : Type v\ninst✝² : CommSemiring R\ninst✝¹ : Ring A\ninst✝ : Algebra R A\na : A\n⊢ ¬0 ∈ σ a ↔ IsUnit a",
"tactic": "rw [zero_mem_iff, Classical.not_not]"
}
] | [
124,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Order/Basic.lean | csInf_mem_closure | [] | [
2780,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2779,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_lt | [] | [
73,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | left_eq_mul₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.12127\nM₀ : Type u_1\nG₀ : Type ?u.12133\nM₀' : Type ?u.12136\nG₀' : Type ?u.12139\nF : Type ?u.12142\nF' : Type ?u.12145\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\nha : a ≠ 0\n⊢ a = a * b ↔ b = 1",
"tactic": "rw [eq_comm, mul_eq_left₀ ha]"
... | [
212,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.mul_neg | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.74049\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\na b : R\n⊢ a * -b = -(a * b)",
"tactic": "simp"
}
] | [
112,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.of_mul_of | [] | [
218,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_of_re_nonneg | [] | [
277,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Ico_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Ico ↑a ⊤ = Ici a",
"tactic": "simp [← Ici_inter_Iio]"
}
] | [
82,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.length_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12605\ns✝ t : Finset α\nf : α → β\nn : ℕ\ns : Finset α\n⊢ List.length (toList s) = card s",
"tactic": "rw [toList, ← Multiset.coe_card, Multiset.coe_toList, card_def]"
}
] | [
216,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
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