file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.coe_copy | [] | [
710,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.sup_apply | [] | [
113,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.le_mabs | [] | [
186,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Polynomial/Inductions.lean | Polynomial.divX_eq_zero_iff | [
{
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"tactic": "simpa [eq_comm, h] using divX_mul_X_add p"
},
{
"state_after": "no goals",
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64,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/GroupTheory/OrderOfElement.lean | pow_eq_mod_orderOf | [
{
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"tactic": "rw [Nat.mod_add_div]"
},
{
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235,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/GroupTheory/Congruence.lean | Con.kerLift_range_eq | [] | [
1041,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
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Mathlib/Data/PNat/Interval.lean | PNat.card_Ico | [
{
"state_after": "a b : ℕ+\n⊢ card (Ico a b) = card (Ico ↑a ↑b)",
"state_before": "a b : ℕ+\n⊢ card (Ico a b) = ↑b - ↑a",
"tactic": "rw [← Nat.card_Ico]"
},
{
"state_after": "a b : ℕ+\n⊢ card (Ico a b) = card (map (Function.Embedding.subtype fun n => 0 < n) (Ico a b))",
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76,
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72,
1
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Mathlib/Topology/Sequences.lean | IsSeqClosed.seqClosure_eq | [] | [
103,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/MeasureTheory/Measure/Stieltjes.lean | iSup_eq_iSup_subseq_of_antitone | [] | [
119,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_right_of_le | [] | [
801,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
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Mathlib/Data/Fintype/Basic.lean | Finset.mem_univ | [] | [
76,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_eq_zero_iff | [
{
"state_after": "x : ℝ≥0\ny : ℝ\n⊢ ↑x ^ y = ↑0 ↔ ↑x = 0 ∧ y ≠ 0",
"state_before": "x : ℝ≥0\ny : ℝ\n⊢ x ^ y = 0 ↔ x = 0 ∧ y ≠ 0",
"tactic": "rw [← NNReal.coe_eq, coe_rpow, ← NNReal.coe_eq_zero]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ≥0\ny : ℝ\n⊢ ↑x ^ y = ↑0 ↔ ↑x = 0 ∧ y ≠ 0",... | [
62,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.hom_inv_id_apply | [] | [
85,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_mul_le_sum_mul_comp_perm | [] | [
503,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.smul | [
{
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1143,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
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Mathlib/Init/Data/Int/Basic.lean | Int.natAbs_add_neg | [
{
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"tactic": "simp [Nat.succ_add, Nat.add_succ]"
}
] | [
144,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
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Mathlib/Topology/LocalAtTarget.lean | Set.restrictPreimage_inducing | [
{
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"state_... | [
38,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
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Mathlib/Data/Finset/Sort.lean | Finset.sorted_zero_eq_min'_aux | [
{
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104,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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Mathlib/Data/String/Basic.lean | String.lt_iff_toList_lt | [
{
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106,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_eq_of_le | [] | [
590,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
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] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLen_le_powerset | [
{
"state_after": "α : Type u_1\nn : ℕ\ns : Multiset α\nl : List α\n⊢ List.map ofList (sublistsLen n l) <+~ List.map ofList (sublists' l)",
"state_before": "α : Type u_1\nn : ℕ\ns : Multiset α\nl : List α\n⊢ powersetLen n (Quotient.mk (isSetoid α) l) ≤ powerset (Quotient.mk (isSetoid α) l)",
"tactic": "s... | [
274,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_coord_zero | [
{
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184,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
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Std/Data/Option/Lemmas.lean | Option.bind_comm | [
{
"state_after": "no goals",
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"tactic": "cases a <;> cases b <;> rfl"
}
] | [
102,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
1
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.comp_assoc | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.lowerBound?_exists | [
{
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"state_before": "α : Type u_1\ncmp : α → α → Ordering\ncut : α → Ordering\nt : ... | [
269,
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256,
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] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideCoequalizer.cotrident_π | [] | [
700,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
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Mathlib/Data/Nat/Choose/Multinomial.lean | Finset.sum_pow | [
{
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"state_before": "α : Type u_2\ninst✝¹ : DecidableEq ... | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.extend_pi | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : PseudoMetricSpace α\ninst✝ : Fintype ι\nf : α → ι → ℝ\ns : Set α\nK : ℝ≥0\nhf : LipschitzOnWith K f s\nthis : ∀ (i : ι), ∃ g, LipschitzWith K g ∧ EqOn (fun x => f x i) g s\n⊢ ∃ g, LipschitzWith K g ∧ EqOn f g s",
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687,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter | [] | [
68,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.IsProj.isCompl | [
{
"state_after": "R : Type u_1\ninst✝⁹ : Ring R\nE : Type u_2\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.446187\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.446703\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.447666\ninst✝² : Semiring S\nM : Type ... | [
430,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Algebra/Lie/OfAssociative.lean | LieRing.lie_apply | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.model_infiniteTheory_iff | [
{
"state_after": "no goals",
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"tactic": "simp [infi... | [
1059,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_add_measure_left | [] | [
675,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_mono_right | [] | [
772,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.toFun_eq_coe | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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] |
Mathlib/Data/Fin/Interval.lean | Fin.Iic_eq_finset_subtype | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_monoidHom | [
{
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1090,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
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Mathlib/Data/Nat/Basic.lean | Nat.two_lt_of_ne | [
{
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"tactic": "rw [Nat.lt_iff_add_one_le]"
},
{
"state_after": "no goals",
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257,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
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Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.tensor_id | [
{
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267,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.mulHead_head | [
{
"state_after": "case singleton\nι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.617310\ninst✝ : Monoid N\ni j i✝ : ι\nx✝ : M i✝\na✝ : x✝ ≠ 1\nx : M i✝\nhnotone : x * head (singleton x✝ a✝) ≠ 1\n⊢ head (mulHead (singleton x✝ a✝) x hnotone) = x * head (singleton x✝ a✝)\n\ncase appen... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_add | [] | [
224,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_fderivWithin | [
{
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469,
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Mathlib/Data/Set/Function.lean | Set.InjOn.congr | [] | [
621,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
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] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.transvection_mul_apply_same | [
{
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Mathlib/Analysis/Complex/RealDeriv.lean | DifferentiableAt.conformalAt | [
{
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169,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/Group/WithOne/Basic.lean | MulEquiv.withOneCongr_trans | [] | [
164,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_inter | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.399939\nγ : Type ?u.399942\ninst✝ : DecidableEq α\ns t : List α\n⊢ ↑s ∩ ↑t = ↑(List.b... | [
2517,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2517,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_casesOn₁ | [] | [
603,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.isBigO_sub_exp_rpow | [
{
"state_after": "E : Type u_1\ninst✝ : NormedAddCommGroup E\na : ℝ\nf g : ℂ → E\nl : Filter ℂ\nhBf : ∃ c, c < a ∧ ∃ B, f =O[comap (↑Complex.abs) atTop ⊓ l] fun z => expR (B * ↑Complex.abs z ^ c)\nhBg : ∃ c, c < a ∧ ∃ B, g =O[comap (↑Complex.abs) atTop ⊓ l] fun z => expR (B * ↑Complex.abs z ^ c)\nthis :\n ∀ {c... | [
104,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.smul_def | [] | [
644,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_singleton | [] | [
1811,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1809,
9
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_add_zero | [
{
"state_after": "a : Ordinal\n⊢ (sup fun n => ((fun x => a + x)^[n]) 0) = sup fun n => a * ↑n",
"state_before": "a : Ordinal\n⊢ nfp (fun x => a + x) 0 = a * ω",
"tactic": "simp_rw [← sup_iterate_eq_nfp, ← sup_mul_nat]"
},
{
"state_after": "case e_f\na : Ordinal\n⊢ (fun n => ((fun x => a + x)^[n... | [
574,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.cast_eq_cast | [
{
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"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R... | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Std/Logic.lean | Decidable.not_and_not_right | [] | [
597,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
596,
1
] |
Mathlib/Order/BoundedOrder.lean | eq_bot_of_minimal | [] | [
394,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.SemiconjBy.zpow_right | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA X Y : M\nhx : IsUnit (det X)\nhy : IsUnit (det Y)\nh : SemiconjBy A X Y\nn : ℕ\n⊢ SemiconjBy A (X ^ ↑n) (Y ^ ↑n)",
"tactic": "simp [h.pow_right n]"
},
{
... | [
213,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ioc_bot_coe | [] | [
1172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.toList_node | [
{
"state_after": "α : Type u_1\nc : RBColor\na : RBNode α\nx : α\nb : RBNode α\n⊢ toList a ++ x :: foldr (fun x x_1 => x :: x_1) b [] = toList a ++ x :: toList b",
"state_before": "α : Type u_1\nc : RBColor\na : RBNode α\nx : α\nb : RBNode α\n⊢ toList (node c a x b) = toList a ++ x :: toList b",
"tactic... | [
338,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
337,
9
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.pi_lift_π_apply | [] | [
57,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/List/Basic.lean | List.map_pmap | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.326579\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\ng : β → γ\nf : (a : α) → p a → β\nl : List α\nH : ∀ (a : α), a ∈ l → p a\n⊢ map g (pmap f l H) = pmap (fun a h => g (f a h)) l H",
"tactic": "induction l <;> [r... | [
3102,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3100,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_image' | [] | [
655,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.update_apply | [
{
"state_after": "α : Sort u\nβ✝ : α → Sort v\nα' : Sort w\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq α'\nf✝ g : (a : α) → β✝ a\na✝ : α\nb✝ : β✝ a✝\nβ : Sort u_1\nf : α → β\na' : α\nb : β\na : α\nh2 : ∀ (h : a = a'), (_ : a' = a) ▸ b = b\n⊢ update f a' b a = if a = a' then b else f a",
"state_before": "α ... | [
558,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.mono | [] | [
793,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.comap_comap | [
{
"state_after": "no goals",
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272,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_pi | [
{
"state_after": "case intro.intro.intro\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x z : V\nleft✝ : x ≠ 0\nr : ℝ\nhr : r < 0\nh : angle x (r • x) = π\n⊢ angle x z + angle (r • x) z = π",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProduc... | [
229,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Logic/Basic.lean | Ne.ite_ne_left_iff | [] | [
1201,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
11
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\ni : σ\nf g : MvPolynomial σ R\n⊢ ↑(pderiv i) (f * g) = ↑(pderiv i) f * g + f * ↑(pderiv i) g",
"tactic": "simp only [(pderiv i).leibniz f g, smul_eq_mul, mul_comm, add_comm]"
}
] | [
122,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_zero_apply | [] | [
1513,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1511,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | Pi.basisFun_repr | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nη : Type u_2\nιs : η → Type ?u.157855\nMs : η → Type ?u.157860\ninst✝³ : Semiring R\ninst✝² : (i : η) → AddCommMonoid (Ms i)\ninst✝¹ : (i : η) → Module R (Ms i)\ninst✝ : Fintype η\nx : η → R\ni : η\n⊢ ↑(↑(basisFun R η).repr x) i = x i",
"tactic... | [
289,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.deriv_cos | [] | [
623,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | HasCompactMulSupport.is_one_at_infty | [
{
"state_after": "α : Type u_2\nβ : Type ?u.45460\nγ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\nf : α → γ\ninst✝¹ : TopologicalSpace γ\ninst✝ : One γ\nh : HasCompactMulSupport f\nN : Set γ\nhN : N ∈ 𝓝 1\n⊢ N ∈ map f (cocompact α)",
"state_before": "α : Type u_2\nβ : Type ?u.45460\nγ : Ty... | [
235,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Order/Lattice.lean | Pi.inf_apply | [] | [
1021,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.smul | [
{
"state_after": "case inl\n𝕜 : Type u_1\n𝕝 : Type u_3\nE : Type u_2\nF : Type ?u.99037\nβ : Type ?u.99040\ninst✝¹⁰ : OrderedSemiring 𝕜\ninst✝⁹ : TopologicalSpace E\ninst✝⁸ : TopologicalSpace F\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : Module 𝕜 F\ninst✝³ : LinearOrder... | [
286,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.ext | [] | [
189,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ici_basis | [] | [
1122,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.toEquiv_mulRight₀ | [] | [
220,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.nonneg_smul_right | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁵ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nN : Type ?u.26709\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nι : Type ?u.26791\ninst✝ : DecidableEq ι\nx y z : M\nr : R\nh : SameRay R x y\nhr :... | [
136,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDeriv_const_smul_apply | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁷ : No... | [
1578,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1575,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | le_of_mul_le_of_one_le | [] | [
985,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioo_mem_nhdsWithin_Iio' | [] | [
465,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/List/Join.lean | List.drop_take_succ_eq_cons_nthLe | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.8051\nL : List α\ni✝ : ℕ\nhi✝ : i✝ < length L\ni : ℕ\nhi : i < length []\n⊢ drop i (take (i + 1) []) = [nthLe [] i hi]\n\ncase cons\nα : Type u_1\nβ : Type ?u.8051\nL : List α\ni✝ : ℕ\nhi✝ : i✝ < length L\nhead : α\ntail : List α\ntail_ih✝ : ∀ {i : ℕ} (hi : ... | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.integral_cos_pow_pos | [] | [
210,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_pi_sub | [] | [
1224,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf'_biUnion | [] | [
956,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Multiset/Interval.lean | Multiset.Icc_eq | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/MeasureTheory/Covering/DensityTheorem.lean | IsUnifLocDoublingMeasure.ae_tendsto_average | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\ninst✝⁸ : MetricSpace α\ninst✝⁷ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝⁶ : IsUnifLocDoublingMeasure μ\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : BorelSpace α\ninst✝³ : IsLocallyFiniteMeasure μ\nE : Type u_1\ninst✝² : NormedAddComm... | [
175,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.eq_zero_iff_forall_not_mem | [] | [
270,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/Rat/NNRat.lean | Rat.lt_toNNRat_iff_coe_lt | [] | [
404,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.comp_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ comp p 1 = ↑C (eval 1 p)",
"tactic": "rw [← C_1, comp_C]"
}
] | [
572,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.iso_comp_eq_snd | [
{
"state_after": "no goals",
"state_before": "𝒜 : Type u_2\ninst✝² : Category 𝒜\nA B C A' B' C' : 𝒜\nf : A ⟶ B\ng : B ⟶ C\nf' : A' ⟶ B'\ng' : B' ⟶ C'\ninst✝¹ : HasZeroMorphisms 𝒜\ninst✝ : HasBinaryBiproducts 𝒜\nh : Splitting f g\n⊢ h.iso.inv ≫ g = biprod.snd",
"tactic": "rw [Iso.inv_comp_eq, h.iso_... | [
199,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.map_equiv_top | [] | [
724,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Order/Antichain.lean | isAntichain_singleton | [] | [
209,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.mem_range_embedding_iff | [
{
"state_after": "case mp\nn : ℕ\nc : Composition n\nj : Fin n\ni : Fin (length c)\n⊢ j ∈ Set.range ↑(embedding c i) → sizeUpTo c ↑i ≤ ↑j ∧ ↑j < sizeUpTo c (Nat.succ ↑i)\n\ncase mpr\nn : ℕ\nc : Composition n\nj : Fin n\ni : Fin (length c)\n⊢ sizeUpTo c ↑i ≤ ↑j ∧ ↑j < sizeUpTo c (Nat.succ ↑i) → j ∈ Set.range ↑(e... | [
394,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_Ioc | [] | [
201,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | Part.mem_ωSup | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.16890\nx : α\nc : Chain (Part α)\n⊢ (x ∈ if h : ∃ a, some a ∈ c then some (choose h) else none) ↔ some x ∈ c",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.16890\nx : α\nc : Chain (Part α)\n⊢ x ∈ ωSup c ↔ some x ∈ c",
"tactic": "simp [OmegaCo... | [
389,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.lt_ord_succ_card | [] | [
1398,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.whiskerLeft_rightUnitor_inv | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\n⊢ inv (f ◁ (ρ_ g).inv) = inv ((ρ_ (f ≫ g)).inv ≫ (α_ f g (𝟙 c)).hom)",
"tactic": "simp"
}
] | [
452,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reverse_neg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\nf : R[X]\n⊢ reverse (-f) = -reverse f",
"tactic": "rw [reverse, reverse, reflect_neg, natDegree_neg]"
}
] | [
383,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.MeasurePreserving.integrable_comp | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.935096\nδ : Type u_1\nm : MeasurableSpace α\nμ ν✝ : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nν : Measure δ\ng : δ → β\nf : α → δ\nhf : MeasurePreserving f\nhg : AEStronglyMeasurable g (Measure.ma... | [
629,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.differentiable_arctan | [] | [
102,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
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