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/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.trans_wOppSide | [] | [
569,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
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Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_zmodeq' | [
{
"state_after": "case nil\nn : ℕ\nb b' : ℤ\nk : ℕ\nh : b ≡ b' [ZMOD ↑k]\n⊢ ofDigits b [] ≡ ofDigits b' [] [ZMOD ↑k]\n\ncase cons\nn : ℕ\nb b' : ℤ\nk : ℕ\nh : b ≡ b' [ZMOD ↑k]\nd : ℕ\nL : List ℕ\nih : ofDigits b L ≡ ofDigits b' L [ZMOD ↑k]\n⊢ ofDigits b (d :: L) ≡ ofDigits b' (d :: L) [ZMOD ↑k]",
"state_bef... | [
530,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_toNat | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\n_h : 0 ≤ ↑n\n⊢ ↑(Int.toNat ↑n) = ↑↑n",
"tactic": "simp only [Int.cast_ofNat, Int.toNat_coe_nat]"
},
{
"state_after": "no goals",
"state_before": "p n : ℕ\nh : 0 ≤ Int.negSucc n\n⊢ ↑(Int.toNat (Int.negSucc n)) = ↑(Int.negSucc n)",
"ta... | [
576,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
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Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | uniformCauchySeqOnFilter_of_deriv | [
{
"state_after": "ι : Type u_3\nl : Filter ι\n𝕜 : Type u_1\ninst✝² : IsROrC 𝕜\nG : Type u_2\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\nhf' : UniformCauchySeqOnFilter f' l (𝓝 x)\nhfg : Cauchy (map (fun n => f n x) l)\nhf : ∀ᶠ (n ... | [
488,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
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Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.div_pf | [] | [
50,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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Mathlib/Order/Bounds/Basic.lean | isLeast_union_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t✝ : Set α\na✝ b a : α\ns t : Set α\n⊢ IsLeast (s ∪ t) a ↔ IsLeast s a ∧ a ∈ lowerBounds t ∨ a ∈ lowerBounds s ∧ IsLeast t a",
"tactic": "simp [IsLeast, lowerBounds_u... | [
384,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_le | [] | [
700,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
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Mathlib/Order/Bounds/Basic.lean | bddAbove_Ioc | [] | [
672,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.comp | [
{
"state_after": "ι : Type u_2\nι' : Type u_1\nR : Type u_3\nK : Type ?u.166980\nA : Type u_4\nA' : Type ?u.166986\nA'' : Type ?u.166989\nV : Type u\nV' : Type ?u.166994\nx : ι → A\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing A'\ninst✝³ : CommRing A''\ninst✝² : Algebra R A\ninst✝¹ : Algebra R A'... | [
138,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
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Mathlib/LinearAlgebra/Contraction.lean | contractLeft_apply | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augmentTruncate_hom_f_succ | [] | [
371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.coe_splitLower | [
{
"state_after": "ι : Type u_1\nM : Type ?u.775\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ (Set.pi univ fun i_1 => Ioc (lower I i_1) (update I.upper i (min x (upper I i)) i_1)) = ↑I ∩ {y | y i ≤ x}",
"state_before": "ι : Type u_1\nM : Type ?u.775\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ ↑(splitLower... | [
72,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_comp_app | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nX Y : SimplicialObject C\ns : Splitting X\nf : X ⟶ Y\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\n⊢ ι s (len A.fst.unop) ≫ X.map (IndexSet.e A).op ≫ f.app Δ =\n ι s (len A.fst.unop) ≫ f.app [len A.fst.unop].op ≫ Y.map (IndexSet.e ... | [
298,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arctan_one | [
{
"state_after": "no goals",
"state_before": "⊢ π / 4 ∈ Ioo (-(π / 2)) (π / 2)",
"tactic": "constructor <;> linarith [pi_pos]"
}
] | [
185,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/List/Zip.lean | List.zip_nil_left | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Init/Algebra/Order.lean | lt_iff_le_not_le | [] | [
65,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Module/BigOperators.lean | Finset.cast_card | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.38166\nR : Type u_1\nM : Type ?u.38172\nι : Type ?u.38175\ninst✝ : CommSemiring R\ns : Finset α\n⊢ ↑(card s) = ∑ a in s, 1",
"tactic": "rw [Finset.sum_const, Nat.smul_one_eq_coe]"
}
] | [
55,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.map_sub | [
{
"state_after": "no goals",
"state_before": "n m k : ℕ\nh₁ : k ≤ n\n⊢ map (fun x => x - k) (Ico n m) = Ico (n - k) (m - k)",
"tactic": "rw [Ico, Ico, tsub_tsub_tsub_cancel_right h₁, map_sub_range' _ _ _ h₁]"
}
] | [
85,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_iSup | [] | [
519,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.constr_apply_fintype | [
{
"state_after": "no goals",
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996,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
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Mathlib/Data/Finset/Sups.lean | Finset.sups_eq_empty | [] | [
146,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
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Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_star_add_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.15141\ninst✝¹ : AddCommMonoid R\ninst✝ : StarAddMonoid R\nx : R\n⊢ IsSelfAdjoint (star x + x)",
"tactic": "simp only [isSelfAdjoint_iff, add_comm, star_add, star_star]"
}
] | [
150,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_mul_deriv_eq_deriv_mul | [
{
"state_after": "ι : Type ?u.1886564\n𝕜 : Type ?u.1886567\nE : Type ?u.1886570\nF : Type ?u.1886573\nA : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedSpace ℝ E\nf✝ : ℝ → E\ng' g φ : ℝ → ℝ\nf f' : ℝ → E\ninst✝² : NormedRing A\ninst✝¹ : NormedAlgebra ℝ A\ninst✝ : CompleteSpa... | [
1337,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.biUnion | [] | [
769,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | MulOpposite.nndist_op | [] | [
1672,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1672,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.one_smul' | [
{
"state_after": "case h\nR : Type u_2\nM : Type u_1\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : ArithmeticFunction M\nx : ℕ\n⊢ ↑(1 • b) x = ↑b x",
"state_before": "R : Type u_2\nM : Type u_1\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nb : ArithmeticFuncti... | [
356,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.not_mem_of_not_mem_closure | [] | [
485,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Subalgebra.finrank_eq_one_iff | [] | [
1416,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.exists_eq_pow_mul_and_not_dvd | [
{
"state_after": "case intro\nα : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nhfin : Finite a b\nc : α\nhc : b = a ^ Part.get (multiplicity a b) hfin * c\n⊢ ∃ c, b = a ^ Part.get (multiplicity a b) hfin * c ∧ ¬a ∣ c",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\nins... | [
232,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_sum | [
{
"state_after": "α✝ : Type ?u.289176\nβ✝ : Type ?u.289179\nγ : Type ?u.289182\nr : α✝ → α✝ → Prop\ns : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα : Type u\nβ : Type v\nf : α ⊕ β → Ordinal\n⊢ ∀ (i : α ⊕ β), f i ≤ max (sup fun a => f (Sum.inl a)) (sup fun b => f (Sum.inr b))\n\nα✝ : Type ?u.289176\nβ✝ : Type ?u.289179\... | [
1347,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
1
] |
Mathlib/Order/Synonym.lean | OrderDual.toDual_le | [] | [
121,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_X_one | [] | [
691,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/Data/Finset/Basic.lean | List.perm_of_nodup_nodup_toFinset_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.469969\nγ : Type ?u.469972\ninst✝ : DecidableEq α\nl l' : List α\na : α\nhl : Nodup l\nhl' : Nodup l'\nh : toFinset l = toFinset l'\n⊢ ↑l = ↑l'",
"state_before": "α : Type u_1\nβ : Type ?u.469969\nγ : Type ?u.469972\ninst✝ : DecidableEq α\nl l' : List α\na : α\nhl... | [
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45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3296,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.nonempty_Iio | [] | [
306,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.fin_curry | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.371824\nγ : Type ?u.371827\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nn : ℕ\nf : α → Fin n → σ\nh : Primrec₂ f\na : α\ni : Fin n\n⊢ Vector.get (Vector.ofFn fun i => f a i) i = f a i",
"stat... | [
1349,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiff.rpow_const_of_le | [] | [
557,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.op_mul | [] | [
285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.differentiable_set_eq_d | [] | [
737,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.eq_of_mem_of_not_mem_erase | [
{
"state_after": "α : Type u_1\nβ : Type ?u.208349\nγ : Type ?u.208352\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\nhs : b ∈ s\nhsa : b ≠ a → ¬b ∈ s\n⊢ b = a",
"state_before": "α : Type u_1\nβ : Type ?u.208349\nγ : Type ?u.208352\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\nhs : b ∈ s\nhsa :... | [
1893,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finmap.lean | Finmap.induction_on₃ | [] | [
158,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.ext_iff | [] | [
841,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_uIcc | [] | [
205,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_pow_abs_sub_uIoc | [
{
"state_after": "case inl\na b : ℝ\nn : ℕ\nhab : a ≤ b\n⊢ (∫ (x : ℝ) in Ι a b, abs (x - a) ^ n) = abs (b - a) ^ (n + 1) / (↑n + 1)\n\ncase inr\na b : ℝ\nn : ℕ\nhab : b < a\n⊢ (∫ (x : ℝ) in Ι a b, abs (x - a) ^ n) = abs (b - a) ^ (n + 1) / (↑n + 1)",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in Ι a b, a... | [
407,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
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Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.continuous | [] | [
364,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
11
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.mul_comp | [] | [
631,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.zero_mem_smul_set_iff | [
{
"state_after": "F : Type ?u.94503\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.94512\ninst✝³ : Zero α\ninst✝² : Zero β\ninst✝¹ : SMulWithZero α β\ns : Set α\nt : Set β\ninst✝ : NoZeroSMulDivisors α β\na : α\nha : a ≠ 0\n⊢ 0 ∈ a • t → 0 ∈ t",
"state_before": "F : Type ?u.94503\nα : Type u_1\nβ : Type u_2\nγ : ... | [
843,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_add_le | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
383,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ici_erase | [
{
"state_after": "case a\nι : Type ?u.113545\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrderTop α\ninst✝ : DecidableEq α\na a✝ : α\n⊢ a✝ ∈ erase (Ici a) a ↔ a✝ ∈ Ioi a",
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682,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
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Std/Data/List/Lemmas.lean | List.sublist_append_left | [] | [
346,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
344,
9
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Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.refl_inv | [] | [
152,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Data/Part.lean | Part.mem_restrict | [
{
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650,
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645,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_finset_sum | [
{
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589,
21
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585,
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Mathlib/Analysis/Calculus/TangentCone.lean | UniqueDiffWithinAt.mono | [] | [
290,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.smul_mem_pointwise_smul_iff₀ | [] | [
314,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_comp | [
{
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230,
17
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228,
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Mathlib/Data/Int/Basic.lean | zpow_coe_nat | [] | [
84,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_of_ne | [
{
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658,
38
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657,
1
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Std/Data/List/Lemmas.lean | List.getLastD_concat | [
{
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"state_before": "α : Type u_1\na b : α\nl : List α\n⊢ getLastD (l ++ [b]) a = b",
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},
{
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643,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
642,
9
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Std/Data/Int/DivMod.lean | Int.div_nonpos | [] | [
105,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
104,
11
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.singleton_mul | [] | [
405,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Differentiable.rpow_const | [] | [
483,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_injective | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.85918\nγ : Type ?u.85921\ninst✝¹ : MeasurableSpace α... | [
303,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
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Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_of_not_mem_incidenceSet | [
{
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"tactic": "rw [incMatrix_apply, Set.indicator_of_not_mem h]"
}
] | [
95,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.card_support_eq_two | [
{
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372,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_eq_self | [] | [
152,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
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Mathlib/Topology/Separation.lean | Ultrafilter.lim_eq_iff_le_nhds | [] | [
1042,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_embDomain_subset | [
{
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307,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
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Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.nat_mul_iff | [
{
"state_after": "no goals",
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"tactic": "rw [mul_comm, mul_nat_iff hn]"
}
] | [
177,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.eq_of_algebraMap_eq | [
{
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144,
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137,
1
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Ioc | [] | [
143,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.iUnion_split | [
{
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"tactic": "simp [split, ← inter_union_distrib_left, ← setOf_or, le_or_lt]"
}
] | [
189,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
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Mathlib/Algebra/Order/Hom/Basic.lean | map_div_le_add | [
{
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248,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Std/Data/Int/DivMod.lean | Int.fmod_lt_of_pos | [] | [
390,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
389,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_mul | [
{
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"tactic": "classical\nrefine' Finset.sup_le fun b hb => _\nhave := s... | [
169,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_centralizer_iff | [] | [
532,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.uncurry_bicompl | [] | [
840,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Basis.toBasis_toOrthonormalBasis | [
{
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514,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
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Mathlib/Data/List/Chain.lean | List.chain_map_of_chain | [] | [
97,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.biSup_measure_Iic | [
{
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2962,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2955,
1
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Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly₂.map | [
{
"state_after": "case mk'.intro\np : ℕ\nR S : Type u\nσ : Type ?u.1105645\nidx : Type ?u.1105648\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\nf : ⦃R : Type u⦄ → [inst : CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\ng : R →+* S\nx y : 𝕎 R\nφ : ℕ → MvPolynomial (Fin 2 × ℕ) ℤ\nhf : ∀ ⦃R : Type u⦄ [... | [
631,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | IsLinearMap.isLinearMap_neg | [] | [
718,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | memℓp_gen_iff | [
{
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108,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.one_eq_bit1 | [
{
"state_after": "n : ℕ\n⊢ 1 = bit1 0",
"state_before": "n✝ n : ℕ\nh : n = 0\n⊢ 1 = bit1 n",
"tactic": "subst h"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 1 = bit1 0",
"tactic": "rfl"
}
] | [
89,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.not_limZero_of_pos | [] | [
670,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | AlgHom.map_det | [] | [
342,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : HasPullback f g\n⊢ (pullbackSymmetry f g).hom ≫ pullback.fst = pullback.snd",
"tactic": "simp [pullbackSymmetry]"
}
] | [
1524,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_insert_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.94215\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidableEq α\nh : a < b\n⊢ insert a (Ioo a b) = Ico a b",
"tactic": "rw [← coe_inj, coe_insert, coe_Ioo, coe_Ico, Set.insert_eq, Set.union_comm, Set.... | [
576,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Algebra/Order/Invertible.lean | invOf_nonpos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedSemiring α\na : α\ninst✝ : Invertible a\n⊢ ⅟a ≤ 0 ↔ a ≤ 0",
"tactic": "simp only [← not_lt, invOf_pos]"
}
] | [
28,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff_not_isMin | [] | [
622,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | isDedekindDomain_iff_isDedekindDomainInv | [] | [
595,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_inf | [] | [
166,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.to_ringEquiv_symm | [] | [
869,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/CategoryTheory/Types.lean | equivEquivIso_inv | [] | [
417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_pos_iff_support_of_nonneg | [] | [
1248,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.list_casesOn | [] | [
1021,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Faces.lean | AlgebraicTopology.DoldKan.HigherFacesVanish.of_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nY Z : C\nq n : ℕ\nφ : Y ⟶ X.obj [n + 1].op\nv : HigherFacesVanish q φ\nf : Z ⟶ Y\nj : Fin (n + 1)\nhj : n + 1 ≤ ↑j + q\n⊢ (f ≫ φ) ≫ δ X (Fin.succ j) = 0",
"tactic": "rw [assoc,... | [
67,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.inverse_graph | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\ninst✝⁶ : Ring R\nE : Type u_1\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module R E\nF : Type u_2\ninst✝³ : AddCommGroup F\ninst✝² : Module R F\nG : Type ?u.694525\ninst✝¹ : AddCommGroup G\ninst✝ : Module R G\nf : E →ₗ.[R] F\nhf : LinearMap.ker f.toFun = ⊥... | [
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48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_eq_iff_im | [] | [
433,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
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Mathlib/LinearAlgebra/Basis.lean | Basis.equiv_trans | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nι' : Type u_5\nR : Type u_2\nR₂ : Type ?u.554939\nK : Type ?u.554942\nM : Type u_6\nM' : Type u_7\nM'' : Type u_3\nV : Type u\nV' : Type ?u.554956\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid M'\ninst✝... | [
693,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.sum_eq | [
{
"state_after": "α : Type ?u.504241\nβ : Type ?u.504244\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ (2 * d + 1) ^ n - 1 = (∑ i : Fin n, d * (2 * d + 1) ^ ↑i) * 2",
"state_before": "α : Type ?u.504241\nβ : Type ?u.504244\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ ∑ i : Fin n, d * (2 * d + 1) ^ ↑i = ((2 * d + 1) ^ n - 1) / 2",
"... | [
209,
55
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206,
1
] |
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