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 |
|---|---|---|---|---|---|---|
Std/Data/List/Basic.lean | List.takeD_eq_takeDTR | [
{
"state_after": "case h.h.h.h\nα : Type u_1\nf : Nat\nn : List α\nl : α\n⊢ takeD f n l = takeDTR f n l",
"state_before": "⊢ @takeD = @takeDTR",
"tactic": "funext α f n l"
},
{
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"state_before": "case h.h.h.h\nα : Type u_1\nf : Nat\nn : List α\nl : α\n⊢ takeD f n l =... | [
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48
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607,
10
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Mathlib/Data/Set/Lattice.lean | Set.image_sInter_subset | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.185546\nι : Sort ?u.185549\nι' : Sort ?u.185552\nι₂ : Sort ?u.185555\nκ : ι → Sort ?u.185560\nκ₁ : ι → Sort ?u.185565\nκ₂ : ι → Sort ?u.185570\nκ' : ι' → Sort ?u.185575\nS : Set (Set α)\nf : α → β\n⊢ (f '' ⋂ (i : Set α) (_ : i ∈ S), i) ⊆ ⋂ (s : Set α) (_... | [
1488,
29
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1486,
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Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | ContinuousOn.clog | [] | [
272,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
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Mathlib/Data/Polynomial/Div.lean | Polynomial.degree_divByMonic_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q✝ p q : R[X]\nhp0 : p = 0\n⊢ degree (p /ₘ q) ≤ degree p",
"tactic": "simp only [hp0, zero_divByMonic, le_refl]"
},
{
"state_after": "R : Type u\nS : Type v\nT : T... | [
296,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_sum_index | [] | [
2103,
44
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2097,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.prod_mono_right | [] | [
1729,
24
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1728,
1
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_add_one | [
{
"state_after": "no goals",
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"tactic": "simp only [← Nat.cast_succ, pow_succ', zpow_ofNat]"
},
{
"state_after": "no goal... | [
160,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.exists_seq_tendsto | [
{
"state_after": "case intro\nι : Type ?u.364441\nι' : Type ?u.364444\nα : Type u_1\nβ : Type ?u.364450\nγ : Type ?u.364453\nf : Filter α\ninst✝¹ : IsCountablyGenerated f\ninst✝ : NeBot f\nB : ℕ → Set α\nh : HasAntitoneBasis f B\n⊢ ∃ x, Tendsto x atTop f",
"state_before": "ι : Type ?u.364441\nι' : Type ?u.3... | [
1811,
26
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1807,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_pow_X_add_C | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\nr : R\ni : ℕ\n✝ : Nontrivial R\n⊢ leadingCoeff ((X + ↑C r) ^ i) = 1",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\nr : R\ni : ℕ\n⊢ leadingCoeff ((X + ↑C r) ^ i) = 1",
"tactic": "nont... | [
1444,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1442,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_cthickening_of_edist_le | [] | [
1034,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
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Mathlib/Data/Nat/Order/Lemmas.lean | Nat.div_lt_div_of_lt_of_dvd | [
{
"state_after": "a✝ b✝ m n k a b d : ℕ\nhdb : d ∣ b\nh : a < b\n⊢ d * (a / d) < b",
"state_before": "a✝ b✝ m n k a b d : ℕ\nhdb : d ∣ b\nh : a < b\n⊢ a / d < b / d",
"tactic": "rw [Nat.lt_div_iff_mul_lt hdb]"
},
{
"state_after": "no goals",
"state_before": "a✝ b✝ m n k a b d : ℕ\nhdb : d ∣ ... | [
258,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
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Mathlib/Data/Fintype/Card.lean | Infinite.of_injective_to_set | [
{
"state_after": "α : Type u_1\nβ : Type ?u.65760\nγ : Type ?u.65763\ns : Set α\nhs : s ≠ Set.univ\nf : α → ↑s\nhf : Injective f\nh : Fintype α\n⊢ False",
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991,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.Compatible.sieveExtend | [
{
"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\nhx : Compatible x\nY₁✝ Y₂✝ Z✝ : C\ng₁✝ : Z✝ ⟶ Y₁✝\ng₂✝ : Z✝ ⟶ Y₂✝\nf₁✝ : Y₁✝ ⟶ X\nf₂✝ : Y₂✝ ⟶ X\nh₁ : (generate R).arrows f₁✝\nh₂ : (generate R)... | [
195,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/Data/Part.lean | Part.elim_toOption | [
{
"state_after": "case inl\nα✝ : Type ?u.8538\nβ✝ : Type ?u.8541\nγ : Type ?u.8544\nα : Type u_1\nβ : Type u_2\na : Part α\ninst✝ : Decidable a.Dom\nb : β\nf : α → β\nh : a.Dom\n⊢ Option.elim (toOption a) b f = f (get a h)\n\ncase inr\nα✝ : Type ?u.8538\nβ✝ : Type ?u.8541\nγ : Type ?u.8544\nα : Type u_1\nβ : Ty... | [
321,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk_pow | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Data/Set/Ncard.lean | Set.le_ncard_diff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.126847\ns✝ t✝ : Set α\na b x y : α\nf : α → β\ns t : Set α\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard t ≤ ncard (t \\ s) + ncard s",
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520,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_add_le | [] | [
670,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Topology/Order/Basic.lean | disjoint_nhds_atBot | [] | [
1544,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
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Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean | AlgebraicTopology.DoldKan.hσ'_eq_zero | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq n m : ℕ\nhnq : n < q\nhnm : ComplexShape.Rel c m n\n⊢ (if n < q then 0 else (-1) ^ (n - q) • σ X { val := n - q, isLt := (_ : n - q < Nat.succ n) }) ≫\n eqToHom (_ : X.obj [n + 1].op = X.obj [m].op) =\n ... | [
112,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.Measure.lintegral_rnDeriv_lt_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.38581\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\ninst✝ : IsFiniteMeasure μ\n⊢ (∫⁻ (x : α) in univ, rnDeriv μ ν x ∂ν) < ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.38581\nm : MeasurableSpace α\nμ✝ ν✝ μ ν : Measure α\ninst✝ : IsFiniteMeasure μ\n⊢ (∫⁻ (x : α),... | [
210,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.add_def' | [
{
"state_after": "no goals",
"state_before": "a b : Rat\n⊢ a + b = mkRat (a.num * ↑b.den + b.num * ↑a.den) (a.den * b.den)",
"tactic": "rw [add_def, normalize_eq_mkRat]"
}
] | [
184,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
183,
1
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Mathlib/Data/Set/Sigma.lean | Set.sigma_preimage_right | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_zero_right' | [] | [
389,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.hasColimit_mapGlueData_diagram | [] | [
354,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_omega_opow_opow | [] | [
380,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Algebra/Group/Units.lean | divp_self | [] | [
443,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMaxOn.comp_mono | [] | [
253,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
8
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.left_comm | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type ?u.275396\ninst✝⁵ : CommSemiring R\ninst✝⁴ : CommSemiring S\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nx : A\nr : R\ny : A\n⊢ x * (↑(algebraMap R A) r * y) = ↑(algebraMap R A... | [
374,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_mk | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.53063\nι : Type ?u.53066\nα : Type u_1\nβ : Type ?u.53072\ninst✝¹ : DivisionRing α\ninst✝ : CharZero α\na b : ℤ\n⊢ ↑(a /. b) = ↑a / ↑b",
"tactic": "simp only [divInt_eq_div, cast_div, cast_coe_int]"
}
] | [
285,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.trans_refl | [
{
"state_after": "case w\nC : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\n⊢ (α ≪≫ refl Y).hom = α.hom",
"state_before": "C : Type u\ninst✝ : Category C\nX Y Z : C\nα : X ≅ Y\n⊢ α ≪≫ refl Y = α",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case w\nC : Type u\ninst✝ ... | [
198,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.isConnected_setOf_wOppSide | [
{
"state_after": "case intro\nR : Type ?u.487918\nV : Type u_1\nV' : Type ?u.487924\nP : Type u_2\nP' : Type ?u.487930\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : NormedSpace ℝ V\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor V P\ns : AffineSubspace ℝ P\nx p : P\nhp : p ∈ ↑s\n⊢ IsConnected {y | WOppSid... | [
917,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
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] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.sign_of_cycleType' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\n⊢ ↑sign σ = prod (map (fun n => -(-1) ^ n) (cycleType σ))",
"tactic": "induction σ using cycle_induction_on with\n| base_one => simp\n| base_cycles σ hσ => simp [hσ.cycleType, hσ.sign]\n| i... | [
161,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_lt_tan_of_nonneg_of_lt_pi_div_two | [
{
"state_after": "x y : ℝ\nhx₁ : 0 ≤ x\nhy₂ : y < π / 2\nhxy : x < y\n⊢ sin x / cos x < sin y / cos y",
"state_before": "x y : ℝ\nhx₁ : 0 ≤ x\nhy₂ : y < π / 2\nhxy : x < y\n⊢ tan x < tan y",
"tactic": "rw [tan_eq_sin_div_cos, tan_eq_sin_div_cos]"
},
{
"state_after": "no goals",
"state_before... | [
967,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | bilinFormOfRealInner_orthogonal | [] | [
230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
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Mathlib/Analysis/Convex/Basic.lean | Antitone.convex_le | [] | [
397,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Ico | [] | [
126,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | coe_nnreal_ennreal_nndist | [] | [
328,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_injective_of_surjective | [] | [
1576,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1575,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.τ_symm_apply_infinity | [
{
"state_after": "no goals",
"state_before": "A B : GroupCat\nf : A ⟶ B\n⊢ ↑τ.symm ∞ =\n fromCoset\n { val := (MonoidHom.range f).toSubmonoid.toSubsemigroup.carrier,\n property :=\n (_ :\n ∃ y,\n Function.swap leftCoset (MonoidHom.range f).toSubmonoid.toSubsem... | [
204,
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202,
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Mathlib/SetTheory/Game/PGame.lean | PGame.equiv_congr_right | [] | [
883,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.ToPartrec.stepRet_then | [
{
"state_after": "case cons₁\nk' : Cont\na✝² : Code\na✝¹ : List ℕ\na✝ : Cont\na_ih✝ : ∀ {v : List ℕ}, stepRet (Cont.then a✝ k') v = Cfg.then (stepRet a✝ v) k'\nv : List ℕ\n⊢ stepNormal a✝² (Cont.cons₂ v (Cont.then a✝ k')) a✝¹ = Cfg.then (stepNormal a✝² (Cont.cons₂ v a✝) a✝¹) k'\n\ncase comp\nk' : Cont\na✝¹ : Co... | [
595,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/Topology/Algebra/Valuation.lean | Valued.loc_const | [
{
"state_after": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\nx : R\nh : ↑v x ≠ 0\n⊢ ∃ γ, {y | ↑v (y - x) < ↑γ} ⊆ {y | ↑v y = ↑v x}",
"state_before": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R... | [
155,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.leadingCoeff_of_injective | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nf : R →+* S\nhf : Injective ↑f\np : R[X]\n⊢ coeff (map f p) (natDegree (map f p)) = ↑f (coeff p (natDegree p))",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝¹ : Se... | [
354,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Topology/Semicontinuous.lean | ContinuousAt.lowerSemicontinuousAt | [] | [
290,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.append_cancel_left | [
{
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Std/Data/List/Basic.lean | List.take_eq_takeTR | [
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.sum_nat_mod | [
{
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_id | [] | [
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Mathlib/Data/Set/Pairwise/Basic.lean | Set.pairwiseDisjoint_range_singleton | [
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Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.id_mem_maximalAtlas | [
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Mathlib/Data/Set/Basic.lean | Set.ite_inter_self | [
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2247,
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Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_midpoint_left | [] | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_zero | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.boundedBy_measure | [] | [
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Mathlib/Algebra/Order/Field/Basic.lean | left_lt_add_div_two | [
{
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Mathlib/Data/Fin/Basic.lean | Fin.coe_eq_castSucc | [
{
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Mathlib/Logic/Denumerable.lean | Nat.Subtype.ofNat_range | [] | [
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Mathlib/Algebra/IsPrimePow.lean | not_isPrimePow_one | [] | [
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.FinMeasAdditive.map_empty_eq_zero | [
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Mathlib/Order/Filter/Prod.lean | Filter.tendsto_prod_iff | [
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Mathlib/Order/Zorn.lean | exists_maximal_of_chains_bounded | [
{
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Mathlib/ModelTheory/Definability.lean | Set.definable_finset_biInter | [
{
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131,
34
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128,
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Std/Data/List/Lemmas.lean | List.head?_eq_head | [] | [
443,
19
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441,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.right_eq_zero_of_add_eq_zero | [] | [
160,
26
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159,
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Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.support_tsub | [
{
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.mkPiAlgebra_apply | [] | [
993,
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992,
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Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.id_map | [] | [
102,
62
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102,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_add_left | [] | [
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27
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925,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.inducedOuterMeasure_eq_extend' | [] | [
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89
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1466,
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.exists_finite_support | [] | [
295,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
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Mathlib/Init/Data/Quot.lean | Quot.EqvGen_sound | [] | [
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Mathlib/Order/Hom/Basic.lean | OrderIso.withTopCongr_symm | [] | [
1330,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
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Mathlib/Data/Pi/Algebra.lean | Function.bijective_pi_map | [] | [
423,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.hasStrictFDerivAt_rpow_of_pos | [
{
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Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_lt_right | [] | [
137,
95
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137,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WSameSide.map | [
{
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Mathlib/Algebra/Order/Ring/Defs.lean | neg_lt_self_iff | [
{
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}
] | [
1107,
90
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1106,
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioo.pos | [] | [
346,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.sub_const | [
{
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"tactic": "simpa only [sub_eq_add_neg] using h.add_const (-a)"
}
] | [
451,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
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src/lean/Init/SimpLemmas.lean | Bool.or_eq_true | [
{
"state_after": "no goals",
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108,
33
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107,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.condition | [] | [
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33
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864,
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src/lean/Init/SimpLemmas.lean | and_self | [] | [
82,
86
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
82,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.inter_ae_eq_empty_of_ae_eq_empty_right | [
{
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550,
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547,
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
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Mathlib/Tactic/Nontriviality/Core.lean | Mathlib.Tactic.Nontriviality.subsingleton_or_nontrivial_elim | [] | [
22,
46
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20,
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_sup_of_normal_right' | [] | [
335,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
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Mathlib/RingTheory/Ideal/Over.lean | Ideal.comap_eq_of_scalar_tower_quotient | [
{
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142,
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Mathlib/Computability/Primrec.lean | Primrec.list_range | [
{
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"state_before": "α : Type ?u.312965\nβ : Type ?u.312... | [
1118,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_mk_of_le | [] | [
502,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
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Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.toPrefunctor_id | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
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Mathlib/Logic/Equiv/Fin.lean | finSuccAboveEquiv_apply | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.map_comp_map | [
{
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978,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
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Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_unique | [] | [
83,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.copy_eq | [] | [
167,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/Convex/Slope.lean | StrictConvexOn.secant_strict_mono | [
{
"state_after": "case inl\n𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : StrictConvexOn 𝕜 s f\na x y : 𝕜\nha : a ∈ s\nhx : x ∈ s\nhy : y ∈ s\nhxa✝ : x ≠ a\nhya : y ≠ a\nhxy : x < y\nhxa : x < a\n⊢ (f x - f a) / (x - a) < (f y - f a) / (y - a)\n\ncase inr\n𝕜 : Type u_1\ninst✝ : ... | [
336,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Algebra/Group/Units.lean | IsUnit.mul_right_inj | [] | [
776,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_le | [] | [
1329,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.mul_star_self_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.47608\nE : Type u_1\nα : Type ?u.47614\ninst✝² : NonUnitalNormedRing E\ninst✝¹ : StarRing E\ninst✝ : CstarRing E\nx : E\n⊢ x * x⋆ ≠ 0 ↔ x ≠ 0",
"tactic": "simp only [Ne.def, mul_star_self_eq_zero_iff]"
}
] | [
153,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_symm_some | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | constantCoeff_wittStructureInt | [
{
"state_after": "p : ℕ\nR : Type ?u.2047179\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℤ\nh : ↑constantCoeff Φ = 0\nn : ℕ\ninj : Function.Injective ↑(Int.castRingHom ℚ)\n⊢ ↑constantCoeff (wittStructureInt p Φ n) = 0",
"state_before": "p : ℕ\nR : Type ?u.2047179\nidx ... | [
387,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
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