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/Data/Set/Function.lean | Set.BijOn.congr | [] | [
962,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Data/List/Zip.lean | List.map_fst_zip | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type ?u.82177\nδ : Type ?u.82180\nε : Type ?u.82183\nhead✝¹ : α\nas : List α\nhead✝ : β\nbs : List β\nh : length as ≤ length bs\n⊢ map Prod.fst (zip (head✝¹ :: as) (head✝ :: bs)) = head✝¹ :: as",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.82177\nδ ... | [
188,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_mul_left' | [] | [
54,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.nnnorm_le_mul_nnnorm_of_ae_le_mul | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.418576\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nc : ℝ≥0\nf : { x // x ∈ Lp E p }\ng : { x // x ∈ Lp F p }\nh : ∀ᵐ (x : α) ∂μ, ‖↑... | [
365,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.finite_support | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\nf : Π₀ (i : ι), β i\nem✝ : (a : Prop) → Decidable a\n⊢ Set.Finite {i | ↑f i ≠ 0}",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ... | [
570,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
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Mathlib/Analysis/Convex/Segment.lean | Prod.image_mk_openSegment_left | [
{
"state_after": "case h.mk\n𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.343510\nι : Type ?u.343513\nπ : ι → Type ?u.343518\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx₁ x₂ : E\ny : F\nx' : E\ny' : F\n⊢ (x', y') ∈ (fun ... | [
627,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.distortion_le_iff | [] | [
683,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_trim_simpleFunc | [
{
"state_after": "α : Type ?u.1706708\nE : Type ?u.1706711\nF : Type u_2\n𝕜 : Type ?u.1706717\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : CompleteSpace E\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedSpace 𝕜 E\ninst✝⁴ : SMulCommClass ℝ 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² ... | [
1758,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
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Mathlib/Data/Sym/Card.lean | Sym2.card_subtype_not_diag | [
{
"state_after": "case h.e'_2\nα : Type u_1\nβ : Type ?u.100368\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n⊢ Fintype.card { a // ¬IsDiag a } = Finset.card (image Quotient.mk' (offDiag univ))",
"state_before": "α : Type u_1\nβ : Type ?u.100368\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n⊢ Fintype.card { a /... | [
193,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_of_monotone_of_filter | [] | [
1720,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1718,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.toIsometryEquiv_symm | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | thickening_closedBall | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.340066\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx✝ y z : E\nδ ε : ℝ\nhε : 0 < ε\nhδ : 0 ≤ δ\nx : E\n⊢ thickening ε (Metric.closedBall x δ) = Metric.ball x (ε + δ)"... | [
331,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Submodule.dfinsupp_sumAddHom_mem | [] | [
316,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_lt_mul_of_neg_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : b < a\nhc : c < 0\nthis✝ : -c > 0\nthis : b * -c < a * -c\n⊢ -(b * c) < -(a * c)",
"tactic": "rwa [← Int.neg_mul_eq_mul_neg, ← Int.neg_mul_eq_mul_neg] at this"
}
] | [
1227,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1222,
11
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasLimits_of_hasLimits_createsLimits | [] | [
177,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Algebra/Star/CHSH.lean | TsirelsonInequality.tsirelson_inequality_aux | [
{
"state_after": "R : Type u\n⊢ Real.sqrt 2 ^ 4 = Real.sqrt 2 * (Real.sqrt 2)⁻¹ * 4",
"state_before": "R : Type u\n⊢ Real.sqrt 2 * Real.sqrt 2 ^ 3 = Real.sqrt 2 * (2 * (Real.sqrt 2)⁻¹ + 4 * ((Real.sqrt 2)⁻¹ * 2⁻¹))",
"tactic": "ring_nf"
},
{
"state_after": "R : Type u\n⊢ Real.sqrt 2 ^ 4 = 1 * 4"... | [
177,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_add_right' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoMod hp (a + p) b = toIcoMod hp a b + p",
"tactic": "simpa only [one_zsmul] using toIcoMod_add_zsmul' hp a b 1"
}
] | [
479,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mk_preimage_prod_right_eq_empty | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.27167\nδ : Type ?u.27170\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb✝ : β\nha : ¬a ∈ s\nb : β\n⊢ b ∈ Prod.mk a ⁻¹' s ×ˢ t ↔ b ∈ ∅",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.27167\nδ : Type ?u.27170\ns s₁ s₂ : Set α\nt t₁ t₂ : ... | [
245,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_insert_one | [] | [
888,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_algebraMap_eq_algebraMap | [] | [
1380,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.congr_arg | [] | [
154,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.130013\ninst✝ : Fintype ι\na r : ℝ\n⊢ ↑↑volume (Metric.ball a r) = ofReal (2 * r)",
"tactic": "rw [ball_eq_Ioo, volume_Ioo, ← sub_add, add_sub_cancel', two_mul]"
}
] | [
112,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.prod_left_fst | [] | [
1013,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | continuousOn_coordChange | [] | [
424,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Std/Data/List/Lemmas.lean | List.eraseP_append_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nx : α\nxs l₂ : List α\nh : ∀ (b : α), b ∈ x :: xs → ¬p b = true\n⊢ eraseP p (x :: xs ++ l₂) = x :: xs ++ eraseP p l₂",
"tactic": "simp [(forall_mem_cons.1 h).1, eraseP_append_right _ (forall_mem_cons.1 h).2]"
}
] | [
980,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
976,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_subtype | [
{
"state_after": "α : Type u_1\nβ : Type ?u.55899\nγ : Type ?u.55902\ninst✝¹ : Fintype α\np : α → Prop\ninst✝ : DecidablePred p\n⊢ ∀ (x : α), x ∈ filter p univ ↔ p x",
"state_before": "α : Type u_1\nβ : Type ?u.55899\nγ : Type ?u.55902\ninst✝¹ : Fintype α\np : α → Prop\ninst✝ : DecidablePred p\n⊢ card { x /... | [
845,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.toSubmodule_bot | [
{
"state_after": "case h\nR : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nx : A\n⊢ x ∈ ↑Subalgebra.toSubmodule ⊥ ↔ x ∈ Submodule.span R {1}",
"state_before": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSe... | [
902,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
900,
1
] |
Mathlib/Order/Bounds/Basic.lean | BddBelow.inter_of_right | [] | [
410,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_le | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\nm n : ZNum\n⊢ ¬↑n < ↑m ↔ m ≤ n",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\nm n : ZNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"tactic": "rw [← not_lt]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrd... | [
1412,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Algebra/SMulWithZero.lean | zero_smul | [] | [
74,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_sInf | [] | [
425,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_comp | [] | [
1292,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1290,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Complex.iter_deriv_exp | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.7221\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : NormedAlgebra 𝕜 ℂ\nn : ℕ\n⊢ (deriv^[n + 1]) exp = exp",
"tactic": "rw [iterate_succ_apply, deriv_exp, iter_deriv_exp n]"
}
] | [
60,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/CategoryTheory/Closed/FunctorCategory.lean | CategoryTheory.Functor.ihom_map | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.id_apply_of_ne | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : Preadditive C\nR : Type u\ninst✝ : Semiring R\nM : Mat R\ni j : ↑M\nh : i ≠ j\n⊢ 𝟙 M i j = 0",
"tactic": "simp [id_apply, h]"
}
] | [
603,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.coe_coe | [] | [
532,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.exists_memBaseSet_isPartition | [
{
"state_after": "ι : Type u_1\ninst✝ : Fintype ι\nI✝ J : Box ι\nc c₁ c₂ : ℝ≥0\nr✝ r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I✝\nl✝ l₁ l₂ l : IntegrationParams\nI : Box ι\nhc : Prepartition.distortion ⊤ ≤ c\nr : (ι → ℝ) → ↑(Set.Ioi 0)\n⊢ ∃ π, MemBaseSet l I c r π ∧ IsPartition π",
"state_... | [
535,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_dvd_iff_map_hom_eq_zero | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q✝ : MvPolynomial σ R\nf q : R →+* S₁\nr : R\nhr : ∀ (r' : R), ↑q r' = 0 ↔ r ∣ r'\nφ : MvPolynomial σ R\n⊢ (∀ (i : σ →₀ ℕ), r ∣ coeff... | [
1375,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Convex.is_linear_image | [] | [
197,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/PFun.lean | PFun.Preimage_def | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.C_eq_algebraMap | [] | [
154,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/NumberTheory/Liouville/Measure.lean | volume_setOf_liouville | [
{
"state_after": "no goals",
"state_before": "⊢ ↑↑volume {x | Liouville x} = 0",
"tactic": "simpa only [ae_iff, Classical.not_not] using ae_not_liouville"
}
] | [
126,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.eq_inv_iff_mul_eq_one | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type ?u.1908912\nk : Type u_2\ninst✝ : Field k\nφ ψ : MvPowerSeries σ k\nh : ↑(constantCoeff σ k) ψ ≠ 0\n⊢ φ = ψ⁻¹ ↔ φ * ψ = 1",
"tactic": "rw [← MvPowerSeries.eq_mul_inv_iff_mul_eq h, one_mul]"
}
] | [
1001,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
11
] |
Std/Data/Range/Lemmas.lean | Std.Range.forIn'_eq_forIn_range' | [
{
"state_after": "m : Type u_1 → Type u_2\nβ : Type u_1\ninst✝ : Monad m\nr : Range\ninit : β\nstart stop step : Nat\nf : (a : Nat) → a ∈ { start := start, stop := stop, step := step } → β → m (ForInStep β)\n⊢ forIn' { start := start, stop := stop, step := step } init f =\n forIn\n (List.pmap Subtype.mk... | [
86,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
43,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.left_unique | [] | [
563,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_group_smul | [] | [
241,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Data/Set/Basic.lean | MonotoneOn.inter | [] | [
2894,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2892,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.degree_normalize | [
{
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Mathlib/Data/Multiset/Basic.lean | Multiset.erase_le_erase | [] | [
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Mathlib/Data/Sum/Basic.lean | Sum.elim_map | [
{
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | summable_sum_mul_range_of_summable_mul | [
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Mathlib/LinearAlgebra/CrossProduct.lean | cross_anticomm | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_sub_eq_arctan_of_inner_eq_zero | [
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Mathlib/Order/Interval.lean | NonemptyInterval.dual_pure | [] | [
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Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mul | [
{
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src/lean/Init/Prelude.lean | Nat.ble_eq_true_of_le | [] | [
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Mathlib/Data/Set/Finite.lean | Finset.finite_toSet_toFinset | [
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Mathlib/LinearAlgebra/Dimension.lean | Module.rank_le_one_iff_top_isPrincipal | [
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Mathlib/Order/JordanHolder.lean | CompositionSeries.append_natAdd | [
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Mathlib/Analysis/Normed/Group/Basic.lean | mul_mem_ball_iff_norm | [
{
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Mathlib/Order/ModularLattice.lean | wellFounded_lt_exact_sequence | [
{
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_greatest | [] | [
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Std/Data/String/Lemmas.lean | String.Iterator.ValidFor.toEnd' | [
{
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593,
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Mathlib/Topology/Separation.lean | Filter.coclosedCompact_le_cofinite | [] | [
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Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.sumInr_injective | [] | [
315,
63
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314,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.bsup_lt_ord_of_isRegular | [
{
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.span_zero | [] | [
227,
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226,
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.neg | [
{
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.eq_bot_iff_forall | [] | [
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75
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Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.coe_sub_interval | [] | [
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Mathlib/Deprecated/Submonoid.lean | Monoid.image_closure | [
{
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Mathlib/Data/List/Rotate.lean | List.IsRotated.forall | [] | [
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26
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459,
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Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.disjoint_map_compl | [
{
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163,
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158,
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Mathlib/Data/Dfinsupp/Basic.lean | AddSubmonoid.bsupr_eq_mrange_dfinsupp_sumAddHom | [
{
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.dual | [
{
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1079,
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Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.le_leftLim | [
{
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124,
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Mathlib/LinearAlgebra/Dimension.lean | Submodule.rank_le_one_iff_isPrincipal | [
{
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Mathlib/Order/Filter/Extr.lean | isExtrOn_const | [] | [
201,
21
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200,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_zero | [] | [
770,
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Mathlib/Data/Finsupp/Lex.lean | Finsupp.lex_def | [] | [
47,
10
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Mathlib/Data/Char.lean | Char.utf8Size_pos | [
{
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28,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_iff_lt_one_right | [
{
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634,
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632,
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Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_singleton | [
{
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311,
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Mathlib/Topology/Instances/EReal.lean | EReal.nhds_top_basis | [
{
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140,
44
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137,
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Mathlib/Order/FixedPoints.lean | OrderHom.lfp_le_fixed | [] | [
65,
16
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Mathlib/Data/Complex/Exponential.lean | Real.abs_cos_eq_sqrt_one_sub_sin_sq | [
{
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}
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1310,
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1309,
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Mathlib/Topology/Algebra/Group/Basic.lean | isClosed_setOf_map_inv | [
{
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302,
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Mathlib/RingTheory/Int/Basic.lean | Int.Prime.dvd_pow | [
{
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},
{
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284,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_updateColumn | [] | [
210,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
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Mathlib/RingTheory/Ideal/Cotangent.lean | Ideal.to_quotient_square_comp_toCotangent | [] | [
114,
29
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112,
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Mathlib/Data/Finsupp/ToDfinsupp.lean | sigmaFinsuppEquivDfinsupp_smul | [
{
"state_after": "case h.h\nι : Type u_4\nR✝ : Type ?u.89337\nM : Type ?u.89340\nη : ι → Type u_3\nN : Type u_2\ninst✝³ : Semiring R✝\nR : Type u_1\ninst✝² : Monoid R\ninst✝¹ : AddMonoid N\ninst✝ : DistribMulAction R N\nr : R\nf : (i : ι) × η i →₀ N\ni✝ : ι\na✝ : η i✝\n⊢ ↑(↑(↑sigmaFinsuppEquivDfinsupp (r • f)) ... | [
368,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_int_of_map_zero | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nn : ℤ\n⊢ ↑f ↑n = ↑f 0 + ↑n",
"tactic": "rw [← f.map_add_int, zero_add]"
}
] | [
391,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cos_pow | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : n + 2 ≠ 0\n⊢ (∫ (x : ℝ) in a..b, cos x ^ (n + 2)) =\n (cos b ^ (n + 1) * sin b - cos a ^ (n + 1) * sin a) / (↑n + 2) + (↑n + 1) / (↑n + 2) * ∫ (x : ℝ) in a..b, cos x ^ n",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, cos x ^ (n + 2)) =\n (cos b ^ (n +... | [
739,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/Data/Set/Function.lean | Set.val_codRestrict_apply | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.Nonempty.image₂ | [] | [
127,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Data/Finmap.lean | Finmap.toFinmap_nil | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.algHom_subsingleton | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁵ : CommSemiring R\nM : Submonoid R\nS : Type u_3\ninst✝⁴ : CommSemiring S\ninst✝³ : Algebra R S\nP : Type u_2\ninst✝² : CommSemiring P\ninst✝¹ : IsLocalization M S\ng✝ : R →+* P\nhg : ∀ (y : { x // x ∈ M }), IsUnit (↑g✝ ↑y)\ninst✝ : Algebra R... | [
550,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.exists_pow_inf_eq_pow_smul | [] | [
435,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.continuousOn_symm | [
{
"state_after": "ι : Type ?u.50161\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\nZ : Type ?u.50175\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nproj : Z → B\ninst✝² : TopologicalSpace Z\ninst✝¹ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx : Z\ne' : Trivialization F TotalSpace... | [
638,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_monotone | [] | [
437,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
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