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/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.HasLift.iff | [
{
"state_after": "case mp\nC : Type u_1\ninst✝ : Category C\nA B X Y : C\nf : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\ng : B ⟶ Y\nsq : CommSq f i p g\n⊢ HasLift sq → Nonempty (LiftStruct sq)\n\ncase mpr\nC : Type u_1\ninst✝ : Category C\nA B X Y : C\nf : A ⟶ X\ni : A ⟶ B\np : X ⟶ Y\ng : B ⟶ Y\nsq : CommSq f i p g\n⊢ Nonemp... | [
206,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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src/lean/Init/Prelude.lean | Nat.pred_le_pred | [] | [
1626,
64
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1623,
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Mathlib/Data/List/ProdSigma.lean | List.nil_product | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.le_top_of_mem | [] | [
345,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.mem_skewAdjointSubmodule | [
{
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603,
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600,
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Mathlib/Data/Nat/Dist.lean | Nat.dist_add_add_left | [
{
"state_after": "k n m : ℕ\n⊢ dist (n + k) (m + k) = dist n m",
"state_before": "k n m : ℕ\n⊢ dist (k + n) (k + m) = dist n m",
"tactic": "rw [add_comm k n, add_comm k m]"
},
{
"state_after": "no goals",
"state_before": "k n m : ℕ\n⊢ dist (n + k) (m + k) = dist n m",
"tactic": "apply di... | [
86,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AlgHom.map_fieldRange | [] | [
281,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_commute | [] | [
595,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
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Mathlib/Analysis/Normed/Order/UpperLower.lean | IsUpperSet.mem_interior_of_forall_lt | [
{
"state_after": "case intro\nα : Type ?u.2735\nι : Type u_1\ninst✝ : Finite ι\ns : Set (ι → ℝ)\nx y : ι → ℝ\nδ : ℝ\nhs : IsUpperSet s\nhx : x ∈ closure s\nh : ∀ (i : ι), x i < y i\nval✝ : Fintype ι\n⊢ y ∈ interior s",
"state_before": "α : Type ?u.2735\nι : Type u_1\ninst✝ : Finite ι\ns : Set (ι → ℝ)\nx y :... | [
92,
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77,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_id | [
{
"state_after": "case h\nG : Type ?u.238328\nG' : Type ?u.238331\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.238340\ninst✝² : AddGroup A\nH K✝ : Subgroup G\nk : Set G\nN : Type u_1\ninst✝¹ : Group N\nP : Type ?u.238367\ninst✝ : Group P\nK : Subgroup N\nx✝ : N\n⊢ x✝ ∈ comap (MonoidHom.id N) K ↔ x✝ ∈ K",
... | [
1389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
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Mathlib/Data/List/MinMax.lean | List.minimum_eq_coe_iff | [] | [
391,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/Data/Set/Basic.lean | Set.setOf_true | [] | [
660,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Data/Set/Intervals/OrderIso.lean | OrderIso.preimage_Ioi | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\nb : β\nx : α\n⊢ x ∈ ↑e ⁻¹' Ioi b ↔ x ∈ Ioi (↑(symm e) b)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ne : α ≃o β\nb : β\n⊢ ↑e ⁻¹' Ioi b = Ioi (↑(symm e) b)",
... | [
46,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/Data/Fintype/Basic.lean | Fin.univ_def | [] | [
811,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_erase | [
{
"state_after": "case inl\nι : Type ?u.150239\nα : Type ?u.150242\nM : Type u_1\nN : Type ?u.150248\nP : Type ?u.150251\nM₀ : Type ?u.150254\nG : Type ?u.150257\nR : Type ?u.150260\ninst✝¹ : DecidableEq M\ninst✝ : CommMonoid M\na : M\nl : List M\nh : a ∈ a :: l\n⊢ a * prod (List.erase (a :: l) a) = prod (a :: ... | [
557,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.separatingLeft_toLinearMap₂'_iff_separatingLeft_toLinearMap₂ | [] | [
685,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
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Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.empty_subset | [] | [
837,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.smul_im | [
{
"state_after": "no goals",
"state_before": "d a : ℤ\nb : ℤ√d\n⊢ (↑a * b).im = a * b.im",
"tactic": "simp"
}
] | [
322,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.exp_mul | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ exp (x * y) = exp x ^ y",
"tactic": "rw [rpow_def_of_pos (exp_pos _), log_exp]"
}
] | [
61,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.comp_apply | [] | [
723,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
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Mathlib/RingTheory/Subring/Basic.lean | Subring.gc_map_comap | [] | [
622,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.add_modByMonic | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : Semiring S\np₁ p₂ : R[X]\nhq : Monic q\n⊢ (p₁ + p₂) %ₘ q = p₁ %ₘ q + p₂ %ₘ q\n\ncase neg\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : Semiring... | [
87,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.mulLeft_symm | [] | [
144,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | existsUnique_sub_zsmul_mem_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : Archimedean α\na : α\nha : 0 < a\nb c : α\n⊢ ∃! x, b - ↑(Equiv.neg ℤ) x • a ∈ Ioc c (c + a)",
"tactic": "simpa only [Equiv.neg_apply, neg_zsmul, sub_neg_eq_add] using\n existsUnique_add_zsmul_mem_I... | [
110,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/RingTheory/Localization/Module.lean | Basis.localizationLocalization_apply | [] | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.power_nat_le_max | [
{
"state_after": "case inl\nc : Cardinal\nn : ℕ\nhc : ℵ₀ ≤ c\n⊢ c ^ ↑n ≤ max c ℵ₀\n\ncase inr\nc : Cardinal\nn : ℕ\nhc : c < ℵ₀\n⊢ c ^ ↑n ≤ max c ℵ₀",
"state_before": "c : Cardinal\nn : ℕ\n⊢ c ^ ↑n ≤ max c ℵ₀",
"tactic": "cases' le_or_lt ℵ₀ c with hc hc"
},
{
"state_after": "no goals",
"stat... | [
968,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.prod_rcons | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : ι → Type u_2\ninst✝² : (i : ι) → Monoid (M i)\nN : Type ?u.392300\ninst✝¹ : Monoid N\ninst✝ : (i : ι) → DecidableEq (M i)\ni : ι\np : Pair M i\nhm : p.head = 1\n⊢ prod (rcons p) = ↑of p.head * prod p.tail",
"tactic": "rw [rcons, dif_pos hm,... | [
350,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_getLast?_eq_getLast | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.35296\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx : α\nhx : x ∈ getLast? []\n⊢ False",
"tactic": "simp at hx"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.35296\nα : Type u\nβ : Type v\nγ : Type ... | [
798,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | Hausdorffification.lift_of | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isUpperSet_iInter | [] | [
156,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.map_rel_iff | [] | [
91,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Order/BoundedOrder.lean | not_lt_bot | [] | [
326,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.toContinuousLinearMap₁_coe | [] | [
127,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.map_sin | [
{
"state_after": "case h\nA : Type u_2\nA' : Type u_1\ninst✝⁷ : Ring A\ninst✝⁶ : Ring A'\ninst✝⁵ : Algebra ℚ A\ninst✝⁴ : Algebra ℚ A'\ninst✝³ : Ring A\ninst✝² : Ring A'\ninst✝¹ : Algebra ℚ A\ninst✝ : Algebra ℚ A'\nn : ℕ\nf : A →+* A'\nn✝ : ℕ\n⊢ ↑(coeff A' n✝) (↑(map f) (sin A)) = ↑(coeff A' n✝) (sin A')",
"... | [
141,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_le_right | [] | [
964,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
11
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.coe_toRealAffineIsometryEquiv | [
{
"state_after": "case H\nE : Type u_3\nPE : Type u_1\nF : Type u_4\nPF : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : MetricSpace PE\ninst✝⁴ : NormedAddTorsor E PE\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : MetricSpace PF\ninst✝ : NormedAddTorsor F PF\nf :... | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherianRing_iff_ideal_fg | [] | [
499,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_of_sub_eq_zero | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nh : n - m = 0\n⊢ subNatNat m n = ↑(m - n)",
"tactic": "rw [subNatNat, h, ofNat_eq_coe]"
}
] | [
28,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
27,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.mul_inv_cancel_iff_isUnit | [] | [
139,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.dual_comp | [] | [
1422,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.25342\nβ : Type u_3\nβ' : Type ?u.25348\nγ : Type u_1\nγ' : Type ?u.25354\nδ : Type ?u.25357\nδ' : Type ?u.25360\nε : Type ?u.25363\nε' : Type ?u.25366\nζ : Type ?u.25369\nζ' : Type ?u.25372\nν : Type ?u.25375\ninst✝⁷ : DecidableEq α'\... | [
150,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Topology/Category/TopCat/OpenNhds.lean | TopologicalSpace.OpenNhds.inclusion_obj | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Order/RelClasses.lean | IsAsymm.isAntisymm | [] | [
120,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Logic/Basic.lean | ExistsUnique.unique₂ | [
{
"state_after": "ι : Sort ?u.25704\nα✝ : Sort ?u.25709\nκ : ι → Sort ?u.25706\np✝ q✝ : α✝ → Prop\nα : Sort u_1\np : α → Sort u_2\ninst✝ : ∀ (x : α), Subsingleton (p x)\nq : (x : α) → p x → Prop\ny₁ y₂ : α\nhpy₁ : p y₁\nhqy₁ : q y₁ hpy₁\nhpy₂ : p y₂\nhqy₂ : q y₂ hpy₂\nh : ∃! x, ∃ hx, q x hx\n⊢ y₁ = y₂",
"st... | [
954,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Order/SymmDiff.lean | inf_symmDiff_distrib_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.60714\nα : Type u_1\nβ : Type ?u.60720\nπ : ι → Type ?u.60725\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b ⊓ c = (a ⊓ c) ∆ (b ⊓ c)",
"tactic": "simp_rw [@inf_comm _ _ _ c, inf_symmDiff_distrib_left]"
}
] | [
412,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.smul_monomial | [
{
"state_after": "R : Type u\na✝ b✝ : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nS : Type u_1\ninst✝ : SMulZeroClass S R\na : S\nn : ℕ\nb : R\n⊢ a • Finsupp.single n b = Finsupp.single n (a • b)",
"state_before": "R : Type u\na✝ b✝ : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nS : Type u_1\ninst✝ : SMu... | [
461,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.zsmul_sub_eq | [] | [
254,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.addHom_ext | [
{
"state_after": "case intro.intro\nR : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nM : Type u_1\ninst✝ : AddMonoid M\nf g : R[X] →+ M\nh : ∀ (n : ℕ) (a : R), ↑f (↑(monomial n) a) = ↑g (↑(monomial n) a)\nn : ℕ\na : R\n⊢ ↑f (↑(monomial n) a) = ↑g (↑(monomial n) a)",
"state_before": "R : Type... | [
813,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.singleton_smul | [] | [
159,
24
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158,
1
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Mathlib/Order/LocallyFinite.lean | Icc_ofDual | [
{
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859,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
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Mathlib/Init/Function.lean | Function.injective_id | [] | [
123,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.dvd_total | [] | [
305,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
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Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | IsScalarTower.adjoin_range_toAlgHom | [
{
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154,
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Std/Data/List/Lemmas.lean | List.Sublist.eraseP | [
{
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996,
33
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989,
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Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.ext | [] | [
63,
17
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62,
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Mathlib/Data/Finset/Sym.lean | Finset.sym2_empty | [] | [
71,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.ediv_lt_of_lt_mul | [] | [
451,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
11
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Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.coe_mulLeft₀ | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineBasis.finiteDimensional | [] | [
770,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift.principalSeg_top' | [
{
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}
] | [
1310,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1309,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.mem_prehaar_empty | [
{
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147,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Order/Bounds/Basic.lean | IsGreatest.isLeast_image2_of_isLeast | [] | [
1548,
82
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1545,
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Mathlib/Data/Finset/Interval.lean | Finset.Ioo_eq_filter_ssubsets | [] | [
65,
6
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64,
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Mathlib/Order/WithBot.lean | WithTop.untop'_top | [] | [
701,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
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Mathlib/Topology/Homotopy/Path.lean | Path.Homotopy.target | [] | [
75,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/Stieltjes.lean | MeasureTheory.tendsto_measure_Ioc_atBot | [
{
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"state_before": "α : Type u_1\nmα : MeasurableSpace α\ninst✝² :... | [
162,
79
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146,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_pair_le_of_mem_of_mem | [
{
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1356,
19
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1353,
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Mathlib/Data/Set/Image.lean | Set.image_inter_preimage | [
{
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512,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_re_zero_left | [
{
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565,
53
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564,
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Mathlib/Order/Filter/Basic.lean | Filter.generate_eq_biInf | [
{
"state_after": "no goals",
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}
] | [
678,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
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Mathlib/Order/ConditionallyCompleteLattice/Group.lean | ciSup_mul_ciSup_le | [] | [
66,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Algebra/Module/LinearMap.lean | LinearMap.sub_comp | [] | [
939,
6
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937,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_X | [] | [
1597,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_prod | [] | [
706,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
704,
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Mathlib/Data/List/Basic.lean | List.dropLast_append_getLast | [
{
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"state_before": "ι : Type ?u.30890\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ... | [
741,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_withDensity_eq_integral_smul | [
{
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1261,
57
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1217,
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.neg_neg_iff | [] | [
378,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_image | [] | [
939,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_self_of_le_one | [
{
"state_after": "case inl\nz : ℝ\nh_one_le : 1 ≤ z\nhx : ⊥ ≤ 1\n⊢ ⊥ ^ z ≤ ⊥\n\ncase inr\nx : ℝ≥0\nz : ℝ\nhx : x ≤ 1\nh_one_le : 1 ≤ z\nh : 0 < x\n⊢ x ^ z ≤ x",
"state_before": "x : ℝ≥0\nz : ℝ\nhx : x ≤ 1\nh_one_le : 1 ≤ z\n⊢ x ^ z ≤ x",
"tactic": "rcases eq_bot_or_bot_lt x with (rfl | (h : 0 < x))"
}... | [
239,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubalgebra.mem_toLieSubmodule | [] | [
319,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_div | [] | [
618,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
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Mathlib/Data/Quot.lean | Quot.surjective_lift | [] | [
112,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
9
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.card_le_multiplicity | [
{
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203,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Algebra/Field/Defs.lean | Field.toIsField | [] | [
206,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Std/Data/Int/DivMod.lean | Int.fdiv_nonpos | [] | [
108,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
107,
1
] |
Mathlib/Algebra/Order/Monoid/ToMulBot.lean | WithZero.toMulBot_zero | [] | [
37,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.integrableOn_univ | [
{
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"tactic": "rw [IntegrableOn, Measure.restrict_un... | [
114,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/Analysis/Calculus/Taylor.lean | hasDerivWithinAt_taylorWithinEval | [
{
"state_after": "case zero\n𝕜 : Type ?u.286028\nE : Type u_1\nF : Type ?u.286034\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx y : ℝ\nn : ℕ\ns s' : Set ℝ\nhs'_unique : UniqueDiffWithinAt ℝ s' y\nhs_unique : UniqueDiffOn ℝ s\nhs' : s' ∈ 𝓝[s] y\nhy : y ∈ s'\nh : s' ⊆ s\nhf✝ : ContDiffOn... | [
204,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.toLp_norm_le | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.16506630\nG : Type ?u.16506633\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedAddCommGroup G\ninst✝⁷ : TopologicalSpace α\ninst✝⁶ : BorelSpace α\nin... | [
1774,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1771,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_X_mul | [
{
"state_after": "no goals",
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"tactic": "rw [X_mul, eval₂_mul_X]"
}
] | [
196,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.smul_def | [] | [
1338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.eventually_mem_spanningSets | [] | [
3527,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3525,
1
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Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.frequently | [] | [
2844,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2842,
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Mathlib/Data/Polynomial/Div.lean | Polynomial.X_dvd_iff | [
{
"state_after": "no goals",
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"tactic": "rw [hfg, mul_comm, coeff_mul_X_zero]"
},
{
"state_after": "no goals",
"state_bef... | [
43,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/Order/Bounded.lean | Set.unbounded_gt_inter_gt | [] | [
455,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_nonpos_of_nonpos_of_nonneg | [
{
"state_after": "no goals",
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"tactic": "simpa only [zero_mul] using mul_le_mul_of_nonneg_right ha hb"
}
] | [
392,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value₂_eventually₂ | [
{
"state_after": "X : Type u\nα : Type v\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderClosedTopology α\ns : Set X\nhs : IsPreconnected s\nl₁ l₂ : Filter X\ninst✝¹ : NeBot l₁\ninst✝ : NeBot l₂\nhl₁ : l₁ ≤ 𝓟 s\nhl₂ : l₂ ≤ 𝓟 s\nf g : X → α\nhf : Continuous (res... | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Coplanar.subset | [] | [
637,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Std/Logic.lean | not_congr | [] | [
22,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
22,
1
] |
Mathlib/Algebra/Ring/Defs.lean | add_one_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝² : Add α\ninst✝¹ : MulOneClass α\ninst✝ : RightDistribClass α\na b : α\n⊢ (a + 1) * b = a * b + b",
"tactic": "rw [add_mul, one_mul]"
}
] | [
158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
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