file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Antichain.lean | IsAntichain.isWeakAntichain | [] | [
390,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
11
] |
Mathlib/Algebra/Order/WithZero.lean | le_div_iff₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nhc : c ≠ 0\n⊢ a ≤ b / c ↔ a * c ≤ b",
"tactic": "rw [div_eq_mul_inv, le_mul_inv_iff₀ hc]"
}
] | [
249,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_inj | [] | [
354,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.homogeneousHull_toIdeal_eq_self | [] | [
579,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_eq_sub | [
{
"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⊢ toIocDiv hp a b = toIocDiv hp 0 (b - a)",
"tactic": "rw [toIocDiv_sub_eq_toIocDiv_add, zero_add]"
}
] | [
773,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_eq_of_inj_on_of_image_eq | [
{
"state_after": "no goals",
"state_before": "k : Type u_4\nV : Type u_5\nP : Type u_2\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type u_3\ns₂ : Finset ι₂\np : ι → P\nhi : ∀ (i : ι), i ∈ s → ∀ (j : ι), j ∈ s → p i = p j →... | [
985,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.unique_continuousLinearMapOfBilin | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : CompleteSpace E\nB : E →L⋆[𝕜] E →L[𝕜] 𝕜\nv f : E\nis_lax_milgram : ∀ (w : E), inner f w = ↑(↑B v) w\n⊢ ∀ (v_1 : E), inner f v_1 = inner (↑B♯ v) v_1",
"state_before": ... | [
188,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueSet_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nG H : SimpleGraph α\nn : ℕ\na b c : α\ns : Finset α\n⊢ cliqueSet G n = ∅ ↔ CliqueFree G n",
"tactic": "simp_rw [CliqueFree, Set.eq_empty_iff_forall_not_mem, mem_cliqueSet_iff]"
}
] | [
254,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_span_singleton' | [] | [
172,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOnFilter.tendsto_at | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\nh : TendstoUniformlyOnFilter F f p p'\nhx : 𝓟 {x} ≤ p'\nu : Set (β × β)\nhu : u ∈ 𝓤 β\n⊢ (fun x_1 => (f x, F x_1 x)) ⁻¹' u ∈ p",
... | [
173,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.inv_subset_closure | [
{
"state_after": "α : Type ?u.649\nG : Type u_1\nA : Type ?u.655\nS✝ : Type ?u.658\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns✝ S : Set G\ns : G\nhs : s ∈ S⁻¹\n⊢ s⁻¹ ∈ closure S",
"state_before": "α : Type ?u.649\nG : Type u_1\nA : Type ?u.655\nS✝ : Type ?u.658\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns✝ S : Set... | [
52,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | Nat.cast_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : AddMonoidWithOne R\n⊢ ↑1 = 1",
"tactic": "rw [cast_succ, Nat.cast_zero, zero_add]"
}
] | [
135,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_iInf_dom | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort u_1\nf : α → β\nu₁ : ι → UniformSpace α\nu₂ : UniformSpace β\ni : ι\nhf : UniformContinuous f\n⊢ Tendsto (fun x => (f x.fst, f x.snd)) (𝓤 α) (𝓤 β)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ... | [
1415,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.LeftInverse.cast_eq | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort u_2\nγ : β → Sort v\nf : α → β\ng : β → α\nh : LeftInverse g f\nC : (a : α) → γ (f a)\na : α\n⊢ cast (_ : γ (f (g (f a))) = γ (f a)) (C (g (f a))) = C a",
"tactic": "rw [cast_eq_iff_heq, h]"
}
] | [
1049,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Order/Lattice.lean | Antitone.min | [] | [
1185,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
11
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.congr | [] | [
486,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.coe_mul | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.mk_right_unitor_inv | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Order/Basic.lean | ge_of_eq | [] | [
336,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_lt_mul' | [] | [
526,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_add_pred_of_pos | [
{
"state_after": "m n✝ k l n i : ℕ\nhi : i ≠ 0\n⊢ n ≤ i + n - 1",
"state_before": "m n✝ k l n i : ℕ\nhi : i ≠ 0\n⊢ n ≤ i + (n - 1)",
"tactic": "refine le_trans ?_ add_tsub_le_assoc"
},
{
"state_after": "no goals",
"state_before": "m n✝ k l n i : ℕ\nhi : i ≠ 0\n⊢ n ≤ i + n - 1",
"tactic":... | [
327,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_apply_one_sub | [
{
"state_after": "k : Type u_2\nV1 : Type u_3\nP1 : Type u_1\nV2 : Type ?u.538087\nP2 : Type ?u.538090\nV3 : Type ?u.538093\nP3 : Type ?u.538096\nV4 : Type ?u.538099\nP4 : Type ?u.538102\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ : AddCommGroup V2\nin... | [
631,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.isNoetherianRing | [
{
"state_after": "R : Type u_1\ninst✝⁷ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\nP : Type ?u.117121\ninst✝⁴ : CommRing P\ng : R →+* P\nT : Submonoid P\nhy : M ≤ Submonoid.comap g T\nQ : Type ?u.117953\ninst✝³ : CommRing Q\ninst✝² : Algebra P Q\ninst✝¹ : IsLocalizati... | [
103,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Int/Sqrt.lean | Int.exists_mul_self | [
{
"state_after": "no goals",
"state_before": "x : ℤ\nx✝ : ∃ n, n * n = x\nn : ℤ\nhn : n * n = x\n⊢ sqrt x * sqrt x = x",
"tactic": "rw [← hn, sqrt_eq, ← Int.ofNat_mul, natAbs_mul_self]"
}
] | [
36,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.epi_of_nonzero_to_simple | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasEqualizers C\nX Y : C\ninst✝¹ : Simple Y\nf : X ⟶ Y\ninst✝ : HasImage f\nw : f ≠ 0\n⊢ Epi (factorThruImage f ≫ image.ι f)",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasE... | [
104,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_of_nonneg | [
{
"state_after": "no goals",
"state_before": "a : Int\nh : 0 ≤ a\n⊢ ↑(toNat a) = a",
"tactic": "rw [toNat_eq_max, Int.max_eq_left h]"
}
] | [
1372,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1371,
9
] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | SimpleGraph.isUniform_comm | [] | [
79,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/Homology/QuasiIso.lean | quasiIso_of_comp_right | [] | [
66,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_ne_coe_ennreal_iff | [] | [
516,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Analysis/LocallyConvex/BalancedCoreHull.lean | nhds_basis_closed_balanced | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nι : Type ?u.126319\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousSMul 𝕜 E\nU : Set E\ninst✝ : RegularSpace E\ns : Set E\nhs : s ∈ 𝓝 0 ∧ IsClosed s\n⊢ ∃ i', (i' ∈ 𝓝 0 ∧ IsClose... | [
279,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Deprecated/Subring.lean | RingHom.isSubring_preimage | [] | [
61,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.inf_eq_right | [
{
"state_after": "case inl.intro.intro.intro\nα : Type u_1\ninst✝ : LinearOrderedField α\na b : CauSeq α abs\nε : α\nε0 : 0 < ε\ni : ℕ\nh : ∀ (j : ℕ), j ≥ i → ε ≤ ↑(a - b) j\n⊢ a ⊓ b ≈ b\n\ncase inr\nα : Type u_1\ninst✝ : LinearOrderedField α\na b : CauSeq α abs\nh : b ≈ a\n⊢ a ⊓ b ≈ b",
"state_before": "α ... | [
940,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
11
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.quot_hom_ext | [] | [
315,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.pow_card_apply | [] | [
894,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_csinh | [] | [
551,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | fderivWithin.comp₃ | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_5\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_1\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_2\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type u_4\ninst✝¹ : No... | [
167,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.fderiv | [] | [
980,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
11
] |
Std/Data/Int/DivMod.lean | Int.ofNat_dvd | [
{
"state_after": "m n : Nat\nx✝ : ↑m ∣ ↑n\na : Int\nae : ↑n = ↑m * a\n⊢ m ∣ n",
"state_before": "m n : Nat\n⊢ ↑m ∣ ↑n ↔ m ∣ n",
"tactic": "refine ⟨fun ⟨a, ae⟩ => ?_, fun ⟨k, e⟩ => ⟨k, by rw [e, Int.ofNat_mul]⟩⟩"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nx✝ : ↑m ∣ ↑n\na : In... | [
642,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
634,
14
] |
Mathlib/Algebra/AddTorsor.lean | eq_of_vsub_eq_zero | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np1 p2 : P\nh : p1 -ᵥ p2 = 0\n⊢ p1 = p2",
"tactic": "rw [← vsub_vadd p1 p2, h, zero_vadd]"
}
] | [
133,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_norm_le | [] | [
259,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
9
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.gcdB_zero_left | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\ns : R\n⊢ (xgcd 0 s).snd = 1",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\ns : R\n⊢ gcdB 0 s = 1",
"tactic": "unfold gcdB"
},
{
"state_after": "no goals",
"state_before": "R : ... | [
275,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | Ordinal.zero_nadd | [
{
"state_after": "no goals",
"state_before": "a b c : Ordinal\n⊢ 0 ♯ a = a",
"tactic": "rw [nadd_comm, nadd_zero]"
}
] | [
294,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.units_coeff_zero_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q : R[X]\nc : R[X]ˣ\np : R[X]\n⊢ coeff (↑c) 0 • p = ↑c * p",
"tactic": "rw [← Polynomial.C_mul', ← Polynomial.eq_C_of_degree_eq_zero (degree_coe_units c)]"
}
] | [
845,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Topology/Order.lean | nhds_sInf | [] | [
666,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.toQuadraticForm_associated | [] | [
814,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.dvd_lcm | [] | [
72,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_eq_of_lt | [] | [
358,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
355,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | norm_mk_lt | [] | [
198,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.monotone_comap | [] | [
312,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
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Mathlib/Computability/Primrec.lean | Primrec.nat_iff | [] | [
237,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/Data/Complex/Exponential.lean | Real.neg_one_le_cos | [] | [
1279,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_subtype_of_mem | [
{
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878,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.isLocalization_iff_of_algEquiv | [] | [
769,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
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Mathlib/Algebra/BigOperators/Ring.lean | Finset.sum_mul_sum | [
{
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Mathlib/Data/List/Basic.lean | List.drop_left' | [
{
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2151,
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Mathlib/Deprecated/Submonoid.lean | isSubmonoid_iUnion_of_directed | [] | [
121,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.coe_mul | [
{
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}
] | [
334,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.lift.mk | [] | [
729,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
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Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.eq_iff' | [
{
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416,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Finsupp.sum_inner | [
{
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537,
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534,
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Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.natIsoOfCompFullyFaithful_inv | [
{
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235,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Reachable.rfl | [] | [
1872,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1872,
11
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_const | [
{
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"tactic": "rw [iSup, range_const, csSup_singleton]"
}
] | [
832,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
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Mathlib/Data/Finset/Lattice.lean | Finset.induction_on_max_value | [
{
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66
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1661,
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Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | Matrix.det_eq_sign_charpoly_coeff | [
{
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198,
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195,
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Mathlib/Data/List/Perm.lean | List.Perm.take_inter | [
{
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1163,
22
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1158,
1
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Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | MeasurableEquiv.coe_smul₀ | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_X_mul | [
{
"state_after": "no goals",
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"tactic": "rw [(commute_X p).eq, coeff_mul_X]"
}
] | [
270,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_transpose_apply' | [] | [
599,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.symm_eqOn_of_inter_eq_of_eqOn | [] | [
582,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | eventually_norm_pow_le | [] | [
387,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/GroupTheory/Subgroup/Saturated.lean | Subgroup.saturated_iff_zpow | [
{
"state_after": "case mp\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ Saturated H → ∀ (n : ℤ) (g : G), g ^ n ∈ H → n = 0 ∨ g ∈ H\n\ncase mpr\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ (∀ (n : ℤ) (g : G), g ^ n ∈ H → n = 0 ∨ g ∈ H) → Saturated H",
"state_before": "G : Type u_1\ninst✝ : Group G\n... | [
58,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.of_mul_add_right_right | [
{
"state_after": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime x (y + z * x)\n⊢ IsCoprime x y",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\nh : IsCoprime x (z * x + y)\n⊢ IsCoprime x y",
"tactic": "rw [add_comm] at h"
},
{
"state_after": "no goals",
"state... | [
221,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Set/Function.lean | Set.piecewise_insert | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73354\nγ : Type ?u.73357\nι : Sort ?u.73360\nπ : α → Type ?u.73365\nδ : α → Sort u_2\ns : Set α\nf g : (i : α) → δ i\ninst✝² : (j : α) → Decidable (j ∈ s)\ninst✝¹ : DecidableEq α\nj : α\ninst✝ : (i : α) → Decidable (i ∈ insert j s)\n⊢ (fun i => if i = j ∨ i ∈ s then f... | [
1380,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1373,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableAt.smul | [] | [
205,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.weak | [] | [
927,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
926,
1
] |
Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comap_comp | [
{
"state_after": "case h\nσ : Type u_2\nτ : Type u_3\nυ : Type u_4\nR : Type u_1\ninst✝ : CommSemiring R\nf : MvPolynomial σ R →ₐ[R] MvPolynomial τ R\ng : MvPolynomial τ R →ₐ[R] MvPolynomial υ R\nx : υ → R\n⊢ comap (AlgHom.comp g f) x = (comap f ∘ comap g) x",
"state_before": "σ : Type u_2\nτ : Type u_3\nυ ... | [
83,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/Covering.lean | IsCoveringMap.isLocallyHomeomorph | [] | [
169,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mex_le_lsub | [] | [
2035,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2034,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_add | [] | [
777,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.Neg.aux_of | [] | [
1193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atBot_mul_atTop | [
{
"state_after": "ι : Type ?u.197158\nι' : Type ?u.197161\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.197170\ninst✝ : StrictOrderedRing α\nl : Filter β\nf g : β → α\nhf : Tendsto f l atBot\nhg : Tendsto g l atTop\nthis : Tendsto (fun x => -f x * g x) l atTop\n⊢ Tendsto (fun x => f x * g x) l atBot",
"state_bef... | [
916,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_closedBall' | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2003002\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Nor... | [
460,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.toFractionRing_injective | [
{
"state_after": "K : Type u\ninst✝ : CommRing K\nx : FractionRing K[X]\n⊢ { toFractionRing := x } = { toFractionRing := { toFractionRing := x }.toFractionRing }",
"state_before": "K : Type u\ninst✝ : CommRing K\nx y : FractionRing K[X]\nxy : { toFractionRing := x }.toFractionRing = { toFractionRing := y }.... | [
136,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | iSup_eq_iSup_subseq_of_monotone | [] | [
322,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.tendstoUniformlyOn_iff | [] | [
628,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.FinMeasSupp.integrable | [] | [
382,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_eq_univ | [] | [
203,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.HD_below_aux2 | [] | [
313,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.induction_on_monomial | [
{
"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\nM : MvPolynomial σ R → Prop\nh_C : ∀ (a : R), M (↑C a)\nh_X : ∀ (p : MvPolynomial σ R) (n : σ), M p → M (p * ... | [
406,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.neg_im | [] | [
919,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
16
] |
Mathlib/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Functor.IsLocalization.of_equivalence_target | [
{
"state_after": "C : Type u_4\nD : Type u_6\ninst✝⁴ : Category C\ninst✝³ : Category D\nL : C ⥤ D\nW : MorphismProperty C\nE✝ : Type ?u.77743\ninst✝² : Category E✝\nE : Type u_1\ninst✝¹ : Category E\nL' : C ⥤ E\neq : D ≌ E\ninst✝ : IsLocalization L W\ne : L ⋙ eq.functor ≅ L'\nh : MorphismProperty.IsInvertedBy W... | [
435,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
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Mathlib/Topology/Separation.lean | exists_compact_superset_iff | [] | [
1309,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1306,
1
] |
Mathlib/Data/Setoid/Basic.lean | Quotient.subsingleton_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.22286\ns : Setoid α\n⊢ (∀ (x y : Quotient s), x = y) ↔ ∀ {x y : α}, ⊤ → Setoid.Rel s x y",
"state_before": "α : Type u_1\nβ : Type ?u.22286\ns : Setoid α\n⊢ Subsingleton (Quotient s) ↔ s = ⊤",
"tactic": "simp only [_root_.subsingleton_iff, eq_top_iff, Setoid.l... | [
468,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
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Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly.comp | [
{
"state_after": "case mk'.intro\np : ℕ\nR S : Type u\nσ : Type ?u.528965\nidx : Type ?u.528968\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ng f : ⦃R : Type u_1⦄ → [inst : CommRing R] → 𝕎 R → 𝕎 R\nhg : IsPoly p g\nφ : ℕ → MvPolynomial ℕ ℤ\nhf : ∀ ⦃R : Type u_1⦄ [inst : CommRing R] (x : 𝕎 R), (f x).coeff = fun n... | [
279,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Order/Hom/Basic.lean | WithBot.toDualTopEquiv_symm_bot | [] | [
1264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
Mathlib/Algebra/Order/Monoid/Defs.lean | Mul.to_covariantClass_right | [] | [
83,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.mem_ae_of_mem_ae_map | [] | [
2704,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2702,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsLowerSet.top_mem | [] | [
290,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Std/Data/List/Lemmas.lean | List.suffix_or_suffix_of_suffix | [] | [
1678,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1676,
1
] |
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