file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_le_of_le_left | [] | [
400,
73
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398,
1
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Mathlib/Data/Set/Image.lean | Set.isCompl_range_some_none | [] | [
1187,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.two_le_length_toList_iff_mem_support | [
{
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"tactic": "simp"
}
] | [
242,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
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Mathlib/Algebra/Group/Ext.lean | CommMonoid.toMonoid_injective | [
{
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"state_before": "M : Type u\n⊢ Function.Injective (@toMonoid M)",
"tactic": "r... | [
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48,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_inf | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.122332\n𝕜 : Type ?u.122335\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑(edgeSet G)\ninst✝² : Fintype ↑(edgeSet G₁)\ninst✝¹ : Fintype ↑(edgeSet G₂)\... | [
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20
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Mathlib/Algebra/Hom/Group.lean | OneHom.comp_apply | [] | [
1113,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
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Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_id | [
{
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283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_vec_bit1_eq_alt1 | [
{
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"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.49849\nn' : Type ?u.49852\no' : Type ?u.49855\nx : α\nu : Fin n →... | [
379,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.add_mul | [
{
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"tactic": "simp only [coeff_mul, add_mul, Finset.sum_add_distrib, LinearMap.map_... | [
282,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
11
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Mathlib/FieldTheory/Subfield.lean | SubfieldClass.rat_smul_mem | [
{
"state_after": "no goals",
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"tactic": "simpa only [Rat.smul_def] using mul_mem (coe_rat_m... | [
108,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.mem_sub_of_nodup | [
{
"state_after": "α : Type u_1\nβ : Type ?u.20962\nγ : Type ?u.20965\nr : α → α → Prop\ns✝ t✝ : Multiset α\na✝ : α\ninst✝ : DecidableEq α\na : α\ns t : Multiset α\nd : Nodup s\nh : a ∈ s - t\nh' : a ∈ t\n⊢ count a (s - t) = 0",
"state_before": "α : Type u_1\nβ : Type ?u.20962\nγ : Type ?u.20965\nr : α → α →... | [
255,
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_nonneg | [] | [
101,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
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Mathlib/Topology/Order/Basic.lean | Dense.Ioi_eq_biUnion | [
{
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"state_before": "α : Type u\nβ : Ty... | [
798,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
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Mathlib/Data/List/Lattice.lean | List.forall_mem_of_forall_mem_union_left | [] | [
126,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Data/Fin/Basic.lean | Fin.mk_bit0 | [] | [
768,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_hom | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.39786\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.39795\ninst✝² : CommMonoid α\ns✝ t : Multiset α\na : α\nm : Multiset ι\nf✝ g : ι → α\ninst✝¹ : CommMonoid β\ns : Multiset α\nF : Type u_3\ninst✝ : MonoidHomClass F α β\nf : F\nl : List α\n⊢ prod (map (↑f... | [
161,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Lattice.lean | Set.iInter_and | [] | [
777,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_C_mul_X' | [
{
"state_after": "no goals",
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"tactic": "simpa only [C_mul_X_eq_monomial] using support_monomial' 1 c"
}
] | [
849,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.exists_coprime_of_gcd_pos | [
{
"state_after": "case intro.intro.intro.intro\nd : ℤ\na : ℤ√d\nhgcd : 0 < Int.gcd a.re a.im\nre im : ℤ\nH1 : Int.gcd re im = 1\nHre : a.re = re * ↑(Int.gcd a.re a.im)\nHim : a.im = im * ↑(Int.gcd a.re a.im)\n⊢ ∃ b, a = ↑↑(Int.gcd a.re a.im) * b ∧ IsCoprime b.re b.im",
"state_before": "d : ℤ\na : ℤ√d\nhgcd ... | [
422,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
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Mathlib/Topology/MetricSpace/Basic.lean | nndist_pi_def | [] | [
1988,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
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Mathlib/Data/Finset/Basic.lean | Finset.self_mem_range_succ | [] | [
3018,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3017,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_eq_zero_iff | [] | [
850,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fintype/BigOperators.lean | Finset.prod_toFinset_eq_subtype | [
{
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"state_before": "α : Type u_2\nβ : Type ?u.57115\nγ : Type ?u.57118\nM : Ty... | [
252,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
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Mathlib/Data/List/Infix.lean | List.inits_append | [
{
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"tactic": "simp"
}
] | [
383,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_mem_iff | [
{
"state_after": "no goals",
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673,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
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Mathlib/Algebra/Group/Basic.lean | leftInverse_div_mul_left | [] | [
855,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
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Std/Logic.lean | Bool.eq_false_iff | [] | [
768,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
767,
1
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Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | FreeAlgebra.toTensor_ι | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommSemiring R\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\n⊢ ↑toTensor (ι R m) = ↑(TensorAlgebra.ι R) m",
"tactic": "simp [toTensor]"
}
] | [
323,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.apply_eq_prod_smul_coeff | [
{
"state_after": "case h.e'_2.h.e'_1.h\n𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz z₀ : 𝕜\ny : Fin n → 𝕜\nx✝ : Fin n\n⊢ y x✝ = y x... | [
282,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/RingTheory/Valuation/Quotient.lean | Valuation.supp_quot | [
{
"state_after": "case a\nR : Type u_1\nΓ₀ : Type u_2\ninst✝¹ : CommRing R\ninst✝ : LinearOrderedCommMonoidWithZero Γ₀\nv : Valuation R Γ₀\nJ : Ideal R\nhJ : J ≤ supp v\n⊢ supp (onQuot v hJ) ≤ Ideal.map (Ideal.Quotient.mk J) (supp v)\n\ncase a\nR : Type u_1\nΓ₀ : Type u_2\ninst✝¹ : CommRing R\ninst✝ : LinearOrd... | [
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13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/GroupTheory/NoncommPiCoprod.lean | Subgroup.independent_of_coprime_order | [
{
"state_after": "no goals",
"state_before": "G : Type u_2\ninst✝² : Group G\nι : Type u_1\nhdec : DecidableEq ι\nhfin : Fintype ι\nH : ι → Subgroup G\nf g : (i : ι) → { x // x ∈ H i }\nhcomm : ∀ (i j : ι), i ≠ j → ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\ninst✝¹ : Finite ι\ninst✝ : (i : ι) → Fintype { ... | [
346,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.op_comp | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nontrivial_of_exists_lt | [] | [
2508,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2505,
1
] |
Mathlib/Data/Countable/Defs.lean | Countable.of_equiv | [] | [
72,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_diagonal_right | [
{
"state_after": "case a.mk.h.mk\nR : Type ?u.10684\nα : Type u_6\nα' : Type ?u.10690\nβ : Type u_1\nβ' : Type ?u.10696\nγ : Type u_2\nγ' : Type ?u.10702\nl : Type u_4\nm : Type u_5\nn : Type u_3\np : Type ?u.10714\nq : Type ?u.10717\nr : Type ?u.10720\nl' : Type ?u.10723\nm' : Type ?u.10726\nn' : Type ?u.10729... | [
139,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.le_iInf_lintegral | [
{
"state_after": "α : Type u_2\nβ : Type ?u.283804\nγ : Type ?u.283807\nδ : Type ?u.283810\nm : MeasurableSpace α\nμ ν : Measure α\nι : Sort u_1\nf : ι → α → ℝ≥0∞\n⊢ (∫⁻ (a : α), iInf (fun i => f i) a ∂μ) ≤ ⨅ (i : ι), ∫⁻ (a : α), f i a ∂μ",
"state_before": "α : Type u_2\nβ : Type ?u.283804\nγ : Type ?u.2838... | [
286,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Topology/Maps.lean | OpenEmbedding.continuous | [] | [
578,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | Memℓp.add | [
{
"state_after": "case inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf g : (i : α) → E i\nhf : Memℓp f 0\nhg : Memℓp g 0\n⊢ Memℓp (f + g) 0\n\ncase inr.inl\nα : Type u_1\nE : α → Type u_2\nq : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf g : (i : α) → E i\nhf ... | [
246,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_Iio_atTop | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\na b : α\ns : Set α\nl : Filter β\nf✝ : α → β\nf : β → ↑(Iio a)\n⊢ Tendsto (Subtype.val ∘ f) l (𝓝[Iio a] a) ↔ Tendsto (fun x => ↑(f x)) l (𝓝[Iio a] a)",... | [
2578,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2576,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.hasDerivAt_arcsin | [] | [
62,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Computability/Encoding.lean | Computability.unary_decode_encode_nat | [] | [
202,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/Order/Basic.lean | Monotone.map_iSup_of_continuousAt | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁶ : CompleteLinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : CompleteLinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderClosedTopology β\ninst✝ : Nonempty γ\nι : Sort u_1\nf : α → β\ng : ι → α\nCf : ContinuousAt f (i... | [
2674,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2671,
1
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Mathlib/RepresentationTheory/Basic.lean | Representation.asModuleEquiv_map_smul | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero | [] | [
243,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.nodup_of_pairwise_disjoint_cycles | [] | [
583,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Monotone.lean | Real.log_mul_self_monotoneOn | [
{
"state_after": "x y : ℝ\n⊢ ∀ ⦃a : ℝ⦄, 1 ≤ a → ∀ ⦃b : ℝ⦄, 1 ≤ b → a ≤ b → log a * a ≤ log b * b",
"state_before": "x y : ℝ\n⊢ MonotoneOn (fun x => log x * x) {x | 1 ≤ x}",
"tactic": "simp only [MonotoneOn, mem_setOf_eq]"
},
{
"state_after": "x✝ y✝ x : ℝ\nhex : 1 ≤ x\ny : ℝ\nhey : 1 ≤ y\nhxy : x... | [
42,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/List/Range.lean | List.get_finRange | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn i : ℕ\nh : i < length (finRange n)\n⊢ get (finRange n) { val := i, isLt := h } = { val := i, isLt := (_ : i < n) }",
"tactic": "simp only [finRange, get_range, get_pmap]"
}
] | [
210,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.eq_iff_prime_padicValNat_eq | [
{
"state_after": "case mp\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a = b → ∀ (p : ℕ), Prime p → padicValNat p a = padicValNat p b\n\ncase mpr\na b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ (∀ (p : ℕ), Prime p → padicValNat p a = padicValNat p b) → a = b",
"state_before": "a b : ℕ\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a = b ↔ ∀ (p : ℕ... | [
919,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Data/Int/Parity.lean | Int.two_not_dvd_two_mul_add_one | [
{
"state_after": "no goals",
"state_before": "m n✝ n : ℤ\n⊢ ¬2 ∣ 2 * n + 1",
"tactic": "simp [add_emod]"
}
] | [
122,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_le | [] | [
670,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.eqvGen_rel_eq | [
{
"state_after": "case h.h.a\nR : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr : R → R → Prop\nx₁ x₂ : R\n⊢ EqvGen (Rel r) x₁ x₂ ↔ RingConGen.Rel r x₁ x₂",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² :... | [
146,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Algebra/Squarefree.lean | Squarefree.ne_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : MonoidWithZero R\ninst✝ : Nontrivial R\nhm : Squarefree 0\n⊢ False",
"state_before": "R : Type u_1\ninst✝¹ : MonoidWithZero R\ninst✝ : Nontrivial R\nm : R\nhm : Squarefree m\n⊢ m ≠ 0",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"state_befo... | [
62,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Relabelling.equiv | [] | [
1120,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.order_dual | [] | [
66,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
11
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.quot_out | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.3437948\nα : Type u_1\ninst✝ : CommMonoid α\na : Associates α\n⊢ Associates.mk (Quot.out a) = a",
"tactic": "rw [← quot_mk_eq_mk, Quot.out_eq]"
}
] | [
1903,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1902,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_exists_right_inv | [] | [
952,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | cauchySeq_range_of_norm_bounded | [
{
"state_after": "ι : Type ?u.7861\nα : Type ?u.7864\nE : Type u_1\nF : Type ?u.7870\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : SeminormedAddCommGroup F\nf : ℕ → E\ng : ℕ → ℝ\nhg : CauchySeq fun n => ∑ i in range n, g i\nhf : ∀ (i : ℕ), ‖f i‖ ≤ g i\nε : ℝ\nhε : ε > 0\n⊢ ∃ N, ∀ (n : ℕ), n ≥ N → dist (∑ i in ran... | [
91,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/List/Zip.lean | List.zip_append | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type ?u.20405\nδ : Type ?u.20408\nε : Type ?u.20411\nr₁ : List α\nl₂ r₂ : List β\nh : length [] = length l₂\n⊢ zip ([] ++ r₁) ([] ++ r₂) = zip [] [] ++ zip r₁ r₂",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.20405\nδ : Type ?u.20408\nε : Type ?u.204... | [
119,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.irreducible_X | [] | [
428,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_le_coe_add_dist | [] | [
1038,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1037,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryCofan.ι_app_right | [] | [
267,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_iff_eventually | [] | [
1112,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1110,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Icc_succ_left | [] | [
387,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Topology/ContinuousOn.lean | IsOpenMap.continuousOn_image_of_leftInvOn | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.329305\nδ : Type ?u.329308\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns : Set α\nh : IsOpenMap (Set.restrict s f)\nfinv : β → α\nhleft : LeftInvOn finv f ... | [
813,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.lift_injective | [
{
"state_after": "R : Type\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nd : ℤ\nr : { r // r * r = ↑d }\nhd : ∀ (n : ℤ), d ≠ n * n\na : ℤ√d\nha : ↑(↑lift r) a = 0\nh_inj : Function.Injective Int.cast\n⊢ a = 0",
"state_before": "R : Type\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nd : ℤ\nr : { r // r * r = ↑d }\nh... | [
1077,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Init/Logic.lean | exists_unique_of_exists_of_unique | [] | [
243,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAsLocalEquiv_target | [] | [
670,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousAt.zpow | [] | [
543,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/TwoPointing.lean | TwoPointing.pi_snd | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq_map_apply | [] | [
1563,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1560,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeightsIndicator_eq_one_of_card_eq_add_one | [
{
"state_after": "k : Type u_1\nV : Type ?u.518014\nP : Type ?u.518017\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.518536\ns₂ : Finset ι₂\ninst✝¹ : CharZero k\ninst✝ : Fintype ι\nn : ℕ\nh : card s = n + 1\n⊢ ∑ i in s,... | [
936,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
933,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real_nonneg | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.78208\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nr : ℝ≥0\n⊢ toJordanDecomposition (↑r • s) = ↑r • toJordanDecomposition s",
"state_before": "α : Type u_1\nβ : Type ?u.78208\ninst✝ : MeasurableSpace α\ns : SignedMeasure α\nr : ℝ\nhr : 0 ≤ r\n⊢ toJ... | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
9
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.sup_eq_add | [] | [
476,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.sub | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.136181\ninst✝⁴ : OrderedRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\ns t : Set E\nhs : StarConvex 𝕜 x s\nht : StarConvex 𝕜 y t\n⊢ StarConvex 𝕜 (x + -y) (s + -t)",
"state_before": "... | [
378,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Set/Basic.lean | Set.ssubset_iff_of_subset | [] | [
412,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.exists_elementarilyEquivalent_card_eq | [
{
"state_after": "case intro.intro.inl\nL : Language\nT : Theory L\nα : Type w\nn : ℕ\nM : Type w'\ninst✝¹ : Structure L M\ninst✝ : Infinite M\nκ : Cardinal\nh1 : ℵ₀ ≤ κ\nh2 : lift (card L) ≤ lift κ\nN : Bundled (Structure L)\nhNκ : (#↑N) = κ\nNM : Nonempty (↑N ↪ₑ[L] M)\n⊢ ∃ N, (M ≅[L] ↑N) ∧ (#↑N) = κ\n\ncase i... | [
283,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Deprecated/Group.lean | Multiplicative.isMonoidHom | [] | [
462,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/LinearAlgebra/Ray.lean | units_smul_eq_neg_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝³ : LinearOrderedCommRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : NoZeroSMulDivisors R M\nu : Rˣ\nv : Module.Ray R M\n⊢ u • v = -v ↔ ↑u < 0",
"tactic": "rw [← neg_inj, neg_neg, ← Module.Ray.neg_units_smul, un... | [
587,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Topology/MetricSpace/ShrinkingLemma.lean | exists_locallyFinite_subset_iUnion_ball_radius_lt | [
{
"state_after": "α : Type u\nι : Type v\ninst✝¹ : MetricSpace α\ninst✝ : ProperSpace α\nc : ι → α\nx : α\nr : ℝ\ns : Set α\nhs : IsClosed s\nR : α → ℝ\nhR : ∀ (x : α), x ∈ s → 0 < R x\nthis : ∀ (x : α), x ∈ s → Filter.HasBasis (𝓝 x) (fun r => 0 < r ∧ r < R x) fun r => ball x r\n⊢ ∃ ι c r r',\n (∀ (i : ι), ... | [
109,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.tendsto_approxOn_L1_nnnorm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.930924\nβ : Type u_2\nι : Type ?u.930930\nE : Type u_1\nF : Type ?u.930936\n𝕜 : Type ?u.930939\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns :... | [
245,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Deprecated/Ring.lean | IsSemiringHom.to_isMonoidHom | [] | [
77,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | ofAdd_image_multiples_eq_powers_ofAdd | [
{
"state_after": "M : Type ?u.302290\nA : Type u_1\nB : Type ?u.302296\ninst✝ : AddMonoid A\nx : A\n⊢ ↑(Submonoid.powers (↑Multiplicative.ofAdd x)) = ↑Multiplicative.ofAdd '' ↑(AddSubmonoid.multiples x)",
"state_before": "M : Type ?u.302290\nA : Type u_1\nB : Type ?u.302296\ninst✝ : AddMonoid A\nx : A\n⊢ ↑M... | [
714,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Topology/Order.lean | nhds_inf | [] | [
672,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/RingTheory/FiniteType.lean | Algebra.FiniteType.polynomial | [
{
"state_after": "R : Type u_1\nA : Type u\nB : Type ?u.8031\nM : Type ?u.8034\nN : Type ?u.8037\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup N\ninst✝ : Module R N\n⊢ adjoin R {X} =... | [
84,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/Data/List/OfFn.lean | List.exists_iff_exists_tuple | [] | [
269,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.eq_bot_of_card_eq | [] | [
157,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.sub_val | [
{
"state_after": "ι : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁵ : AddCommMonoid ι\ninst✝⁴ : DecidableEq ι\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nx : Submonoid A\ny1 y2 : HomogeneousLocalization 𝒜 x\n⊢ val y1 + -val y2 = val y1 - val... | [
444,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_mul_div_right | [
{
"state_after": "no goals",
"state_before": "x y z : Nat\nH : 0 < z\n⊢ (x + y * z) / z = x / z + y",
"tactic": "rw [Nat.mul_comm, add_mul_div_left _ _ H]"
}
] | [
586,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
585,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.zipWith_apply | [] | [
952,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.arctan_neg | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arctan (-x) = -arctan x",
"tactic": "simp [arctan_eq_arcsin, neg_div]"
}
] | [
189,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/Group/Units.lean | isUnit_of_mul_isUnit_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.62918\ninst✝ : CommMonoid M\nx y : M\nhu : IsUnit (x * y)\nz : M\nhz : x * y * z = 1\n⊢ x * (y * z) = 1",
"tactic": "rwa [← mul_assoc]"
}
] | [
697,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndunion_le_add | [] | [
176,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_hyperplane | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.82526\nβ : Type u_3\ninst✝⁷ : OrderedSemiring 𝕜\ninst✝⁶ : AddCommMonoid E\ninst✝⁵ : AddCommMonoid F\ninst✝⁴ : Module 𝕜 E\ninst✝³ : Module 𝕜 F\ns : Set E\nx : E\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : Module 𝕜 β\ninst✝ : OrderedSMul 𝕜 β\nf : E → ... | [
269,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.moebius_apply_isPrimePow_not_prime | [
{
"state_after": "case intro.intro.intro.intro\nR : Type ?u.591476\np k : ℕ\nhp : Prime p\nhk : 0 < k\nhn : IsPrimePow (p ^ k)\nhn' : ¬Prime (p ^ k)\n⊢ ↑μ (p ^ k) = 0",
"state_before": "R : Type ?u.591476\nn : ℕ\nhn : IsPrimePow n\nhn' : ¬Prime n\n⊢ ↑μ n = 0",
"tactic": "obtain ⟨p, k, hp, hk, rfl⟩ := (i... | [
1000,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.hasFDerivAtFilter_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.474760\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
839,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Analysis/Convex/Strict.lean | StrictConvex.mem_smul_of_zero_mem | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.228762\nE : Type u_2\nF : Type ?u.228768\nβ : Type ?u.228771\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nx : E\nhs : StrictConvex 𝕜 s\nzero_mem... | [
421,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsSymm.ortho_comm | [] | [
912,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mulEquivOfQuotient_apply | [] | [
1691,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1690,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.norm_unitary_smul | [] | [
245,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_map | [] | [
219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
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