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/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.lift_reindex | [] | [
498,
48
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496,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_mapsTo | [] | [
175,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
11
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Mathlib/Analysis/NormedSpace/Units.lean | NormedRing.inverse_add_norm_diff_second_order | [
{
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213,
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209,
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.map_expand_pow_char | [
{
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262,
30
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256,
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Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | affineIndependent_iff_not_collinear_set | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type ?u.277216\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ : P\n⊢ ¬Collinear k (Set.range ![p₁, p₂, p₃]) ↔ ¬Collinear k {p₁, p₂, p₃}",
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89
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461,
1
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Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_right' | [
{
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},
{
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122,
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Mathlib/Data/List/Infix.lean | List.mem_of_mem_suffix | [] | [
510,
15
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509,
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Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.comp_f | [
{
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"tactic": "rfl"
}
] | [
124,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Mathlib/Topology/Category/Compactum.lean | Compactum.basic_inter | [
{
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"tactic": "ext G"
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{
"stat... | [
217,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
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Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.coe_injective | [] | [
459,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
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Mathlib/GroupTheory/Abelianization.lean | abelianizationCongr_of | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Data/Set/Image.lean | Subtype.range_val | [] | [
1400,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1399,
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.inverse_zero | [
{
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152,
43
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150,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.isOpen_sUnion_countable | [
{
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"tactic": "rwa... | [
738,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_spanSingleton | [
{
"state_after": "R : Type u_2\ninst✝⁶ : CommRing R\nS : Submonoid R\nP : Type u_1\ninst✝⁵ : CommRing P\ninst✝⁴ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1296088\ninst✝³ : CommRing R₁\nK : Type ?u.1296094\ninst✝² : Field K\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nx : P\n⊢ ↑{ val := span ... | [
1302,
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1300,
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.of_subsingleton | [
{
"state_after": "no goals",
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"tactic": "simp ... | [
209,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/Data/Complex/Exponential.lean | Real.sin_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sin 0 = 0",
"tactic": "simp [sin]"
}
] | [
1177,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_neg | [
{
"state_after": "no goals",
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"tactic": "rw [← neg_neg b, toIcoDiv_neg, neg_neg, neg_neg, neg_add', neg_neg, add_sub_c... | [
397,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_induction' | [
{
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542,
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Mathlib/Data/Complex/Exponential.lean | Real.exp_le_exp | [] | [
1525,
27
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1524,
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Colorable.mono | [
{
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"tactic": "simp [h]"
}
] | [
203,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.coeff_weightedHomogeneousComponent | [] | [
341,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.natDegree_mul_comm | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q✝ r : R[X]\nhp : Monic p\nq : R[X]\nh : q = 0\n⊢ natDegree (p * q) = natDegree (q * p)\n\ncase neg\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q✝ r : R[X]\nhp : Monic p\nq : ... | [
197,
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193,
1
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Mathlib/Algebra/Module/Basic.lean | Int.smul_one_eq_coe | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.325888\nR✝ : Type ?u.325891\nk : Type ?u.325894\nS : Type ?u.325897\nM : Type ?u.325900\nM₂ : Type ?u.325903\nM₃ : Type ?u.325906\nι : Type ?u.325909\nR : Type u_1\ninst✝ : Ring R\nm : ℤ\n⊢ m • 1 = ↑m",
"tactic": "rw [zsmul_eq_mul, mul_one]"
}
... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Image.lean | Finset.forall_mem_map | [
{
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91,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_inf | [] | [
1471,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1470,
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Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.coe_toNonUnitalAlgHom | [] | [
108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
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Std/Data/RBMap/Alter.lean | Std.RBNode.Path.zoom_zoomed₂ | [
{
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235,
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
227,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_sub_self | [
{
"state_after": "no goals",
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"tactic": "rw [toIcoMod, sub_sub_cancel_left, neg_smul]"
}
] | [
136,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/Topology/SubsetProperties.lean | ClosedEmbedding.compactSpace | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.96598\nπ : ι → Type ?u.96603\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nh : CompactSpace β\nf : α → β\nhf : ClosedEmbedding f\n⊢ IsCompact (range f)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.96598\nπ : ι → Type ?u... | [
940,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
11
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Iio_infinite | [] | [
81,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
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Mathlib/Analysis/Convex/Quasiconvex.lean | Monotone.quasiconcaveOn | [] | [
213,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_eq_one | [] | [
491,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
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Mathlib/MeasureTheory/MeasurableSpace.lean | exists_measurable_piecewise | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.93731\nδ : Type ?u.93734\nδ' : Type ?u.93737\nι✝ : Sort uι\ns t✝ u : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nmγ : MeasurableSpace γ\nι : Type u_1\ninst✝¹ : Countable ι\ninst✝ : Nonempty ι\nt : ι → Set α\nt_meas : ∀ (n : ι), MeasurableSet (t... | [
816,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_singleton_self | [
{
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"tactic": "rw [← cons_zero]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.25331\n... | [
344,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/LinearAlgebra/Projection.lean | Submodule.coe_prodEquivOfIsCompl' | [] | [
118,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addMonoidHom_comp | [
{
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228,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Connected.lean | Inducing.isPreconnected_image | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.24377\nπ : ι → Type ?u.24382\ninst✝¹ : TopologicalSpace α\ns✝ t u v : Set α\ninst✝ : TopologicalSpace β\ns : Set α\nf : α → β\nhf : Inducing f\nh : IsPreconnected (f '' s)\n⊢ IsPreconnected s",
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375,
23
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366,
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Mathlib/Topology/Constructions.lean | nhds_toAdd | [] | [
139,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Analysis/SpecificLimits/Normed.lean | tsum_geometric_of_abs_lt_1 | [] | [
314,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/Topology/Instances/RealVectorSpace.lean | map_real_smul | [] | [
30,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
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Mathlib/Order/Minimal.lean | maximals_singleton | [
{
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"tactic": "rintro b (rfl : b = a)"
},
{
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68,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/Analysis/Convex/Segment.lean | segment_eq_uIcc | [] | [
530,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.finish_isSpecial | [
{
"state_after": "u : XgcdType\nhs : u.wp + u.zp + u.wp * u.zp = u.x * u.y\n⊢ u.wp + (u.y * qp u + u.zp) + u.wp * (u.y * qp u + u.zp) = ((u.wp + 1) * qp u + u.x) * u.y",
"state_before": "u : XgcdType\nhs : IsSpecial u\n⊢ IsSpecial (finish u)",
"tactic": "dsimp [IsSpecial, finish] at hs⊢"
},
{
"s... | [
286,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.biUnion_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nt : (a : α) → a ∈ s → Set β\nhs : Set.Countable s\nthis : Countable ↑s\n⊢ Set.Countable (⋃ (a : α) (h : a ∈ s), t a h) ↔ ∀ (a : α) (ha : a ∈ s), Set.Countable (t a ha)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort... | [
201,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_le_one_iff_subset_singleton | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.54709\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : Nonempty α\nH : card s ≤ 1\n⊢ ∃ x, s ⊆ {x}\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.54709\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : Nonempty α\n⊢ (∃ x, s ⊆ {x}) → card s ≤ 1",
"state_before": "α... | [
551,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | OpenEmbedding.singletonChartedSpace_chartAt_eq | [] | [
1037,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.continuous_proj | [] | [
157,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.add_lt_add_right | [
{
"state_after": "case intro\ny z : PartENat\nhz : z ≠ ⊤\nm : ℕ\nh : ↑m < y\n⊢ ↑m + z < y + z",
"state_before": "x y z : PartENat\nh : x < y\nhz : z ≠ ⊤\n⊢ x + z < y + z",
"tactic": "rcases ne_top_iff.mp (ne_top_of_lt h) with ⟨m, rfl⟩"
},
{
"state_after": "case intro.intro\ny : PartENat\nm : ℕ\n... | [
469,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
11
] |
Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.hasse_preconnected_of_succ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.5179\ninst✝² : LinearOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\na b : α\n⊢ ReflTransGen (hasse α).Adj a b",
"state_before": "α : Type u_1\nβ : Type ?u.5179\ninst✝² : LinearOrder α\ninst✝¹ : SuccOrder α\ninst✝ : IsSuccArchimedean α\na b : α\n⊢ Reac... | [
91,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Std/Data/List/Lemmas.lean | List.pairwise_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nR : α → α → Prop\nl₁ l₂ : List α\n⊢ Pairwise R (l₁ ++ l₂) ↔ Pairwise R l₁ ∧ Pairwise R l₂ ∧ ∀ (a : α), a ∈ l₁ → ∀ (b : α), b ∈ l₂ → R a b",
"tactic": "induction l₁ <;> simp [*, or_imp, forall_and, and_assoc, and_left_comm]"
}
] | [
1289,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1287,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_iff_forall_nat_le | [] | [
436,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearEquiv.fst_comp_prodComm | [
{
"state_after": "no goals",
"state_before": "N : Type u_1\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.401591\nM₆ : Type ?u.401594\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst... | [
755,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augment_d_succ_succ | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_cons₂ | [] | [
1140,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.neg_imK | [] | [
252,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
9
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mk_d_1_0 | [
{
"state_after": "ι : Type ?u.323151\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nX₀ X₁ X₂ : V\nd₀ : X₀ ⟶ X₁\nd₁ : X₁ ⟶ X₂\ns : d₀ ≫ d₁ = 0\nsucc :\n (t : (X₀ : V) ×' (X₁ : V) ×' (X₂ : V) ×' (d₀ : X₀ ⟶ X₁) ×' (d₁ : X₁ ⟶ X₂) ×' d₀ ≫ d₁ = 0) →\n (X₃ : V) ×' (d₂ : t.snd.snd.fst ⟶ X₃) ×' t.snd.... | [
1010,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Algebra/MonoidAlgebra/Grading.lean | AddMonoidAlgebra.mem_grade_iff' | [
{
"state_after": "M : Type u_2\nι : Type ?u.7453\nR : Type u_1\ninst✝¹ : DecidableEq M\ninst✝ : CommSemiring R\nm : M\na : AddMonoidAlgebra R M\n⊢ (∃ b, a = Finsupp.single m b) ↔ a ∈ LinearMap.range (Finsupp.lsingle m)",
"state_before": "M : Type u_2\nι : Type ?u.7453\nR : Type u_1\ninst✝¹ : DecidableEq M\n... | [
80,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_take_mul_prod_drop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.51930\nα : Type ?u.51933\nM : Type u_1\nN : Type ?u.51939\nP : Type ?u.51942\nM₀ : Type ?u.51945\nG : Type ?u.51948\nR : Type ?u.51951\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na : M\ni : ℕ\n⊢ prod (take i []) * prod ... | [
170,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.of_le | [] | [
537,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.dvd_of_le_of_aleph0_le | [] | [
75,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.of_graph | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.161236\nγ : Type ?u.161239\nδ : Type ?u.161242\nσ : Type ?u.161245\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → ℕ\nh₂ : PrimrecRel fun a b => f a = b\ng : α → ℕ\npg : ... | [
812,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Order/SymmDiff.lean | sdiff_symmDiff_eq_sup | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.32704\nα : Type u_1\nβ : Type ?u.32710\nπ : ι → Type ?u.32715\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ (a \\ b) ∆ b = a ⊔ b",
"tactic": "rw [symmDiff_comm, symmDiff_sdiff_eq_sup, sup_comm]"
}
] | [
189,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Init/CcLemmas.lean | imp_eq_of_eq_false_right | [] | [
61,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.unique_ext | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.26168\nγ : Type ?u.26171\nι : Type ?u.26174\nM : Type u_2\nM' : Type ?u.26180\nN : Type ?u.26183\nP : Type ?u.26186\nG : Type ?u.26189\nH : Type ?u.26192\nR : Type ?u.26195\nS : Type ?u.26198\ninst✝¹ : Zero M\ninst✝ : Unique α\nf g : α ... | [
275,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_comp_mul_right_iff | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℝ → E\nc a : ℝ\nha : 0 < a\n⊢ IntegrableOn (fun x => f (x * a)) (Ioi c) ↔ IntegrableOn f (Ioi (c * a))",
"tactic": "simpa only [mul_comm, MulZeroClass.mul_zero] using integrableOn_Ioi_comp_mul_left_iff f c ha"
... | [
950,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.dvd_lcm_left | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ x ∣ 0",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nx y : R\nhxy : gcd x y = 0\n⊢ x ∣ lcm x y",
"tactic": "rw [lcm, hxy, div_zero]"
},
{
"state_after... | [
258,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.apply_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6289\nγ : Type ?u.6292\np : Pmf α\na : α\n⊢ ↑p a = 0 ↔ ¬a ∈ support p",
"tactic": "rw [mem_support_iff, Classical.not_not]"
}
] | [
106,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | gold_irrational | [
{
"state_after": "this : Irrational (sqrt ↑5)\n⊢ Irrational φ",
"state_before": "⊢ Irrational φ",
"tactic": "have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)"
},
{
"state_after": "this✝ : Irrational (sqrt ↑5)\nthis : Irrational (↑1 + sqrt ↑5)\n⊢ Irrational φ",
"state_before":... | [
147,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Relations.realize_antisymmetric | [] | [
1017,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.mono | [] | [
50,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.iUnion_toPrepartition | [] | [
77,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.firstDiff_le_longestPrefix | [
{
"state_after": "E : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\ns : Set ((n : ℕ) → E n)\nhs : IsClosed s\nx y : (n : ℕ) → E n\nhx : ¬x ∈ s\nhy : y ∈ s\n⊢ firstDiff x y + 1 ≤ shortestPrefixDiff x s\n\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace ... | [
542,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comapDomain_single | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nκ : Type u_1\ninst✝¹ : DecidableEq κ\ninst✝ : (i : ι) → Zero (β i)\nh : κ → ι\nhh : Function.Injective h\nk : κ\nx : β (h k)\ni : κ\n⊢ ↑(comapDomain h hh (single (h k) x)) i = ↑(single k x)... | [
1350,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1344,
1
] |
Std/Data/Option/Init/Lemmas.lean | Option.getD_some | [] | [
17,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
9
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.inv_mul_cancel | [] | [
2164,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2163,
11
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.symm_bijective | [] | [
842,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_symm | [] | [
575,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.integral_deterministic | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nι : Type ?u.401033\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nf : β → E\ng : α → β\na : α\nhg : Measur... | [
405,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.ne_cons_iff | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\na : α\nv : Vector α (Nat.succ n)\nv' : Vector α n\n⊢ v ≠ a ::ᵥ v' ↔ head v ≠ a ∨ tail v ≠ v'",
"tactic": "rw [Ne.def, eq_cons_iff a v v', not_and_or]"
}
] | [
71,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.ConcreteCategory.epi_iff_surjective_of_preservesPushout | [] | [
186,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Computability/Halting.lean | ComputablePred.halting_problem_not_re | [] | [
269,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.sdiff_fundamentalFrontier | [] | [
611,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
1
] |
Mathlib/Order/Basic.lean | lt_iff_le_and_ne | [] | [
378,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.cos_two_pi | [
{
"state_after": "no goals",
"state_before": "⊢ cos (2 * ↑π) = 1",
"tactic": "simp [two_mul, cos_add]"
}
] | [
1134,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakBilin.embedding | [] | [
136,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Heyting/Basic.lean | Codisjoint.himp_inf_cancel_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.74711\nα : Type u_1\nβ : Type ?u.74717\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\nh : Codisjoint a b\n⊢ b ⇨ a ⊓ b = a",
"tactic": "rw [himp_inf_distrib, himp_self, inf_top_eq, h.himp_eq_right]"
}
] | [
450,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.of_to_nat | [] | [
508,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.comp_symm_eq | [] | [
432,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.nextCoeff_X_sub_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c✝ d : R\nn m : ℕ\ninst✝² : Ring R\ninst✝¹ : Nontrivial R\ninst✝ : Ring S\nc : S\n⊢ nextCoeff (X - ↑C c) = -c",
"tactic": "rw [sub_eq_add_neg, ← map_neg C c, nextCoeff_X_add_C]"
}
] | [
1478,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
] |
Mathlib/Data/Finset/MulAntidiagonal.lean | Finset.isPwo_support_mulAntidiagonal | [] | [
113,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.int_cast_eq_int_cast_iff' | [] | [
463,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.map_lfp | [] | [
82,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumElim_apply | [] | [
1319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.right_mem_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5009\ninst✝ : Preorder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ b ∈ Ico a b ↔ False",
"tactic": "simp [lt_irrefl]"
}
] | [
213,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.MultispanIndex.multispan_obj_right | [] | [
276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_zero | [] | [
286,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Comonad.Coalgebra.id_f | [] | [
411,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.l_unique | [] | [
218,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Subgroup.rank_closure_finite_le_nat_card | [
{
"state_after": "M : Type ?u.118917\nN : Type ?u.118920\ninst✝⁴ : Monoid M\ninst✝³ : AddMonoid N\nG : Type u_1\nH : Type ?u.118932\ninst✝² : Group G\ninst✝¹ : AddGroup H\ns : Set G\ninst✝ : Finite ↑s\nthis : Fintype ↑s\n⊢ Group.rank { x // x ∈ closure s } ≤ Nat.card ↑s",
"state_before": "M : Type ?u.118917... | [
460,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
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