file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Real/CauSeq.lean | IsCauSeq.cauchy₃ | [] | [
116,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes | [
{
"state_after": "R✝ : Type u\ninst✝¹ : CommRing R✝\nR : Type u_1\ninst✝ : CommRing R\nx y : PrimeSpectrum R\nh : x ⤳ y\n⊢ (toOpen R ⊤ ≫ germ (Sheaf.presheaf (structureSheaf R)) { val := y, property := True.intro }) ≫\n stalkSpecializes (Sheaf.presheaf (structureSheaf R)) h =\n toOpen R ⊤ ≫ germ (Sheaf.... | [
1022,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
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Mathlib/Data/Finset/Basic.lean | Finset.coe_union | [] | [
1367,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1366,
1
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_le_edist_of_mem | [] | [
87,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/CategoryTheory/NatTrans.lean | CategoryTheory.congr_app | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF G : C ⥤ D\nα β : NatTrans F G\nh : α = β\nX : C\n⊢ α.app X = β.app X",
"tactic": "aesop_cat"
}
] | [
70,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_eq_zero_of_differentiableOn_of_addHaar_eq_zero | [
{
"state_after": "E : Type u_1\nF : Type ?u.556355\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ ... | [
603,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/Bool/Set.lean | Bool.range_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : Bool → α\n⊢ range f = {f false, f true}",
"tactic": "rw [← image_univ, univ_eq, image_pair]"
}
] | [
32,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.ofStream_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl : List α\ns : Stream' α\n⊢ ↑(l ++ₛ s) = append ↑l ↑s",
"tactic": "induction l <;> simp [*, Stream'.nil_append_stream, Stream'.cons_append_stream]"
}
] | [
826,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Order/Bounds/Basic.lean | AntitoneOn.mem_lowerBounds_image | [] | [
1221,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
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Mathlib/Data/Finset/Image.lean | Finset.range_sdiff_zero | [
{
"state_after": "case zero\nα : Type ?u.151859\nβ : Type ?u.151862\nγ : Type ?u.151865\n⊢ range (Nat.zero + 1) \\ {0} = image Nat.succ (range Nat.zero)\n\ncase succ\nα : Type ?u.151859\nβ : Type ?u.151862\nγ : Type ?u.151865\nk : ℕ\nhk : range (k + 1) \\ {0} = image Nat.succ (range k)\n⊢ range (Nat.succ k + 1)... | [
763,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.eq_iff_abs_toReal_eq_of_sign_eq | [
{
"state_after": "no goals",
"state_before": "θ ψ : Angle\nh : sign θ = sign ψ\n⊢ θ = ψ ↔ abs (toReal θ) = abs (toReal ψ)",
"tactic": "simpa [h] using @eq_iff_sign_eq_and_abs_toReal_eq θ ψ"
}
] | [
966,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | matPolyEquiv_coeff_apply_aux_2 | [
{
"state_after": "case refine_1\nR : Type u_1\nA : Type ?u.521163\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\ni j : n\np : R[X]\nk : ℕ\n⊢ ∀ (p q : R[X]),\n coeff (↑matPolyEquiv (stdBasisMatrix i j p)) k = stdBasisMatrix i j (coef... | [
257,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.epsilon_mul_omega | [] | [
198,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subset_left_of_subset_union | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.29699\nπ : ι → Type ?u.29704\ninst✝ : TopologicalSpace α\ns t u v : Set α\nhu : IsOpen u\nhv : IsOpen v\nhuv : Disjoint u v\nhsuv : s ⊆ u ∪ v\nhsu : Set.Nonempty (s ∩ u)\nhs : IsPreconnected s\nhsv : ¬Disjoint s v\n⊢ False",
"state_before": "α : Type u\n... | [
436,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_iff_integrable | [] | [
369,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.powerlt_mono_left | [] | [
2298,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2298,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_inv | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
11
] |
Mathlib/Order/SymmDiff.lean | symmDiff_assoc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.71775\nα : Type u_1\nβ : Type ?u.71781\nπ : ι → Type ?u.71786\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b ∆ c = a ∆ (b ∆ c)",
"tactic": "rw [symmDiff_symmDiff_left, symmDiff_symmDiff_right]"
}
] | [
478,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toSubMulAction_strictMono | [] | [
167,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Functor.map_injective | [] | [
78,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.subsingleton_reverse_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Cycle α\n⊢ Subsingleton (reverse s) ↔ Subsingleton s",
"tactic": "simp [length_subsingleton_iff]"
}
] | [
606,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_sub_one_of_lt | [] | [
1264,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1264,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulHom.prod_apply | [] | [
354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.neighborSet_subgraphOfAdj_subset | [] | [
938,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_pow | [] | [
157,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec2_add | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝ : Add α\na₀ a₁ b₀ b₁ : α\n⊢ ![a₀, a₁] + ![b₀, b₁] = ![a₀ + b₀, a₁ + b₁]",
"tactic": "rw [cons_add_cons, cons_add_cons, empty_add_empty]"
}
] | [
471,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.injective_of_isPartialInv_right | [] | [
324,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.natDegree_sub_eq_of_prod_eq | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : Semiring R\ninst✝ : NoZeroDivisors R\np q p₁ p₂ q₁ q₂ : R[X]\nhp₁ : p₁ ≠ 0\nhq₁ : q₁ ≠ 0\nhp₂ : p₂ ≠ 0\nhq₂ : q₂ ≠ 0\nh_eq : p₁ * q₂ = p₂ * q₁\n⊢ ↑(natDegree p₁) + ↑(natDegree q₂) = ↑(natDegree p₂) + ↑(natDegree q₁)",
"state_befo... | [
208,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.nnnorm_le_of_ae_bound | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type ?u.431143\nG : Type ?u.431146\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : IsFiniteMeasure μ\nf : { x // x ∈ Lp E p }\nC : ℝ≥0\nhf... | [
423,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Topology/SubsetProperties.lean | exists_preirreducible | [] | [
1758,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essInf_eq_sSup | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nm✝ : MeasurableSpace α\nμ✝ ν : MeasureTheory.Measure α\ninst✝ : ConditionallyCompleteLinearOrder β\nx : β\nf✝ : α → β\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf : α → β\n⊢ sSup {a | ∀ᶠ (n : β) in map f (Measure.ae μ), a ≤ n} = sSup {a | ↑↑μ {x | f x < a}... | [
100,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.basisRepr_apply | [
{
"state_after": "S : Type ?u.690539\nR : Type u_1\nR₁ : Type ?u.690545\nM : Type u_2\nM₁ : Type ?u.690551\ninst✝⁶ : Semiring R\ninst✝⁵ : CommSemiring R₁\ninst✝⁴ : AddCommMonoid M\ninst✝³ : AddCommMonoid M₁\ninst✝² : Module R M\ninst✝¹ : Module R M₁\nι : Type u_3\ninst✝ : Fintype ι\nv : Basis ι R M\nQ : Quadrat... | [
1151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1148,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.valid_endPos | [
{
"state_after": "no goals",
"state_before": "s : String\n⊢ s.data ++ [] = s.data",
"tactic": "simp"
}
] | [
153,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
153,
9
] |
Mathlib/Analysis/Convex/Segment.lean | right_mem_segment | [] | [
122,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_inv_smul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : Group α\ninst✝ : MulAction α β\nc : α\nx : β\n⊢ c • c⁻¹ • x = x",
"tactic": "rw [smul_smul, mul_right_inv, one_smul]"
}
] | [
45,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Zero.lean | CategoryTheory.Functor.zero_of_map_zero | [] | [
61,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.inv_re | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5379086\ninst✝ : IsROrC K\nz : K\n⊢ ↑re z⁻¹ = ↑re z / ↑normSq z",
"tactic": "rw [inv_def, normSq_eq_def', mul_comm, ofReal_mul_re, conj_re, div_eq_inv_mul]"
}
] | [
556,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Data/Set/Basic.lean | Set.symmDiff_eq_empty | [] | [
2106,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2105,
1
] |
Mathlib/Algebra/LinearRecurrence.lean | LinearRecurrence.sol_eq_of_eq_init | [
{
"state_after": "α : Type u_1\ninst✝ : CommSemiring α\nE : LinearRecurrence α\nu v : ℕ → α\nhu : IsSolution E u\nhv : IsSolution E v\n⊢ Set.EqOn u v ↑(range E.order) → u = v",
"state_before": "α : Type u_1\ninst✝ : CommSemiring α\nE : LinearRecurrence α\nu v : ℕ → α\nhu : IsSolution E u\nhv : IsSolution E ... | [
169,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Antitone.concaveOn_univ_of_deriv | [] | [
1147,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
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Mathlib/Analysis/SpecialFunctions/NonIntegrable.lean | intervalIntegrable_sub_inv_iff | [
{
"state_after": "case mp\nE : Type ?u.34598\nF : Type ?u.34601\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : SecondCountableTopology E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedAddCommGroup F\na b c : ℝ\n⊢ IntervalIntegrable (fun x => (x - c)⁻¹) volume a b → a = b ∨ ¬c ∈ [[a, b]]\n\ncase mp... | [
170,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.Cocone.w | [
{
"state_after": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u₃\ninst✝¹ : Category C\nD : Type u₄\ninst✝ : Category D\nF : J ⥤ C\nc : Cocone F\nj j' : J\nf : j ⟶ j'\n⊢ c.ι.app j ≫ ((const J).obj c.pt).map f = c.ι.app j",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK ... | [
182,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasStrictDerivAt.cpow | [
{
"state_after": "no goals",
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"tactic": "simp... | [
157,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
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] |
src/lean/Init/Data/Array/BasicAux.lean | Array.of_push_eq_push | [
{
"state_after": "α : Type u_1\na b : α\nas bs : Array α\nh : List.concat as.data a = List.concat bs.data b\n⊢ as = bs ∧ a = b",
"state_before": "α : Type u_1\na b : α\nas bs : Array α\nh : push as a = push bs b\n⊢ as = bs ∧ a = b",
"tactic": "simp [push] at h"
},
{
"state_after": "α : Type u_1\... | [
15,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
11,
1
] |
Mathlib/Order/Lattice.lean | inf_sup_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DistribLattice α\nx y z : α\n⊢ x ⊓ (y ⊔ z) = x ⊓ (x ⊔ z) ⊓ (y ⊔ z)",
"tactic": "rw [inf_sup_self]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : DistribLattice α\nx y z : α\n⊢ x ⊓... | [
774,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.coe_constVSub_symm | [] | [
473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_triangle4 | [] | [
125,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.frange_one | [
{
"state_after": "R : Type u\nS : Type ?u.46907\ninst✝ : Semiring R\n⊢ image (fun n => coeff 1 n) (support 1) ⊆ {1}",
"state_before": "R : Type u\nS : Type ?u.46907\ninst✝ : Semiring R\n⊢ frange 1 ⊆ {1}",
"tactic": "simp only [frange]"
},
{
"state_after": "R : Type u\nS : Type ?u.46907\ninst✝ : ... | [
205,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Mathlib/Data/Nat/Prime.lean | Nat.minFac_eq_two_iff | [
{
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"tactic": "constructor"
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{
"state_after": "case mp\nn : ℕ\nh : minFac n = 2\n⊢ 2 ∣ n",
"state_before": "case mp\nn : ℕ\n⊢ minFac n = 2 → 2 ... | [
445,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
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Mathlib/Data/Nat/Log.lean | Nat.log_le_clog | [
{
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"state_before": "b n : ℕ\n⊢ log b n ≤ clog b n",
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{
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367,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.le_of_lt | [] | [
284,
18
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283,
11
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Mathlib/Data/Multiset/Basic.lean | Multiset.coe_add | [] | [
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6
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622,
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Mathlib/Data/Num/Lemmas.lean | Num.succ'_to_nat | [] | [
295,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
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Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_singleton | [
{
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}
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191,
80
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191,
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Mathlib/Order/Closure.lean | ClosureOperator.closure_sup_closure_le | [] | [
253,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
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Mathlib/Data/Seq/Computation.lean | Computation.liftRel_map | [
{
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"state_befo... | [
1234,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
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Mathlib/Data/Fin/Basic.lean | Fin.bot_eq_zero | [] | [
560,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
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Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_inf | [] | [
128,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.units_lineMap | [
{
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267,
35
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263,
1
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Mathlib/Data/List/Sigma.lean | List.dlookup_kinsert | [
{
"state_after": "no goals",
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"tactic": "simp only [kinsert, dlookup_cons_eq]"
}
] | [
590,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
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Mathlib/Algebra/Order/Pointwise.lean | csInf_div | [
{
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172,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
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Mathlib/Order/LiminfLimsup.lean | Filter.limsInf_le_of_le | [] | [
462,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.continuous_tan | [] | [
72,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.rat_cast_im | [] | [
1371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_copy | [] | [
138,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.cancel_factors_eq | [
{
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"state_before": "α : Type u_1\ninst✝ : Field α\na b ad bd a' b' gcd : α\nha : ad * a = a... | [
93,
25
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80,
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Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.sum_mul_smul | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_add_univ | [
{
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492,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_nonneg_of_forall_set_integral_nonneg_of_sigmaFinite | [
{
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325,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/CategoryTheory/Category/Preorder.lean | Monotone.functor_obj | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Std/Data/List/Lemmas.lean | List.set_eq_modifyNth | [
{
"state_after": "no goals",
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"tactic": "cases l <;> rfl"
}
] | [
775,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
772,
1
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Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly₂.diag | [
{
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356,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/Analysis/Convex/Star.lean | starConvex_iff_segment_subset | [
{
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82,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist | [
{
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137,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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] |
Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.le_inducedMap_mul_self_of_mem_cutMap | [
{
"state_after": "case intro.intro\nF : Type ?u.25469\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.25478\ninst✝³ : LinearOrderedField α\ninst✝² : ConditionallyCompleteLinearOrderedField β\ninst✝¹ : ConditionallyCompleteLinearOrderedField γ\ninst✝ : Archimedean α\na : α\nb : β\nq✝ : ℚ\nha : 0 < a\nq : ℚ\nhb : q ∈ {t... | [
270,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/List/Basic.lean | List.reduceOption_length_eq_iff | [
{
"state_after": "case nil\nι : Type ?u.351472\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ length (reduceOption []) = length [] ↔ ∀ (x : Option α), x ∈ [] → Option.isSome x = true\n\ncase cons\nι : Type ?u.351472\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nhd : Option... | [
3469,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3456,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_le_true | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\nnum✝¹ num✝ : ℤ\nda db : ℕ\ninv✝¹ : Invertible ↑da\ninv✝ : Invertible ↑db\nh✝ : decide (Int.mul num✝¹ (Int.ofNat db) ≤ Int.mul num✝ (Int.ofNat da)) = true\nh : (fun x => ↑x) (Int.mul num✝¹ (Int.ofNat db)) ≤ (fun x => ↑x) (Int.mul num✝ (Int.ofNat da))\n... | [
732,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_mul' | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh : trailingCoeff p * trailingCoeff q ≠ 0\nhp : p ≠ 0\n⊢ trailingDegree (p * q) = trailingDegree p + trailingDegree q",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nh... | [
408,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/List/Card.lean | List.inj_on_of_subset | [] | [
17,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
16,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.ne_zero_iff | [] | [
340,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.smul_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.103781\n𝕜 : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf g : { x // x ∈ Lp E 2 }\nr : 𝕜\n⊢ (∫ (a : α), inner (↑↑(r • f) a) (↑↑g ... | [
216,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_eq_pi_div_two_sub_arccos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arcsin x = π / 2 - arccos x",
"tactic": "simp [arccos]"
}
] | [
346,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNFRec_zero | [
{
"state_after": "C : Ordinal → Sort u_2\nb : Ordinal\nH0 : C 0\nH : (o : Ordinal) → o ≠ 0 → C (o % b ^ log b o) → C o\n⊢ Eq.mpr (_ : C 0 = C 0) H0 = H0",
"state_before": "C : Ordinal → Sort u_2\nb : Ordinal\nH0 : C 0\nH : (o : Ordinal) → o ≠ 0 → C (o % b ^ log b o) → C o\n⊢ CNFRec b H0 H 0 = H0",
"tact... | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | inv_coe_set | [] | [
41,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_toAddSubgroup | [] | [
533,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_of_sub_eq_succ | [
{
"state_after": "no goals",
"state_before": "m n k : Nat\nh : n - m = succ k\n⊢ subNatNat m n = -[k+1]",
"tactic": "rw [subNatNat, h]"
}
] | [
31,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
30,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.div_mem | [] | [
202,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
11
] |
Mathlib/Topology/Spectral/Hom.lean | isSpectralMap_id | [] | [
57,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.limitUncurryIsoLimitCompLim_hom_π_π | [
{
"state_after": "J K : Type v\ninst✝⁵ : SmallCategory J\ninst✝⁴ : SmallCategory K\nC : Type u\ninst✝³ : Category C\nF : J ⥤ K ⥤ C\ninst✝² : HasLimitsOfShape K C\ninst✝¹ : HasLimit (uncurry.obj F)\ninst✝ : HasLimit (F ⋙ lim)\nj : J\nk : K\n⊢ limit.lift (F ⋙ lim) (coneOfConeUncurry (fun j => limit.isLimit (F.obj... | [
204,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_eq_of_zero | [
{
"state_after": "p x : ℝ\n⊢ {y | ↑y = ↑x} = {x}",
"state_before": "p x : ℝ\n⊢ ‖↑x‖ = abs x",
"tactic": "suffices { y : ℝ | (y : AddCircle (0 : ℝ)) = (x : AddCircle (0 : ℝ)) } = {x} by\n rw [quotient_norm_eq, this, image_singleton, Real.norm_eq_abs, csInf_singleton]"
},
{
"state_after": "case h... | [
86,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_pi_mul_I | [] | [
1369,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/Data/Set/Intervals/SurjOn.lean | surjOn_Ioo_of_monotone_surjective | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf : α → β\nh_mono : Monotone f\nh_surj : Surjective f\na b : α\np : β\nhp : p ∈ Ioo (f a) (f b)\n⊢ p ∈ f '' Ioo a b",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : PartialOrder β\nf :... | [
36,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/Int/Log.lean | Int.clog_natCast | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\n⊢ clog b ↑Nat.zero = ↑(Nat.clog b Nat.zero)\n\ncase succ\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb n : ℕ\n⊢ clog b ↑(Nat.succ n) = ↑(Nat.clog b (Nat.succ n))",
"st... | [
237,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.norm_int_le_pow_iff_dvd | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nk : ℤ\nn : ℕ\nthis : ↑p ^ (-↑n) = ↑(↑p ^ (-↑n))\n⊢ ‖↑k‖ ≤ ↑p ^ (-↑n) ↔ ↑(p ^ n) ∣ k",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nk : ℤ\nn : ℕ\n⊢ ‖↑k‖ ≤ ↑p ^ (-↑n) ↔ ↑(p ^ n) ∣ k",
"tactic": "have : (p : ℝ) ^ (-n : ℤ) = (p : ℚ) ^ (-n : ℤ) := by simp... | [
947,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_hasFDerivWithinAt_iff | [] | [
321,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Functor.map_inv_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\n⊢ F.map (inv f) ≫ F.map f = 𝟙 (F.obj Y)",
"tactic": "simp"
}
] | [
632,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.ACounit_X | [] | [
50,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/Homeomorph.lean | Continuous.continuous_symm_of_equiv_compact_to_t2 | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.104526\nδ : Type ?u.104529\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : CompactSpace α\ninst✝ : T2Space β\nf : α ≃ β\nhf : Continuous ↑f\n⊢ ∀ (s : Set α), IsClosed s → IsClosed (↑f.symm ⁻¹' s)",
"state_before": "α : Type u_1\nβ... | [
706,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.leRecOn_surjective | [
{
"state_after": "case refl\nm✝ n✝ k : ℕ\nC : ℕ → Sort u\nn m : ℕ\nnext : {k : ℕ} → C k → C (k + 1)\nHnext : ∀ (n : ℕ), Function.Surjective next\n⊢ Function.Surjective (leRecOn (_ : Nat.le n n) fun {k} => next)\n\ncase step\nm✝¹ n✝ k : ℕ\nC : ℕ → Sort u\nn m✝ : ℕ\nnext : {k : ℕ} → C k → C (k + 1)\nHnext : ∀ (n ... | [
457,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.y_mul_dvd | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn k : ℕ\n⊢ yn a1 n ∣ xn a1 (n * k) * yn a1 n + yn a1 (n * k) * xn a1 n",
"state_before": "a : ℕ\na1 : 1 < a\nn k : ℕ\n⊢ yn a1 n ∣ yn a1 (n * (k + 1))",
"tactic": "rw [Nat.mul_succ, yn_add]"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < ... | [
435,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
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