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/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_eq_empty | [] | [
136,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_nonempty_iff_exists_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\n⊢ Set.Nonempty (s ∩ t) ↔ ∃ x, x ∈ s ∧ x ∈ t",
"tactic": "simp_rw [inter_nonempty]"
}
] | [
524,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | right_eq_mul₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.12533\nM₀ : Type u_1\nG₀ : Type ?u.12539\nM₀' : Type ?u.12542\nG₀' : Type ?u.12545\nF : Type ?u.12548\nF' : Type ?u.12551\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\nhb : b ≠ 0\n⊢ b = a * b ↔ a = 1",
"tactic": "rw [eq_comm, mul_eq_right₀ hb]"
... | [
216,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Std/Data/Int/Lemmas.lean | Int.le.intro_sub | [
{
"state_after": "a b : Int\nn : Nat\nh : b - a = ↑n\n⊢ NonNeg ↑n",
"state_before": "a b : Int\nn : Nat\nh : b - a = ↑n\n⊢ a ≤ b",
"tactic": "simp [le_def, h]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nn : Nat\nh : b - a = ↑n\n⊢ NonNeg ↑n",
"tactic": "constructor"
}
] | [
558,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
557,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_lineMap_left | [] | [
366,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Algebra/Invertible.lean | mul_left_eq_iff_eq_invOf_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nc a b : α\ninst✝¹ : Monoid α\ninst✝ : Invertible c\n⊢ c * a = b ↔ a = ⅟c * b",
"tactic": "rw [← mul_left_inj_of_invertible (c := ⅟c), invOf_mul_self_assoc]"
}
] | [
313,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Topology/Paracompact.lean | Homeomorph.paracompactSpace_iff | [] | [
131,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/Disjoint.lean | codisjoint_iff | [] | [
313,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_add | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Std/Data/List/Lemmas.lean | List.append_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\nb : α\nas✝ : List α\nh : Mem a as✝\ns t : List α\nh' : as✝ = s ++ a :: t\n⊢ b :: as✝ = b :: s ++ a :: t",
"tactic": "rw [h', cons_append]"
}
] | [
88,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
86,
1
] |
Mathlib/Algebra/Quaternion.lean | Cardinal.mk_univ_quaternion | [] | [
1469,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_right_eq_self₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9281\nM₀ : Type u_1\nG₀ : Type ?u.9287\nM₀' : Type ?u.9290\nG₀' : Type ?u.9293\nF : Type ?u.9296\nF' : Type ?u.9299\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\n⊢ a * b = a ↔ a * b = a * 1",
"tactic": "rw [mul_one]"
}
] | [
191,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.IsImage.isoExt_inv_m | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : C\nf : X ⟶ Y\nF F' : MonoFactorisation f\nhF : IsImage F\nhF' : IsImage F'\n⊢ (isoExt hF hF').inv ≫ F.m = F'.m",
"tactic": "simp"
}
] | [
226,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Algebra/Homology/Homology.lean | cyclesMap_arrow | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ninst✝ : HasKernels V\nC₁ C₂ C₃ : HomologicalComplex V c\nf✝ f : C₁ ⟶ C₂\ni : ι\n⊢ cyclesMap f i ≫ Subobject.arrow (cycles C₂ i) = Subobjec... | [
210,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.equivMapDomain_zero | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.144676\nι : Type ?u.144679\nM : Type u_3\nM' : Type ?u.144685\nN : Type ?u.144688\nP : Type ?u.144691\nG : Type ?u.144694\nH : Type ?u.144697\nR : Type ?u.144700\nS : Type ?u.144703\ninst✝ : Zero M\nf : α ≃ β\na✝ : β\n⊢ ↑(equivMapDomain f 0) a✝ =... | [
354,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.sum_lt | [] | [
213,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.subset_ordConnectedComponent | [] | [
51,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_ofAdd | [] | [
2250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2249,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.transnumAuxSeq_zero | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\n⊢ transnumAuxSeq f 0 = ↑f 0",
"tactic": "simp [transnumAuxSeq]"
}
] | [
668,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.join_le | [] | [
1796,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1795,
1
] |
Mathlib/Analysis/Calculus/Deriv/ZPow.lean | iter_deriv_inv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx✝ : 𝕜\ns : Set 𝕜\nm : ℤ\nk : ℕ\nx : 𝕜\n⊢ (deriv^[k]) Inv.inv x = (∏ i in Finset.range k, (-1 - ↑i)) * x ^ (-1 - ↑k)",
"tactic": "simpa ... | [
146,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_const_mul | [] | [
504,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.headI_mul_tail_prod_of_ne_nil | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.69762\nα : Type ?u.69765\nM : Type u_1\nN : Type ?u.69771\nP : Type ?u.69774\nM₀ : Type ?u.69777\nG : Type ?u.69780\nR : Type ?u.69783\ninst✝³ : Monoid M\ninst✝² : Monoid N\ninst✝¹ : Monoid P\nl✝ l₁ l₂ : List M\na : M\ninst✝ : Inhabited M\nl : List M... | [
241,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Std/Data/Int/Lemmas.lean | Int.default_eq_zero | [] | [
23,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
23,
9
] |
Mathlib/Algebra/Associated.lean | Associated.isUnit_iff | [] | [
633,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.pow | [
{
"state_after": "R : 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\nn : ℕ\n⊢ Monic (p * p ^ n)",
"state_before": "R : 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\nn : ℕ\n⊢ Monic (p ^ (n + 1))",
"ta... | [
129,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\n⊢ ↑derivative (X ^ 2) = ↑C 2 * X",
"tactic": "rw [derivative_X_pow, Nat.cast_two, pow_one]"
}
] | [
121,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/Lie/DirectSum.lean | DirectSum.lieAlgebra_ext | [] | [
160,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.two_nsmul_coe_pi | [
{
"state_after": "no goals",
"state_before": "⊢ 2 • ↑π = 0",
"tactic": "simp [← coe_nat_mul_eq_nsmul]"
}
] | [
165,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.glueDist_triangle_inl_inr_inl | [
{
"state_after": "X : Type u\nY : Type v\nZ : Type w\ninst✝² : MetricSpace X\ninst✝¹ : MetricSpace Y\nΦ✝ : Z → X\nΨ✝ : Z → Y\nε✝ : ℝ\ninst✝ : Nonempty Z\nΦ : Z → X\nΨ : Z → Y\nε : ℝ\nH : ∀ (p q : Z), abs (dist (Φ p) (Φ q) - dist (Ψ p) (Ψ q)) ≤ 2 * ε\nx : X\ny : Y\nz : X\n⊢ dist x z ≤ (⨅ (p : Z), dist x (Φ p) + ... | [
135,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
9
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.coeff_inv_units | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Field R\np q : R[X]\nu : R[X]ˣ\nn : ℕ\n⊢ (1 / if n = 0 then coeff (↑u) 0 else 0) = if n = 0 then coeff (↑u⁻¹) 0 else 0",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Field ... | [
411,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.add_eq_union_iff_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.504974\nγ : Type ?u.504977\ninst✝ : DecidableEq α\ns t : Multiset α\n⊢ s + t = s ∪ t ↔ Disjoint s t",
"tactic": "simp_rw [← inter_eq_zero_iff_disjoint, ext, count_add, count_union, count_inter, count_zero,\n Nat.min_eq_zero_iff, Na... | [
2987,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2984,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.measurableSet_eq_fun | [
{
"state_after": "α : Type u_1\nβ : Type ?u.224536\nγ : Type ?u.224539\nι : Type ?u.224542\ninst✝² : Countable ι\nf✝ g✝ : α → β\nm : MeasurableSpace α\nE : Type u_2\ninst✝¹ : TopologicalSpace E\ninst✝ : MetrizableSpace E\nf g : α → E\nhf : StronglyMeasurable f\nhg : StronglyMeasurable g\nthis✝¹ : MeasurableSpac... | [
870,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.has_diff | [
{
"state_after": "α : Type u_1\nd : DynkinSystem α\ns₁ s₂ : Set α\nh₁ : Has d s₁\nh₂ : Has d s₂\nh : s₂ ⊆ s₁\n⊢ Has d ((s₁ \\ s₂)ᶜ)",
"state_before": "α : Type u_1\nd : DynkinSystem α\ns₁ s₂ : Set α\nh₁ : Has d s₁\nh₂ : Has d s₂\nh : s₂ ⊆ s₁\n⊢ Has d (s₁ \\ s₂)",
"tactic": "apply d.has_compl_iff.1"
},... | [
594,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.add_isBigOWith | [] | [
1101,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.IsCodetecting.isCoseparating | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasCoequalizers C\n𝒢 : Set C\n⊢ IsCodetecting 𝒢 → IsCoseparating 𝒢",
"tactic": "simpa only [← isSeparating_op_iff, ← isDetecting_op_iff] using IsDetecting.isSeparating"
}
] | [
163,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.bijective_iff_injective_and_card | [] | [
669,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.differentiableWithinAt_arcsin_Ici | [
{
"state_after": "x : ℝ\n⊢ DifferentiableWithinAt ℝ arcsin (Ici x) x → x ≠ -1",
"state_before": "x : ℝ\n⊢ DifferentiableWithinAt ℝ arcsin (Ici x) x ↔ x ≠ -1",
"tactic": "refine' ⟨_, fun h => (hasDerivWithinAt_arcsin_Ici h).differentiableWithinAt⟩"
},
{
"state_after": "h : DifferentiableWithinAt ... | [
93,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_commute | [] | [
224,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/List/Cycle.lean | List.pmap_prev_eq_rotate_length_sub_one | [
{
"state_after": "case hl\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : Nodup l\n⊢ length (pmap (prev l) l (_ : ∀ (x : α), x ∈ l → x ∈ l)) = length (rotate l (length l - 1))\n\ncase h\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : Nodup l\n⊢ ∀ (n : ℕ) (h₁ : n < length (pmap (prev l)... | [
372,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.closure_induction₂ | [] | [
384,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.ext | [] | [
19,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
18,
18
] |
Mathlib/Algebra/Order/Group/Abs.lean | sub_le_of_abs_sub_le_right | [] | [
297,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.not_mem_of_mem | [] | [
131,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.card | [] | [
63,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_zero | [] | [
88,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.one_out_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.186066\nβ : Type ?u.186069\nγ : Type ?u.186072\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nx : (Quotient.out 1).α\n⊢ 0 < type fun x x_1 => x < x_1",
"tactic": "simp"
}
] | [
1127,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Mathlib/Data/List/Basic.lean | List.comp_map | [] | [
1850,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1849,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | aemeasurable_inv_iff | [
{
"state_after": "no goals",
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479,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_sup | [
{
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1440,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_singleton_subset_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u : Set α\nx : α\ns t : Set α\n⊢ s \\ {x} ⊆ t ↔ s ⊆ {x} ∪ t",
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1939,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1937,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.cast_floor_eq_int_floor | [
{
"state_after": "no goals",
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"tactic": "rw [← Int.floor_toNat, Int.toNat_of_nonneg (Int.floor_nonneg.2 ha)]"
}
] | [
1603,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1602,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | Filter.Tendsto.nnnorm' | [] | [
1194,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1193,
1
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Mathlib/Algebra/Ring/Units.lean | Units.val_neg | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
11
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_sub | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Std/Data/List/Lemmas.lean | List.eraseP_of_forall_not | [
{
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"state_before": "α : Type u_1\np : α → Bool\nl : List α\nh : ∀ (a : α), a ∈ l → ¬p a = true\n⊢ eraseP p l = l",
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},
{
"state_after": "no goals",
"state_b... | [
940,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
937,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_monomial | [
{
"state_after": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff { toFinsupp := Finsupp.single n a } m = if n = m then a else 0",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff (↑(monomial n) a) m = if n = m then a else 0",
"tactic": "rw [← ... | [
675,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.one_sub_K_pos | [] | [
268,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
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Mathlib/Logic/Nonempty.lean | nonempty_sum | [] | [
83,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | continuousAt_extChartAt' | [
{
"state_after": "no goals",
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1091,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.sup_lt_ord_of_isRegular | [
{
"state_after": "no goals",
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"tactic": "rwa [hc.cof_eq]"
}
] | [
1078,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_coe_eq_restrictScalars | [] | [
95,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ENNReal.measurable_of_measurable_nnreal | [] | [
1824,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1821,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.eventually_hasSum_sub | [] | [
503,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_le_pi | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ toReal ↑x✝ ≤ π",
"state_before": "θ : Angle\n⊢ toReal θ ≤ π",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "case h.e'_4\nx✝ : ℝ\n⊢ π = -π + 2 * π",
"state_before": "case h\nx✝ : ℝ\n⊢ toReal ↑x✝ ≤ π",
"tactic": "convert toIo... | [
567,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | lt_of_mul_lt_mul_of_nonpos_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.200981\ninst✝ : LinearOrderedRing α\na b c : α\nh : a * c < b * c\nhc : c ≤ 0\n⊢ b * -c < a * -c",
"tactic": "rwa [mul_neg, mul_neg, neg_lt_neg_iff]"
}
] | [
1155,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
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Mathlib/Data/List/Basic.lean | List.nth_take_of_succ | [] | [
2031,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2030,
1
] |
Mathlib/ModelTheory/Definability.lean | Set.Definable.image_comp | [
{
"state_after": "case intro\nM : Type w\nA : Set M\nL : Language\ninst✝² : Structure L M\nα : Type u₁\nβ : Type u_1\nB : Set M\ns✝ : Set (α → M)\ns : Set (β → M)\nh : Definable A L s\nf : α → β\ninst✝¹ : Finite α\ninst✝ : Finite β\nval✝ : Fintype α\n⊢ Definable A L ((fun g => g ∘ f) '' s)",
"state_before":... | [
240,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | SeminormedGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_one | [
{
"state_after": "case refine'_1\n𝓕 : Type ?u.504291\n𝕜 : Type ?u.504294\nα : Type ?u.504297\nι : Type u_1\nκ : Type u_2\nE : Type ?u.504306\nF : Type ?u.504309\nG : Type u_3\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nf : ι ... | [
1313,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1299,
1
] |
Mathlib/Algebra/QuadraticDiscriminant.lean | discrim_le_zero | [
{
"state_after": "K : Type u_1\ninst✝ : LinearOrderedField K\na b c : K\nh : ∀ (x : K), 0 ≤ a * x * x + b * x + c\n⊢ b * b - 4 * a * c ≤ 0",
"state_before": "K : Type u_1\ninst✝ : LinearOrderedField K\na b c : K\nh : ∀ (x : K), 0 ≤ a * x * x + b * x + c\n⊢ discrim a b c ≤ 0",
"tactic": "rw [discrim, sq]... | [
141,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_succ_iff_deriv_of_open | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
2094,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2091,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalClosure_subset_iff | [] | [
2494,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2493,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.nhds_generateFrom | [
{
"state_after": "α : Type u\ng : Set (Set α)\na : α\nthis : TopologicalSpace α := generateFrom g\n⊢ 𝓝 a = ⨅ (s : Set α) (_ : s ∈ {s | a ∈ s ∧ s ∈ g}), 𝓟 s",
"state_before": "α : Type u\ng : Set (Set α)\na : α\n⊢ 𝓝 a = ⨅ (s : Set α) (_ : s ∈ {s | a ∈ s ∧ s ∈ g}), 𝓟 s",
"tactic": "letI := generateFro... | [
93,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/List/Basic.lean | List.map_const' | [] | [
1888,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1887,
9
] |
Mathlib/Order/LiminfLimsup.lean | Filter.inf_limsup | [] | [
1010,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.mul_add_right_left_iff | [] | [
344,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.ker_def | [] | [
118,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.incidenceSet_subset | [] | [
266,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Rat/Floor.lean | Rat.floor_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nx : ℚ\n⊢ ↑⌊x⌋ ≤ ↑x ∧ ↑x < ↑⌊x⌋ + 1",
"tactic": "exact_mod_cast floor_eq_iff.1 (Eq.refl ⌊x⌋)"
}
] | [
74,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_prod_comm | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.386315\nG : Type ?u.386318\nM : Type u_3\nN : Type ?u.386324\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf✝ g : α → M\na b : α\ns✝ t : Set α\ns : Finset β\nf : α → β → M\nh : ∀ (b : β), b ∈ s → Set.Finite (mulSupport fun a => f a b)\nhU :\n (mulSuppor... | [
1180,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1165,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.orthogonal_eq_bot_iff | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.794030\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace ↑↑K\n⊢ Kᗮ = ⊥ → K = ⊤",
"state_before": "𝕜 : Type u... | [
802,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Data/Set/Image.lean | Set.insert_none_range_some | [] | [
1208,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1207,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.to_ofList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List (Lists α)\n⊢ toList (ofList l) = l",
"tactic": "induction l <;> simp [*]"
}
] | [
101,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vsub_mem_vectorSpan | [] | [
101,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | strictAnti_of_deriv_neg | [] | [
951,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | pow_inj_iff_of_orderOf_eq_zero | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn✝ m✝ : ℕ\ninst✝ : LeftCancelMonoid G\nh : orderOf x = 0\nn m : ℕ\n⊢ x ^ n = x ^ m ↔ n = m",
"tactic": "rw [pow_eq_pow_iff_modEq, h, modEq_zero_iff]"
}
] | [
508,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Power.lean | EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero | [
{
"state_after": "case intro.intro.intro\nV : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\nP : Type u_1\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b c d p : P\nh : Cospherical {a, b, c, d}\nhab : a ≠ b\nhcd : c ≠ d\nhapb : ∠ a p b = 0\nhcpd : ∠ c p d = 0\nk₁ : ℝ\nhab₁ : ... | [
132,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_pow | [] | [
212,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
src/lean/Lean/Data/PersistentHashMap.lean | Lean.PersistentHashMap.size_push | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nks : Array α\nvs : Array β\nh : Array.size ks = Array.size vs\nk : α\nv : β\n⊢ Array.size (Array.push ks k) = Array.size (Array.push vs v)",
"tactic": "simp [h]"
}
] | [
71,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
70,
9
] |
Mathlib/Order/Filter/Partial.lean | Filter.tendsto_iff_ptendsto | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nl₁ : Filter α\nl₂ : Filter β\ns : Set α\nf : α → β\n⊢ Tendsto f (l₁ ⊓ 𝓟 s) l₂ ↔ PTendsto (PFun.res f s) l₁ l₂",
"tactic": "simp only [Tendsto, PTendsto, pmap_res]"
}
] | [
248,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_toSubalgebra | [] | [
92,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.id_comp | [] | [
1345,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
9
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.suppPreservation_iff_liftpPreservation | [
{
"state_after": "case mp\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nh : SuppPreservation\n⊢ LiftPPreservation\n\ncase mpr\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nh : LiftPPreservation\n⊢ SuppPreservation",
"state_before": "n : ℕ\nF : TypeVec n → Type u_1... | [
282,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.div_mem_comm_iff | [] | [
602,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
11
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_eq_blockDiagonal | [] | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_lt_base_pow_length | [
{
"state_after": "case succ.succ\nn : ℕ\nl : List ℕ\nb : ℕ\nhl : ∀ (x : ℕ), x ∈ l → x < succ (succ b)\n⊢ ofDigits (succ (succ b)) l < succ (succ b) ^ List.length l",
"state_before": "n b : ℕ\nl : List ℕ\nhb : 1 < b\nhl : ∀ (x : ℕ), x ∈ l → x < b\n⊢ ofDigits b l < b ^ List.length l",
"tactic": "rcases b ... | [
412,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.num_one | [] | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_eq | [] | [
1294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_biUnion | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.39437\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nι : Type ?u.39449\nκ : Type ?u.39452\ninst✝² : SemilatticeSup α\ninst✝¹ : OrderBot α\ns✝ s₁ s₂ : Finset β\nf g : β → α\na : α\ninst✝ : DecidableEq β\ns : Finset γ\nt : γ → Finset β\nc : α\n⊢ sup (Finse... | [
131,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.ext | [] | [
797,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
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