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/Logic/Function/Basic.lean | Function.Injective2.right | [] | [
935,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
934,
11
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.const_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.87566\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddCommGroup α\nh : Periodic f c\na x : α\n⊢ (fun x => f (a - x)) (x + c) = (fun x => f (a - x)) x",
"tactic": "simp only [← sub_sub, h.sub_eq]"
}
] | [
193,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_sUnion | [] | [
1059,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_ρ_hom | [] | [
216,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.add_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.167848\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝¹ : AddCommSemigroup α\ninst✝ : Neg β\nh : Antiperiodic f c\na x : α\n⊢ (fun x => f (x + a)) (x + c) = -(fun x => f (x + a)) x",
"tactic": "simpa only [add_right_comm] using h ... | [
441,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Polynomial/CancelLeads.lean | Polynomial.dvd_cancelLeads_of_dvd_of_dvd | [] | [
86,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Combinatorics/Partition.lean | Nat.Partition.ofComposition_surj | [
{
"state_after": "case mk\nα : Type ?u.1285\nn : ℕ\nb : Multiset ℕ\nhb₁ : ∀ {i : ℕ}, i ∈ b → 0 < i\nhb₂ : sum b = n\n⊢ ∃ a, ofComposition n a = { parts := b, parts_pos := hb₁, parts_sum := hb₂ }",
"state_before": "α : Type ?u.1285\nn : ℕ\n⊢ Function.Surjective (ofComposition n)",
"tactic": "rintro ⟨b, h... | [
85,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Real/Sqrt.lean | Real.neg_sqrt_lt_of_sq_lt | [] | [
441,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_inter_self | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\n⊢ ↑↑(condCount s) (s ∩ t) = ↑↑(condCount s) t",
"tactic": "rw [condCount, cond_inter_self _ hs.measurableSet]"
}
] | [
103,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Set/Sups.lean | Set.iUnion_image_sup_right | [] | [
183,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.isComplete_image_iff | [] | [
249,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.n_lt_a_pow | [
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\nIH : n < a ^ n\n⊢ n + 1 < a ^ (n + 1)",
"state_before": "a : ℕ\na1 : 1 < a\nn : ℕ\n⊢ n + 1 < a ^ (n + 1)",
"tactic": "have IH := n_lt_a_pow n"
},
{
"state_after": "a : ℕ\na1 : 1 < a\nn : ℕ\nIH : n < a ^ n\nthis : a ^ n + a ^ n ≤ a ^ n * a\n⊢ n + 1 < a ... | [
279,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_pow | [
{
"state_after": "case zero\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\n⊢ ↑(monomial n) r ^ Nat.zero = ↑(monomial (n * Nat.zero)) (r ^ Nat.zero)\n\ncase succ\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\nk : ℕ\nih : ↑(monomial n) r ^ k = ↑(monomi... | [
456,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.norm_eq_of_isometry | [] | [
855,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_div | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Algebra/Ring/Prod.lean | RingHom.coe_prodMap | [] | [
263,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_int_of_summable_nat | [] | [
1033,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_union | [] | [
270,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Order/Basic.lean | comap_coe_Iio_nhdsWithin_Iio | [] | [
2506,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2505,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.liftRel_pure_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nca : Computation α\nb : β\n⊢ LiftRel R ca (pure b) ↔ ∃ a, a ∈ ca ∧ R a b",
"tactic": "rw [LiftRel.swap, liftRel_pure_left]"
}
] | [
1188,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_mono | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.517176\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\nh : ∀ (a : α), a ∈ s → t₁ a ⊆ t₂ a\nthis : ∀ (b : β) (a : α), a ∈ s → b ∈ t₁ a → ∃ a, a ∈ s ∧ b ∈ t₂ a\n⊢ Finset.biUnion s t₁ ⊆ Finset.biUnion s t₂",
"state_before": "α : Type... | [
3609,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3606,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pwFilter_cons_of_pos | [] | [
363,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_lt_mul' | [] | [
1194,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1192,
11
] |
Mathlib/Data/Set/Basic.lean | Set.singleton_union | [] | [
1326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_le_iff_one_le_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a * a⁻¹ ≤ a * b ↔ 1 ≤ a * b",
"tactic": "rw [mul_inv_self]"
}
] | [
130,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.subset_one_iff_eq | [] | [
134,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.degree_add_div | [
{
"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]\nhq0 : q ≠ 0\nhpq : degree q ≤ degree p\nthis : degree (p % q) < degree (q * (p / q))\n⊢ degree q + degree (p / q) = degree p",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b :... | [
260,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | sum_cauchyPowerSeries_eq_integral | [] | [
629,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_const_mul'' | [
{
"state_after": "α : Type u_1\nβ : Type ?u.935279\nγ : Type ?u.935282\nδ : Type ?u.935285\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\nhf : AEMeasurable f\nA : (∫⁻ (a : α), f a ∂μ) = ∫⁻ (a : α), AEMeasurable.mk f hf a ∂μ\n⊢ (∫⁻ (a : α), r * f a ∂μ) = r * ∫⁻ (a : α), f a ∂μ",
"state_befo... | [
704,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_const | [
{
"state_after": "case inl\nα : Type u_2\nE : Type u_1\nF : Type ?u.1256042\n𝕜 : Type ?u.1256045\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : NormedAddCommGroup F\nins... | [
1371,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
] |
Mathlib/Order/BoundedOrder.lean | lt_top_iff_ne_top | [] | [
175,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Nat/ModEq.lean | Dvd.dvd.zero_modEq_nat | [] | [
87,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_one_iff_deriv | [] | [
2156,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2155,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.copy_eq | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.23151\nδ : Type ?u.23154\ne✝ : LocalEquiv α β\ne' : LocalEquiv β γ\ne : LocalEquiv α β\n⊢ copy e ↑e (_ : ↑e = ↑e) ↑(LocalEquiv.symm e) (_ : ↑(LocalEquiv.symm e) = ↑(LocalEquiv.symm e)) e.source\n (_ : e.source = e.source) e.target (_ : e.target = e.... | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.mem_iSup | [
{
"state_after": "ι✝ : Type ?u.22254\nα : Type u_2\nβ : Type ?u.22260\nγ : Type ?u.22263\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nι : Sort u_1\nx : α\ns : ι → Opens α\n⊢ x ∈ ↑(iSup s) ↔ ∃ i, x ∈ s i",
"state_before": "ι✝ : Type ?u.22254\nα : Type u_2\nβ : Type ?... | [
248,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.factors_one | [
{
"state_after": "case h\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\n⊢ FactorSet.prod (factors 1) = FactorSet.prod 0",
"state_... | [
1792,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : Semiring α\nI : Ideal α\na b : α\n⊢ span 0 = ⊥",
"tactic": "rw [← Set.singleton_zero, span_singleton_eq_bot]"
}
] | [
206,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | Antitone.quasilinearOn | [] | [
229,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.CNF_zero | [] | [
85,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/WithBot.lean | WithBot.le_ofDual_iff | [] | [
998,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.add_apply | [] | [
330,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Set/Image.lean | Disjoint.of_image | [] | [
1598,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.trTape_mk' | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\ninst✝² : Inhabited Γ\nΛ : Type ?u.363898\ninst✝¹ : Inhabited Λ\nσ : Type ?u.363904\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nL R : ListBlank Γ\n⊢ trTape enc0 (Tape.... | [
1751,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1750,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_le_card | [
{
"state_after": "α : Type ?u.21105\nr : α → α → Prop\no : Ordinal\n⊢ sInf {a | ∃ ι f, lsub f = o ∧ (#ι) = a} ≤ card o",
"state_before": "α : Type ?u.21105\nr : α → α → Prop\no : Ordinal\n⊢ cof o ≤ card o",
"tactic": "rw [cof_eq_sInf_lsub]"
},
{
"state_after": "no goals",
"state_before": "α ... | [
290,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.forall_forall_merge' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type ?u.68385\nβ : Type v\nβ' : Type ?u.68390\nγ : Type ?u.68393\nφ : Type ?u.68396\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ :... | [
784,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | Matrix.det_comm | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.18410\ninst✝¹⁰ : CommRing R\nM✝ : Type ?u.18416\ninst✝⁹ : AddCommGroup M✝\ninst✝⁸ : Module R M✝\nM' : Type ?u.19001\ninst✝⁷ : AddCommGroup M'\ninst✝⁶ : Module R M'\nι : Type ?u.19543\ninst✝⁵ : DecidableEq ι\ninst✝⁴ : Fintype ι\ne : Basis ι R M✝\nA : ... | [
83,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.cancel_iso_hom_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf : X ≅ Y\ng g' : Y ⟶ Z\n⊢ f.hom ≫ g = f.hom ≫ g' ↔ g = g'",
"tactic": "simp only [cancel_epi]"
}
] | [
538,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.smul_eval | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np✝ q : MvPolynomial σ R\nf x : σ → R\np : MvPolynomial σ R\ns : R\n⊢ ↑(eval x) (s • p) = s * ↑(eval x)... | [
1153,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Analysis/Convex/Integral.lean | ConvexOn.set_average_mem_epigraph | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.1095696\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : MeasureTheory.Measure α\ns : Set E\nt : Set α\nf : α... | [
167,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearEquiv_symm | [] | [
877,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Std/Logic.lean | not_not_not | [] | [
24,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasFDerivWithinAt.cpow | [
{
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108,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/RingTheory/ChainOfDivisors.lean | map_prime_of_factor_orderIso | [
{
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311,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_add | [] | [
1043,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
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Std/Data/List/Lemmas.lean | List.head_eq_of_cons_eq | [] | [
24,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
1
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Mathlib/Data/Set/Basic.lean | Set.antitoneOn_iff_antitone | [
{
"state_after": "no goals",
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"tactic": "simp [Antitone, AntitoneOn]"
}
] | [
2658,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2656,
1
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Mathlib/Data/List/Sigma.lean | List.mem_dlookup_kunion | [
{
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778,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
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Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.postcomp_uniformInducing | [
{
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440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
11
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Mathlib/Topology/Sets/Order.lean | ClopenUpperSet.coe_bot | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_add_not_infiniteNeg | [
{
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"state_before": "x y : ℝ*\n⊢ InfinitePos x → ¬InfiniteNeg y → InfinitePos (x + y)",
"tactic": "intro hip hnin r"
},
{
"state_after": "case intro\nx y : ℝ*\nhip : InfinitePos x\nhnin : ¬InfiniteNeg y\nr ... | [
543,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.mapRange.linearMap_comp | [
{
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218,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Holor.lean | Holor.cprank_upper_bound | [] | [
413,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_comm | [] | [
1002,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_mul | [] | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.mem_antidiagonal | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nx : ℕ × ℕ\n⊢ x ∈ antidiagonal n ↔ x.fst + x.snd = n",
"tactic": "rw [antidiagonal, mem_def, Multiset.Nat.mem_antidiagonal]"
}
] | [
40,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Data/Set/Equitable.lean | Finset.EquitableOn.le_add_one | [] | [
124,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.lhom_ext' | [] | [
76,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nm n : ℕ\n⊢ ↑(coeff R m) (X ^ n) = if m = n then 1 else 0",
"tactic": "rw [X_pow_eq, coeff_monomial]"
}
] | [
1457,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1456,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_commute | [
{
"state_after": "no goals",
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"tactic": "simpa only [cast_def] using (r.1.cast_commute a).div_left (r.2.cast_commute a)"
}
] | [
70,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Std/Data/List/Init/Lemmas.lean | List.foldr_reverse | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : List α\nf : α → β → β\nb : β\n⊢ foldl (fun y x => f x y) b (reverse (reverse l)) = foldl (fun x y => f y x) b l",
"tactic": "simp"
}
] | [
190,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
188,
9
] |
Mathlib/Data/Set/Basic.lean | Set.diff_inter | [] | [
1955,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_one | [] | [
692,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.restrict_self | [] | [
522,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.Path.reverse_comp | [
{
"state_after": "case nil\nU : Type ?u.5751\nV : Type u_1\nW : Type ?u.5757\ninst✝³ : Quiver U\ninst✝² : Quiver V\ninst✝¹ : Quiver W\ninst✝ : HasReverse V\na b c : V\np : Path a b\n⊢ reverse (comp p nil) = comp (reverse nil) (reverse p)\n\ncase cons\nU : Type ?u.5751\nV : Type u_1\nW : Type ?u.5757\ninst✝³ : Q... | [
159,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atTop_iff_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.239844\nι' : Type ?u.239847\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.239856\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nh : Tendsto f l atBot\n⊢ Tendsto (fun x => r * f x) l atTop ↔ r < 0",
"tactic": "simp [te... | [
1152,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.ι_desc_apply' | [] | [
334,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Order/Heyting/Basic.lean | Pi.himp_def | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_imK | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.mem_range_iff_mem_finset_range_of_mod_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.102484\nγ : Type ?u.102487\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns : Finset α\nt : Finset β\na✝ : α\nb c : β\ninst✝ : DecidableEq α\nf : ℤ → α\na : α\nn : ℕ\nhn : 0 < n\nh : ∀ (i : ℤ), f (i % ↑n) = f i\nthis : (∃ i, f (i % ↑n) = a) ↔ ∃... | [
576,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.edist_eq_of_L2 | [
{
"state_after": "no goals",
"state_before": "p : ℝ≥0∞\n𝕜 : Type ?u.293461\n𝕜' : Type ?u.293464\nι : Type u_2\nα : ι → Type ?u.293472\nβ✝ : ι → Type ?u.293477\ninst✝² : Fintype ι\ninst✝¹ : Fact (1 ≤ p)\nβ : ι → Type u_1\ninst✝ : (i : ι) → SeminormedAddCommGroup (β i)\nx y : PiLp 2 β\n⊢ edist x y = (∑ i : ... | [
618,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.lift_mk | [] | [
657,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.pullback_eq_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nJ : Type w\ninst✝³ : SmallCategory J\ninst✝² : FinCategory J\ninst✝¹ : SemilatticeInf α\ninst✝ : OrderTop α\nx y z : α\nf : x ⟶ z\ng : y ⟶ z\n⊢ limit (cospan f g) = Finset.inf Finset.univ (cospan f g).toPrefunctor.obj",
"tactic": "rw [finite_limi... | [
165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_finite | [
{
"state_after": "no goals",
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2226,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2225,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_insert | [] | [
1140,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_injective | [] | [
357,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.cast_le | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedSemiring α\nm n : PosNum\n⊢ ¬↑n < ↑m ↔ m ≤ n",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedSemiring α\nm n : PosNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"tactic": "rw [← not_lt]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝... | [
707,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_eq_zero_iff_eq' | [] | [
288,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Order/Hom/Basic.lean | disjoint_map_orderIso_iff | [] | [
1226,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Dynamics/Flow.lean | isInvariant_iff_image | [
{
"state_after": "no goals",
"state_before": "τ : Type u_1\nα : Type u_2\nϕ : τ → α → α\ns : Set α\n⊢ IsInvariant ϕ s ↔ ∀ (t : τ), ϕ t '' s ⊆ s",
"tactic": "simp_rw [IsInvariant, mapsTo']"
}
] | [
55,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/List/Basic.lean | List.get_pmap | [
{
"state_after": "case nil\nι : Type ?u.337556\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nh✝ : ∀ (a : α), a ∈ l → p a\nn✝ : ℕ\nhn✝ : n✝ < length (pmap f l h✝)\nh : ∀ (a : α), a ∈ [] → p a\nn : ℕ\nhn : n < length (pmap f [] h)\n⊢ get (pmap f ... | [
3198,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3188,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.nat_add_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\n⊢ LiouvilleWith p (↑n + x) ↔ LiouvilleWith p x",
"tactic": "rw [add_comm, add_nat_iff]"
}
] | [
229,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/ContinuousOn.lean | eventually_nhds_nhdsWithin | [] | [
49,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Asymptotics.IsLittleO.sum_range | [
{
"state_after": "α : Type u_1\ninst✝ : NormedAddCommGroup α\nf : ℕ → α\ng : ℕ → ℝ\nh : f =o[atTop] g\nhg : 0 ≤ g\nh'g : Tendsto (fun n => ∑ i in range n, g i) atTop atTop\nA : ∀ (i : ℕ), ‖g i‖ = g i\n⊢ (fun n => ∑ i in range n, f i) =o[atTop] fun n => ∑ i in range n, g i",
"state_before": "α : Type u_1\nin... | [
139,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | totallyBounded_preimage | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nf : α → β\ns : Set β\nhf : UniformEmbedding f\nhs : TotallyBounded s\nt : Set (α × α)\nht : t ∈ comap (fun x => (f x.fst, f x.snd)) (𝓤 β)\n⊢ ∃ t_1, Set.Finite t_1 ∧ f ⁻¹' s ⊆ ⋃ (y : α... | [
396,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.splitMany_empty | [] | [
250,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.sum_smul_index | [
{
"state_after": "case ofFinsupp\nR : Type u\na b✝ : R\nm n : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nS : Type u_1\ninst✝ : AddCommMonoid S\nb : R\nf : ℕ → R → S\nhf : ∀ (i : ℕ), f i 0 = 0\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ sum (b • { toFinsupp := toFinsupp✝ }) f = sum { toFinsupp := toFinsupp✝ } fun n a => f n ... | [
1005,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Data/Part.lean | Part.right_dom_of_union_dom | [] | [
850,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.coe_int_inj | [] | [
545,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | eventually_ne_of_tendsto_norm_atTop' | [] | [
1261,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.ker_prod_ker_le_ker_coprod | [] | [
1324,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
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