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/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.matrix_components | [
{
"state_after": "no goals",
"state_before": "J : Type\ninst✝⁴ : Fintype J\nK : Type\ninst✝³ : Fintype K\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\ninst✝ : HasFiniteBiproducts C\nf : J → C\ng : K → C\nm : (j : J) → (k : K) → f j ⟶ g k\nj : J\nk : K\n⊢ components (matrix m) j k = m j k",
... | [
851,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.ofBijective_symm_apply_apply | [] | [
1419,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarAlgHom.mem_equalizer | [] | [
741,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.sameCycle_zpow_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.78068\nα : Type u_1\nβ : Type ?u.78074\nf g : Perm α\np : α → Prop\nx y z : α\nn : ℤ\n⊢ (∃ b, ↑(f ^ ↑(Equiv.addRight n).symm b) (↑(f ^ n) x) = y) ↔ SameCycle f x y",
"tactic": "simp [SameCycle, zpow_add]"
}
] | [
165,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.IsClosable.leIsClosable | [
{
"state_after": "case intro\nR : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : AddCommGroup E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module R E\ninst✝⁷ : Module R F\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : ContinuousAdd E\ninst✝³ : ContinuousAdd F\ninst✝² : Topolo... | [
94,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | measurableSet_region_between_co | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\nhg : Measurable g\nhs : MeasurableSet s\n⊢ MeasurableSet ({a | a.fst ∈ s} ∩ {a | a.snd ∈ {a_1 | f a.fst ≤ a_1} ∩ {a_1 | a_1 < g a.fst}})",
"state_before": "α : Type u_1\ninst✝ :... | [
513,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Set/Function.lean | Set.eqOn_comp_right_iff | [] | [
896,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.ProbabilityMeasure.le_liminf_measure_open_of_tendsto | [] | [
399,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | one_min | [] | [
377,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.commute_monomial | [
{
"state_after": "case refine'_1\nσ : Type u_1\nR : Type u_2\ninst✝ : Semiring R\nm✝ n✝ : σ →₀ ℕ\nφ ψ : MvPowerSeries σ R\na : R\nn : σ →₀ ℕ\nh : ∀ (n_1 : σ →₀ ℕ), ↑(coeff R n_1) (φ * ↑(monomial R n) a) = ↑(coeff R n_1) (↑(monomial R n) a * φ)\nm : σ →₀ ℕ\n⊢ Commute (↑(coeff R m) φ) a\n\ncase refine'_2\nσ : Typ... | [
266,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.evalEquiv_toLinearMap | [] | [
489,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.decompId_p_naturality | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.51236\ninst✝ : Category C\nP Q : Karoubi C\nf : P ⟶ Q\n⊢ mk P.X (𝟙 P.X) ⟶ mk Q.X (𝟙 Q.X)",
"tactic": "exact Hom.mk f.f (by simp)"
},
{
"state_after": "no goals",
"state_before": "C : Type ?u.51236\ninst✝ : Category C\nP Q : Karoubi ... | [
302,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquivClass.map_eq_one_iff | [] | [
153,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/CategoryTheory/Closed/Monoidal.lean | CategoryTheory.MonoidalClosed.homEquiv_apply_eq | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_iff_imp | [] | [
1189,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_le_one | [] | [
104,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_fintype | [
{
"state_after": "case refine_1\nα✝ β α : Type u\nh : Fintype α\n⊢ ∀ (α β : Type u) [inst : Fintype β] (e : α ≃ β), (#α) = ↑(Fintype.card α) → (#β) = ↑(Fintype.card β)\n\ncase refine_2\nα✝ β α : Type u\nh : Fintype α\n⊢ (#PEmpty) = ↑(Fintype.card PEmpty)\n\ncase refine_3\nα✝ β α : Type u\nh : Fintype α\n⊢ ∀ (α ... | [
462,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.ext_of_toZModPow | [
{
"state_after": "case mp\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nx y : ℤ_[p]\n⊢ (∀ (n : ℕ), ↑(toZModPow n) x = ↑(toZModPow n) y) → x = y\n\ncase mpr\np : ℕ\nhp_prime : Fact (Nat.Prime p)\nx y : ℤ_[p]\n⊢ x = y → ∀ (n : ℕ), ↑(toZModPow n) x = ↑(toZModPow n) y",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Pri... | [
677,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Data/Finset/Sum.lean | Finset.disjSum_ssubset_disjSum_of_ssubset_of_subset | [] | [
99,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.ContinuousMap.inner_toLp | [
{
"state_after": "case h\nα : Type u_1\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : MeasureSpace α\ninst✝³ : BorelSpace α\n𝕜 : Type u_2\ninst✝² : IsROrC 𝕜\nμ : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : CompactSpace α\nf g : C(α, 𝕜)\n⊢ (fun a => inner (↑↑(↑(ContinuousMap.toLp 2 μ 𝕜) f) a) (↑↑(↑(ContinuousMap.... | [
325,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Measurable.inf_const | [] | [
193,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | dvd_geom_sum₂_iff_of_dvd_sub | [
{
"state_after": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x✝ y✝ x y p : R\nh : ↑(Ideal.Quotient.mk (span {p})) x = ↑(Ideal.Quotient.mk (span {p})) y\n⊢ p ∣ ∑ i in range n, x ^ i * y ^ (n - 1 - i) ↔ p ∣ ↑n * y ^ (n - 1)",
"state_before": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x✝ y✝ x y p : R\nh :... | [
49,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_inv_cancel_right | [] | [
303,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
11
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_union_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.46571\ninst✝ : PartialOrder α\na b c : α\nhab : a < b\n⊢ Ioo a b ∪ {a} = Ico a b",
"tactic": "rw [← Ico_diff_left, diff_union_self,\n union_eq_self_of_subset_right (singleton_subset_iff.2 <| left_mem_Ico.2 hab)]"
}
] | [
859,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.neg_apply | [] | [
488,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | iUnion_Ici_eq_Ioi_iInf | [
{
"state_after": "no goals",
"state_before": "ι : Sort u\nα : Type v\nβ : Type w\ninst✝¹ : LinearOrder α\ns : Set α\na : α\nf✝ : ι → α\nR : Type u_1\ninst✝ : CompleteLinearOrder R\nf : ι → R\nno_least_elem : ¬(⨅ (i : ι), f i) ∈ range f\n⊢ (⋃ (i : ι), Ici (f i)) = Ioi (⨅ (i : ι), f i)",
"tactic": "simp o... | [
233,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_rpow_exp_pos_mul_atTop | [
{
"state_after": "no goals",
"state_before": "s b : ℝ\nhb : 0 < b\n⊢ Tendsto (fun x => x ^ s / exp (b * x)) atTop (𝓝 0)",
"tactic": "simpa only [div_eq_mul_inv, exp_neg, neg_mul] using\n tendsto_rpow_mul_exp_neg_mul_atTop_nhds_0 s b hb"
}
] | [
252,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.ae_le_iff_absolutelyContinuous | [
{
"state_after": "α : Type u_1\nβ : Type ?u.405254\nγ : Type ?u.405257\nδ : Type ?u.405260\nι : Type ?u.405263\nR : Type ?u.405266\nR' : Type ?u.405269\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\nh : ae μ ≤ ae ν\ns : Set α\n... | [
2415,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2412,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformlyOnFilter_iff_tendsto | [] | [
100,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/Order.lean | closure_induced | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nt✝ : TopologicalSpace β\nf✝ : α → β\nt : TopologicalSpace β\nf : α → β\na : α\ns : Set α\nthis : TopologicalSpace α := induced f t\n⊢ a ∈ closure s ↔ f a ∈ closure (f '' s)",
"state_before": "α : Type u_2\nβ : Type u_1\nt✝ : TopologicalSpace β\nf✝ : α → β\nt : T... | [
885,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.restrictScalars_injective | [
{
"state_after": "no goals",
"state_before": "K : Type u_3\nL : Type u_1\nL' : Type u_2\ninst✝⁶ : Field K\ninst✝⁵ : Field L\ninst✝⁴ : Field L'\ninst✝³ : Algebra K L\ninst✝² : Algebra K L'\nS : IntermediateField K L\ninst✝¹ : Algebra L' L\ninst✝ : IsScalarTower K L' L\nU V : IntermediateField L' L\nH : restr... | [
658,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Submonoid.subsemiringClosure_eq_closure | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S\ninst✝ : NonAssocSemiring T\nx✝ : R\n⊢ x✝ ∈ subsemiringClosure M ↔ x✝ ∈ Subsemiring.closure ↑M",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : NonAssocSemir... | [
877,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.one_pos | [] | [
839,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_id_of_nontrivial_seminorm | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.418441\n𝕜₃ : Type ?u.418444\nE : Type u_1\nEₗ : Type ?u.418450\nF : Type ?u.418453\nFₗ : Type ?u.418456\nG : Type ?u.418459\nGₗ : Type ?u.418462\n𝓕 : Type ?u.418465\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : SeminormedAddC... | [
296,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/MetricSpace/Baire.lean | IsGδ.dense_iUnion_interior_of_closed | [
{
"state_after": "α : Type u_2\nβ : Type ?u.24679\nγ : Type ?u.24682\nι : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : BaireSpace α\ninst✝ : Encodable ι\ns : Set α\nhs : IsGδ s\nhd : Dense s\nf : ι → Set α\nhc : ∀ (i : ι), IsClosed (f i)\nhU : s ⊆ ⋃ (i : ι), f i\ng : ι → Set α := fun i => frontier (f i)ᶜ\n⊢ ... | [
307,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Computability/Ackermann.lean | not_primrec_ack_self | [
{
"state_after": "⊢ ¬Nat.Primrec fun n => ack n n",
"state_before": "⊢ ¬Primrec fun n => ack n n",
"tactic": "rw [Primrec.nat_iff]"
},
{
"state_after": "no goals",
"state_before": "⊢ ¬Nat.Primrec fun n => ack n n",
"tactic": "exact not_nat_primrec_ack_self"
}
] | [
390,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_mul | [
{
"state_after": "no goals",
"state_before": "x y : EReal\n⊢ toReal (x * y) = toReal x * toReal y",
"tactic": "induction x, y using induction₂_symm with\n| top_zero | zero_bot | top_top | top_bot | bot_bot => simp\n| symm h => rwa [mul_comm, EReal.mul_comm]\n| coe_coe => norm_cast\n| top_pos _ h => simp... | [
990,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Order/Monotone/Union.lean | AntitoneOn.Iic_union_Ici | [] | [
126,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/LinearAlgebra/Orientation.lean | Basis.det_adjustToOrientation | [
{
"state_after": "R : Type u_1\ninst✝⁶ : LinearOrderedCommRing R\nM : Type u_3\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nι : Type u_2\ninst✝³ : Fintype ι\ninst✝² : DecidableEq ι\ninst✝¹ : Nontrivial R\ninst✝ : Nonempty ι\ne : Basis ι R M\nx : Orientation R M ι\n⊢ det (if Basis.orientation e = x then e else... | [
312,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.induction_on_prime | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : UniqueFactorizationMonoid α\nP : α → Prop\na : α\nh₁ : P 0\nh₂ : ∀ (x : α), IsUnit x → P x\nh₃ : ∀ (a p : α), a ≠ 0 → Irreducible p → P a → P (p * a)\n⊢ P a",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst... | [
213,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Logic/Nontrivial.lean | Function.Injective.exists_ne | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_2\ninst✝ : Nontrivial α\nf : α → β\nhf : Injective f\ny : β\nx₁ x₂ : α\nhx : x₁ ≠ x₂\n⊢ ∃ x, f x ≠ y",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : Nontrivial α\nf : α → β\nhf : Injective f\ny : β\n⊢ ∃ x, f x ≠ y",
"tactic": "rcases ex... | [
170,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
11
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.beth_mono | [] | [
448,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | HasFTaylorSeriesUpToOn.compContinuousLinearMap | [
{
"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... | [
377,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiableAt_cos | [] | [
92,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.mono_left | [] | [
934,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_sub_left | [
{
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"tactic":... | [
283,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Algebra/Group/Ext.lean | CommGroup.ext | [] | [
161,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.lift_comp | [] | [
522,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_eq_of_eq_mul_left | [
{
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}
] | [
785,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
783,
11
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.const_sub | [] | [
615,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
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Mathlib/Data/Finset/Pointwise.lean | Finset.card_smul_finset | [] | [
2024,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2023,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_congr | [
{
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1191,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
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Mathlib/Order/CompactlyGenerated.lean | Directed.disjoint_iSup_left | [
{
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"tactic": ... | [
409,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
11
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Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.chart_mem_maximalAtlas | [] | [
921,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
1
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Mathlib/Data/Finset/Basic.lean | Finset.filter_or | [
{
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"tactic": "simp [mem_... | [
2851,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2850,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_self_mul_compl_apply | [
{
"state_after": "no goals",
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"tactic": "simp [ha]... | [
433,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image₂_left_identity | [
{
"state_after": "no goals",
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512,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.cg_def | [] | [
230,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/Order/CompleteLattice.lean | iSup_comm | [] | [
1137,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/MeasureTheory/Integral/CircleTransform.lean | Complex.continuous_circleTransformDeriv | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR✝ : ℝ\nz✝ w✝ : ℂ\nR : ℝ\nhR : 0 < R\nf : ℂ → E\nz w : ℂ\nhf : ContinuousOn f (sphere z R)\nhw : w ∈ ball z R\n⊢ Continuous fun θ => (circleMap z R θ - w)⁻¹ • circleTransform R z w f θ",
"state_before": "E : Type u_1\nin... | [
95,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ι_π | [
{
"state_after": "no goals",
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"tactic": "convert (biproduct.bicone f).ι_π... | [
414,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBicone.binary_fan_snd_toCone | [] | [
1016,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1016,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.of_vector_nil | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mk_pos | [
{
"state_after": "x y : ℝ\nf : CauSeq ℚ abs\n⊢ 0 < f ↔ Pos f",
"state_before": "x y : ℝ\nf : CauSeq ℚ abs\n⊢ 0 < mk f ↔ Pos f",
"tactic": "rw [← mk_zero, mk_lt]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nf : CauSeq ℚ abs\n⊢ 0 < f ↔ Pos f",
"tactic": "exact iff_of_eq (cong... | [
346,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.one_mem | [] | [
51,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_prod | [
{
"state_after": "no goals",
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990,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
987,
1
] |
Mathlib/Data/Finmap.lean | Finmap.induction_on | [
{
"state_after": "case mk.mk\nα : Type u\nβ : α → Type v\nC : Finmap β → Prop\nH : ∀ (a : AList β), C ⟦a⟧\nentries✝ : Multiset (Sigma β)\na : List (Sigma β)\nh : Multiset.NodupKeys (Quot.mk Setoid.r a)\n⊢ C { entries := Quot.mk Setoid.r a, nodupKeys := h }",
"state_before": "α : Type u\nβ : α → Type v\nC : ... | [
146,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.add_apply | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.isUnit | [] | [
618,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
11
] |
Mathlib/Order/CompleteLattice.lean | biInf_mono | [] | [
899,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.runCatch_throw | [] | [
67,
97
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
67,
9
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.σ_comp_σ | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\ni j : Fin (n + 1)\nH : i ≤ j\n⊢ X.map (SimplexCategory.σ (↑Fin.castSucc i)) ≫ X.map (SimplexCategory.σ j) =\n X.map (SimplexCategory.σ (Fin.succ j)) ≫ X.map (SimplexCategory.σ i)",
"state_before": "C : Type u\ninst✝ : Cate... | [
577,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.sUnion_bounded_univ | [] | [
218,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.div_le_div_left | [] | [
519,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
11
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_singleton_zero | [] | [
205,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_col | [
{
"state_after": "case a.h\nl : Type ?u.1213810\nm : Type u_1\nn : Type ?u.1213816\no : Type ?u.1213819\nm' : o → Type ?u.1213824\nn' : o → Type ?u.1213829\nR : Type ?u.1213832\nS : Type ?u.1213835\nα : Type v\nβ : Type w\nγ : Type ?u.1213842\nv : m → α\ni✝ : Unit\nx✝ : m\n⊢ (col v)ᵀ i✝ x✝ = row v i✝ x✝",
"... | [
2681,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2679,
1
] |
Mathlib/Init/Meta/WellFoundedTactics.lean | Nat.zero_lt_one_add | [
{
"state_after": "a : ℕ\nthis : 0 < a + 1\n⊢ 0 < a + 1",
"state_before": "a : ℕ\nthis : 0 < a + 1\n⊢ 0 < 1 + a",
"tactic": "simp [Nat.add_comm]"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\nthis : 0 < a + 1\n⊢ 0 < a + 1",
"tactic": "assumption"
}
] | [
26,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
22,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist.def | [] | [
28,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.const_lintegral_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.897125\nγ : Type ?u.897128\nδ : Type ?u.897131\nm : MeasurableSpace α\nμ ν : Measure α\nc : ℝ≥0∞\ns : Set α\n⊢ lintegral (const α c) (Measure.restrict μ s) = c * ↑↑μ s",
"tactic": "rw [const_lintegral, Measure.restrict_apply Measura... | [
1099,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Topology/Basic.lean | DenseRange.dense_of_mapsTo | [] | [
1842,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1840,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.mul_rpow_of_nonneg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ≥0∞\nz : ℝ\nhz : 0 ≤ z\n⊢ (x * y) ^ z = x ^ z * y ^ z",
"tactic": "simp [hz.not_lt, mul_rpow_eq_ite]"
}
] | [
518,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_congr_ae | [] | [
994,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.units_semiconj_of_translationNumber_eq | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nf₁ f₂ : CircleDeg1Liftˣ\nh : τ ↑f₁ = τ ↑f₂\nn : Multiplicative ℤ\n⊢ τ (↑(MonoidHom.comp (Units.coeHom CircleDeg1Lift) (↑(zpowersHom CircleDeg1Liftˣ) f₁)) n) =\n τ (↑(MonoidHom.comp (Units.coeHom CircleDeg1Lift) (↑(zpowersHom CircleDeg1Li... | [
1013,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | infEdist_inv_inv | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns✝ t : Set E\nx✝ y x : E\ns : Set E\n⊢ infEdist x⁻¹ s⁻¹ = infEdist x s",
"tactic": "rw [← image_inv, infEdist_image isometry_inv]"
}
] | [
65,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.is_greatest | [
{
"state_after": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nm : ℕ\nhm : ∃ h, Part.get (multiplicity a b) h < m\nh : a ^ m ∣ b\n⊢ False",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nm : ℕ\nhm : multiplicity a... | [
117,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_unique' | [] | [
927,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Init/Logic.lean | dif_ctx_simp_congr | [] | [
423,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | HasDerivAt.tendsto_punctured_nhds | [] | [
118,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/LinearAlgebra/Ray.lean | smul_rayOfNeZero | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_insert | [] | [
1171,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.ker_mk_eq | [] | [
105,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.adjointify_η_ε | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nη : 𝟭 C ≅ F ⋙ G\nε : G ⋙ F ≅ 𝟭 D\nX : C\n⊢ F.map\n ((((((η.hom.app X ≫ 𝟙 (G.obj (F.obj X))) ≫ G.map (ε.inv.app (F.obj X))) ≫ 𝟙 (G.obj (F.obj (G.obj (F.obj X))))) ≫\n 𝟙 (G.obj (F.ob... | [
267,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.exists_measurableEmbedding_real | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝³ : TopologicalSpace α\nι : Type ?u.401587\ninst✝² : MeasurableSpace α\ninst✝¹ : PolishSpace α\ninst✝ : BorelSpace α\ns : Set ℝ\nhs : MeasurableSet s\ne : α ≃ᵐ ↑s\n⊢ ∃ f, MeasurableEmbedding f",
"state_before": "α : Type u_1\ninst✝³ : TopologicalS... | [
827,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.hom_ext | [] | [
593,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BooleanRing.sup_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13321\nγ : Type ?u.13324\ninst✝² : BooleanRing α\ninst✝¹ : BooleanRing β\ninst✝ : BooleanRing γ\na b c : α\n⊢ a + b + a * b + c + (a + b + a * b) * c = a + (b + c + b * c) + a * (b + c + b * c)",
"tactic": "ring"
}
] | [
210,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.symm_proj_apply | [] | [
617,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.coe_eq_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nz : ℤ_[p]\n⊢ ↑z = 0 ↔ z = 0",
"tactic": "rw [← coe_zero, Subtype.coe_inj]"
}
] | [
148,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | IsOpen.reProdIm | [] | [
209,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousAt.comp_continuousWithinAt | [] | [
885,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.natTrailingDegree_eq_of_trailingDegree_eq | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝¹ : Semiring R\np q✝ r : R[X]\ninst✝ : Semiring S\nq : S[X]\nh : trailingDegree p = trailingDegree q\n⊢ Option.getD (trailingDegree p) 0 = Option.getD (trailingDegree q) 0",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝¹ : S... | [
154,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
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