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/RingTheory/PowerBasis.lean | PowerBasis.isIntegral_gen | [] | [
212,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/GCDMonoid/Div.lean | Finset.Polynomial.gcd_div_id_eq_one | [] | [
94,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.dist_center_inversion | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b c✝ d x✝ y z : P\nR✝ : ℝ\nc x : P\nR : ℝ\n⊢ dist c (inversion c R x) = R ^ 2 / dist c x",
"tactic": "rw [dist_c... | [
78,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_congr' | [] | [
972,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.toLinearMap_inj | [] | [
174,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_singleton | [] | [
131,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
9
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.cancel_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.36632\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf✝ g : C(α, β)\nf : C(β, γ)\ng₁ g₂ : C(α, β)\nhf : Injective ↑f\nh : comp f g₁ = comp ... | [
282,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.join_zero | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.8097\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(join 0) s = ↑↑0 s",
"state_before": "α : Type u_1\nβ : Type ?u.8097\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\n⊢ join 0 = 0",
"tactic": "ext... | [
121,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_eq_zero_iff | [] | [
1877,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1876,
1
] |
Mathlib/Algebra/Support.lean | Function.mem_mulSupport | [] | [
70,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_add_nat | [] | [
1391,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1390,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_ofLe | [] | [
641,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.one_def | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
src/lean/Init/Core.lean | iff_iff_implies_and_implies | [] | [
658,
80
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
657,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_X_add_C | [
{
"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\nc : R\n⊢ ↑derivative (X + ↑C c) = 1",
"tactic": "rw [derivative_add, derivative_X, derivative_C, add_zero]"
}
] | [
162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.liftAddHom_symm_apply | [] | [
448,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_val | [] | [
443,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_eq_sub_of_hasDerivAt_of_tendsto | [
{
"state_after": "ι : Type ?u.1849419\n𝕜 : Type ?u.1849422\nE : Type u_1\nF✝ : Type ?u.1849428\nA : Type ?u.1849431\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝ : ℝ → E\ng' g φ : ℝ → ℝ\nf f' : ℝ → E\na b : ℝ\nhab : a < b\nfa fb : E\nhderiv : ∀ (x : ℝ), x ∈ Ioo a b → Has... | [
1230,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.surjective_of_injective | [
{
"state_after": "α : Type u_1\nβ : Type ?u.26048\nγ : Type ?u.26051\ninst✝ : Finite α\nf : α → α\nhinj : Injective f\nx : α\n⊢ ∃ a, f a = x",
"state_before": "α : Type u_1\nβ : Type ?u.26048\nγ : Type ?u.26051\ninst✝ : Finite α\nf : α → α\nhinj : Injective f\n⊢ Surjective f",
"tactic": "intro x"
},
... | [
624,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.add_im | [] | [
228,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
9
] |
Mathlib/Data/Nat/Lattice.lean | Nat.not_mem_of_lt_sInf | [
{
"state_after": "no goals",
"state_before": "s : Set ℕ\nm : ℕ\nhm : m < sInf s\n⊢ ¬m ∈ s",
"tactic": "cases eq_empty_or_nonempty s with\n| inl h => subst h; apply not_mem_empty\n| inr h => rw [Nat.sInf_def h] at hm; exact Nat.find_min h hm"
},
{
"state_after": "case inl\nm : ℕ\nhm : m < sInf ∅\... | [
80,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_zero | [
{
"state_after": "no goals",
"state_before": "⊢ cos 0 = 1",
"tactic": "rw [← coe_zero, cos_coe, Real.cos_zero]"
}
] | [
398,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubalgebra.mem_normalizer_iff' | [
{
"state_after": "R : Type u_2\nL : Type u_1\nM : Type ?u.37972\nM' : Type ?u.37975\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : Lie... | [
121,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_lt_top_of_ae_bound | [] | [
438,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.preimage_mk_interior | [] | [
503,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.bipartiteAbove_swap | [] | [
62,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.CostructuredArrow.projectQuotient_factors | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nS : C ⥤ D\nT : D\ninst✝¹ : HasColimits C\ninst✝ : PreservesColimits S\nA : CostructuredArrow S T\nP : (CostructuredArrow S T)ᵒᵖ\nf : P ⟶ A.op\nhf : Mono f\n⊢ S.map (Subobject.arrow (Subobject.mk f.unop.left.op)).unop ≫\n ... | [
157,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.not_sSameSide | [] | [
662,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.norm_inner_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type ?u.580576\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\nx y : F\n⊢ ‖inner x y‖ = ‖inner y x‖",
"tactic": "rw [← inner_conj_symm, norm_conj]"
}
] | [
280,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/Normed/Order/Lattice.lean | norm_inf_sub_inf_le_norm | [] | [
195,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Topology/Order.lean | discreteTopology_iff_nhds_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt t₁ t₂ : TopologicalSpace α\ns : Set α\ninst✝ : TopologicalSpace α\n⊢ DiscreteTopology α ↔ ∀ (x : α), 𝓝[{x}ᶜ] x = ⊥",
"tactic": "simp only [discreteTopology_iff_singleton_mem_nhds, nhdsWithin, inf_principal_eq_bot, compl_compl]"
}
] | [
342,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.bounded_below | [
{
"state_after": "case intro.intro\nV : Type u\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ℝ V\ninst✝ : CompleteSpace V\nB : V →L[ℝ] V →L[ℝ] ℝ\nC : ℝ\nC_ge_0 : 0 < C\ncoercivity : ∀ (u : V), C * ‖u‖ * ‖u‖ ≤ ↑(↑B u) u\n⊢ ∃ C, 0 < C ∧ ∀ (v : V), C * ‖v‖ ≤ ‖↑(continuousLinearMapOfBilin B) v‖",
"... | [
70,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map₂_mk_top_top_eq_top | [
{
"state_after": "R : Type u_3\ninst✝¹⁶ : CommSemiring R\nR' : Type ?u.489165\ninst✝¹⁵ : Monoid R'\nR'' : Type ?u.489171\ninst✝¹⁴ : Semiring R''\nM : Type u_1\nN : Type u_2\nP : Type ?u.489183\nQ : Type ?u.489186\nS : Type ?u.489189\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid N\ninst✝¹¹ : AddCommMonoid ... | [
424,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.natAbs_euclideanDomain_gcd | [
{
"state_after": "case a\na b : ℤ\n⊢ ↑(natAbs (EuclideanDomain.gcd a b)) ∣ ↑(gcd a b)\n\ncase a\na b : ℤ\n⊢ ↑(gcd a b) ∣ ↑(natAbs (EuclideanDomain.gcd a b))",
"state_before": "a b : ℤ\n⊢ natAbs (EuclideanDomain.gcd a b) = gcd a b",
"tactic": "apply Nat.dvd_antisymm <;> rw [← Int.coe_nat_dvd]"
},
{
... | [
253,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel_not_mono_of_nonzero | [] | [
862,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.map_inv | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
11
] |
Mathlib/Topology/Algebra/Monoid.lean | exists_open_nhds_one_mul_subset | [
{
"state_after": "case intro.intro.intro\nι : Type ?u.166179\nα : Type ?u.166182\nX : Type ?u.166185\nM : Type u_1\nN : Type ?u.166191\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\nU : Set M\nhU : U ∈ 𝓝 1\nV : Set M\nVo : IsOpen V\nV1 : 1 ∈ V\nhV : ∀ (v ... | [
513,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/List/MinMax.lean | List.argmax_eq_some_iff | [] | [
250,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | EMetric.exists_continuous_nNReal_forall_closedBall_subset | [
{
"state_after": "case intro.intro\nι : Type u_2\nX : Type u_1\ninst✝ : EMetricSpace X\nK U : ι → Set X\nhK : ∀ (i : ι), IsClosed (K i)\nhU : ∀ (i : ι), IsOpen (U i)\nhKU : ∀ (i : ι), K i ⊆ U i\nhfin : LocallyFinite K\nδ : C(X, ℝ)\nhδ₀ : ∀ (x : X), 0 < ↑δ x\nhδ : ∀ (i : ι) (x : X), x ∈ K i → closedBall x (ENNRe... | [
108,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.ins_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : RBNode α\np : Path α\n⊢ toList (ins p t) = withList p (toList t)",
"tactic": "match p with\n| .root | .left red .. | .right red .. | .left black .. | .right black .. =>\n simp [ins, ins_toList]"
},
{
"state_after": "no goals",
... | [
493,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
490,
9
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.smul_continuousOn | [
{
"state_after": "X : Type u_1\nY : Type ?u.2503222\nE : Type u_3\nR : Type ?u.2503228\ninst✝¹⁰ : MeasurableSpace X\ninst✝⁹ : TopologicalSpace X\ninst✝⁸ : MeasurableSpace Y\ninst✝⁷ : TopologicalSpace Y\ninst✝⁶ : NormedAddCommGroup E\nf✝ : X → E\nμ : Measure X\ns✝ : Set X\ninst✝⁵ : OpensMeasurableSpace X\nA K : ... | [
479,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq1.join_cons | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na b : α\ns : Seq α\nS : Seq (Seq1 α)\n⊢ (match destruct (Seq.cons b s) with\n | none => (a, Seq.join S)\n | some s' => (a, Seq.join (Seq.cons s' S))) =\n (a, Seq.join (Seq.cons (b, s) S))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na ... | [
947,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.inv_smul_mem_iff₀ | [] | [
2040,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2039,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.mkₐ_ker | [] | [
236,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Sigma/Basic.lean | Prod.snd_toSigma | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_eq_card_lt_and_coprime | [
{
"state_after": "n : ℕ\ne : ↑{m | m < n ∧ coprime n m} ≃ { x // x ∈ filter (coprime n) (range n) } :=\n { toFun := fun m => { val := ↑m, property := (_ : ↑m ∈ filter (coprime n) (range n)) },\n invFun := fun m => { val := ↑m, property := (_ : ↑m < n ∧ coprime n ↑m) },\n left_inv :=\n (_ :\n ... | [
62,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.nsmul_coeff | [] | [
377,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Std/Logic.lean | imp_not_comm | [] | [
128,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
128,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.congr_arg | [] | [
505,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
11
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_mul_eq_smul | [] | [
1066,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_eq_inf | [] | [
613,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nonempty_of_mem | [] | [
460,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | Summable.tsum_mul_right | [] | [
62,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/List/Basic.lean | List.replicate_left_inj | [] | [
489,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
9
] |
Mathlib/Analysis/Calculus/TangentCone.lean | IsOpen.uniqueDiffWithinAt | [] | [
323,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mk_preimage_prod_left_fn_eq_if | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.29388\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\ninst✝ : DecidablePred fun x => x ∈ t\nf : γ → α\n⊢ (fun a => (f a, b)) ⁻¹' s ×ˢ t = if b ∈ t then f ⁻¹' s else ∅",
"tactic": "rw [← mk_preimage_prod_... | [
258,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.inv_left₀ | [] | [
72,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_of_add_const_left | [] | [
693,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_add_transpose_self | [] | [
169,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.dist_integralSum_integral_le_of_memBaseSet | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\nc c₁ c₂ ... | [
460,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.i_mul_k | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.21045\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\n⊢ q.i * q.k = c₁ • q.j",
"tactic": "rw [← i_mul_j, ← mul_assoc, i_mul_i, smul_mul_a... | [
89,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_of_le_one | [
{
"state_after": "case inl\nho : 0 ≤ 1\n⊢ Principal (fun x x_1 => x + x_1) 0\n\ncase inr\nho : 1 ≤ 1\n⊢ Principal (fun x x_1 => x + x_1) 1",
"state_before": "o : Ordinal\nho : o ≤ 1\n⊢ Principal (fun x x_1 => x + x_1) o",
"tactic": "rcases le_one_iff.1 ho with (rfl | rfl)"
},
{
"state_after": "n... | [
140,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.boundedBy_eq_self | [] | [
870,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasDerivAt_exp | [] | [
207,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Order/Filter/Extr.lean | IsExtrOn.on_subset | [] | [
293,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.pow_comp | [] | [
638,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/Data/List/Sublists.lean | List.mem_sublistsLen_self | [
{
"state_after": "case slnil\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nl l' : List α\n⊢ [] ∈ sublistsLen (length []) []\n\ncase cons\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\nl l' l₁ l₂ : List α\na : α\ns : l₁ <+ l₂\nIH : l₁ ∈ sublistsLen (length l₁) l₂\n⊢ l₁ ∈ sublistsLen (length l₁) (a :: ... | [
328,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.mul_of'_modOf | [
{
"state_after": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\ng g' : G\n⊢ ↑(x * of' k G g %ᵒᶠ g) g' = ↑0 g'",
"state_before": "k : Type u_1\nG : Type u_2\ninst✝¹ : Semiring k\ninst✝ : AddCancelCommMonoid G\nx : AddMonoidAlgebra k G\ng : G\n⊢ x * ... | [
171,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.pure_one | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.449865\nγ : Type ?u.449868\ninst✝ : DecidableEq α\ns✝ t✝ s t : Multiset α\n⊢ ∀ (a : α), a ∈ toFinset (s ∩ t) ↔ a ∈ toFinset s ∩ toFinset t",
"tactic": "simp"
}
] | [
3172,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3171,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coord_apply_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nι' : Type ?u.90092\nk : Type u_1\nV : Type u_4\nP : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j : ι\ne : ι ≃ ι'\ni : ι\n⊢ ↑(coord b i) (↑b i) = 1",
... | [
173,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.hasSum | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.13763\nδ : Type ?u.13766\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g : β → α\na b : α\ns : Finset β\nha : Summable f\n⊢ HasSum f (Classical.choose (_ : Summable fun b => f b))",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.... | [
80,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.sub_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.191118\nι : Sort x\ninst✝ : AddGroup β\nf g : α → β\nl : Filter α\nh : f =ᶠ[l] g\n⊢ f - g =ᶠ[l] 0",
"tactic": "simpa using ((EventuallyEq.refl l f).sub h).symm"
}
] | [
1611,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1610,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_pred_of_not_isMin | [] | [
943,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Std/Data/List/Lemmas.lean | List.mem_insert_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\n⊢ a ∈ List.insert b l ↔ a = b ∨ a ∈ l",
"tactic": "if h : b ∈ l then\n rw [insert_of_mem h]\n constructor; {apply Or.inr}\n intro\n | Or.inl h' => rw [h']; exact h\n | Or.inr h' => exact h'\nelse... | [
905,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
898,
9
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.eqOn_sclosure | [] | [
909,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Data/Finsupp/Indicator.lean | Finsupp.indicator_of_mem | [] | [
48,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_induction₂ | [] | [
1170,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1163,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.div_const | [
{
"state_after": "α : Type u_1\nβ : Type ?u.126772\nγ : Type ?u.126775\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf : Filter α\nm : α → ℝ≥0∞\na b : ℝ≥0∞\nhm : Tendsto m f (𝓝 a)\nha : a ≠ 0 ∨ b ≠ 0\n⊢ a ≠ 0 ∨ b⁻¹ ≠ ⊤",
"state_before": "α : Type u_1\nβ : Type ?u.126772\nγ : Type ?u.1... | [
556,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
11
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuousAt_const | [] | [
184,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_norm | [] | [
476,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/CategoryTheory/Products/Basic.lean | CategoryTheory.prod_comp | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.comp_symm_eq | [] | [
419,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_lt_add_left_coe | [
{
"state_after": "no goals",
"state_before": "x y : EReal\nh : x < y\nz : ℝ\n⊢ ↑z + x < ↑z + y",
"tactic": "simpa [add_comm] using add_lt_add_right_coe h z"
}
] | [
693,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
Mathlib/Order/WellFoundedSet.lean | Finset.wellFoundedOn_bUnion | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.124371\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\ns : Finset ι\nf : ι → Set α\n⊢ Set.WellFoundedOn (⋃ (i : ι) (_ : i ∈ s), f i) r ↔ ∀ (i : ι), i ∈ s → Set.WellFoundedOn (f i) r",
"tactic": "simpa only [Finset.sup_eq... | [
588,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_of_forall_measure_lt_top_ae_restrict | [] | [
3879,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3877,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.iterate | [] | [
432,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Std/Data/List/Lemmas.lean | List.take_subset | [] | [
1728,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1727,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_eq_none | [] | [
290,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_preserving_piFinSuccAboveEquiv | [] | [
772,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.coprime_dvd_right | [] | [
304,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
303,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.proj_coe | [] | [
148,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.piecewise | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.193105\nι : Type ?u.193108\ninst✝¹ : Countable ι\nf g : α → β\nm : MeasurableSpace α\ninst✝ : TopologicalSpace β\ns : Set α\nx✝ : DecidablePred fun x => x ∈ s\nhs : MeasurableSet s\nhf : StronglyMeasurable f\nhg : StronglyMeasurable g\nx : α\n⊢ Tendsto\n... | [
743,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
11
] |
Mathlib/Data/Sym/Card.lean | Sym2.two_mul_card_image_offDiag | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73737\ninst✝ : DecidableEq α\ns : Finset α\n⊢ ∀ (a : α × α),\n Quotient.mk'' a ∈ image Quotient.mk' (offDiag s) →\n Finset.card (filter (fun x => Quotient.mk' x = Quotient.mk'' a) (offDiag s)) = 2",
"state_before": "α : Type u_1\nβ : Type ?u.73737\ninst✝ :... | [
163,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_withDensity_iff_integrable_smul | [] | [
869,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.150066\nγ : Type ?u.150069\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ s ∪ insert a t = insert a (s ∪ t)",
"tactic": "simp only [insert_eq, union_left_comm]"
}
] | [
1456,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.topologicalClosure_minimal | [] | [
173,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.contraction_degree_eq_or_insep | [
{
"state_after": "case inr\nF : Type u_1\ninst✝¹ : Field F\nq : ℕ\nf : F[X]\nhf : HasSeparableContraction q f\nhq : NeZero q\ninst✝ : CharP F q\ng g' : F[X]\nm m' : ℕ\nh_expand : ↑(expand F (q ^ m)) g = ↑(expand F (q ^ m')) g'\nhg : Separable g\nhg' : Separable g'\nthis :\n ∀ {F : Type u_1} [inst : Field F] (q... | [
130,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_pi | [] | [
677,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.integral_add_measure | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.208871\n𝕜 : Type ?u.208874\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\np : ℝ≥0∞\nG : Type ?u.208976\nF' : Type ?u.208979\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : NormedAddCommGroup F'\ninst✝⁴ : NormedSpace ℝ ... | [
457,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
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