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/LinearAlgebra/LinearIndependent.lean | LinearIndependent.extend_subset | [] | [
1309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1306,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.add_mem | [] | [
182,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.untrop_le_iff | [] | [
177,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.filterMap | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\nf : α → Option β\nl₁ l₂ : List α\np : l₁ ~ l₂\n⊢ List.filterMap f l₁ ~ List.filterMap f l₂",
"tactic": "induction p with\n| nil => simp\n| cons x _p IH =>\n simp only [filterMap]\n cases h : f x\n <;> simp [h,... | [
254,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_self_eq_zero | [
{
"state_after": "𝕜 : Type u_1\nE : Type ?u.538902\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core 𝕜 F\n⊢ inner 0 0 = 0",
"state_before": "𝕜 : Type u_1\nE : Type ?u.538902\nF : Type u_2\ninst✝² : IsROrC 𝕜\ninst✝¹ : AddCommGroup F\ninst✝ : Module 𝕜 F\nc : Core �... | [
261,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitUpper_eq_self | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type ?u.15762\nn : ℕ\nI : Box ι\ni : ι\nx : ℝ\ny : ι → ℝ\n⊢ splitUpper I i x = ↑I ↔ x ≤ lower I i",
"tactic": "simp [splitUpper, update_eq_iff]"
}
] | [
128,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | tendsto_inv_nhdsWithin_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalGroup G\ninst✝³ : TopologicalSpace α\nf : α → G\ns : Set α\nx : α\ninst✝² : TopologicalSpace H\ninst✝¹ : OrderedCommGroup H\ninst✝ : ContinuousInv ... | [
561,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.ortho_comm | [] | [
977,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
976,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_inter_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.204664\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ ∀ (x : α), x ∈ Ico a b ∩ Iio c ↔ x ∈ Ico a (min b c)",
"tactic": "simp (config := { contextual := true }) [iff_def]"
}
] | [
1832,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1831,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isOpen_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.96096\nι : Type ?u.96099\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ IsOpen s ↔ ∀ (x : α), x ∈ s → ∃ ε, ε > 0 ∧ ball x ε ⊆ s",
"tactic": "simp only [isOpen_iff_mem_nhds, mem_nhds_iff]"
}
] | [
1005,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | AffineSubspace.pointwise_vadd_span | [] | [
78,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_quotient_center | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nhH : Group.IsNilpotent G\nn : ℕ\nhn : nilpotencyClass G = n\n⊢ nilpotencyClass (G ⧸ center G) = n - 1",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nhH : Group.IsNilpotent G\n⊢ nilpotenc... | [
639,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/List/Sigma.lean | List.nodupKeys_of_nodupKeys_cons | [] | [
117,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.compl | [] | [
1727,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.iInf_coe | [
{
"state_after": "R : Type u_2\nS : Type ?u.139553\nM : Type u_3\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S M\ninst✝¹ : SMul S R\ninst✝ : IsScalarTower S R M\np✝ q : Submodule R M\nι : Sort u_1\np : ι → Submodule R M\n⊢ (⋂ (p_1 : Submodule R M) (_... | [
259,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/UV.lean | UV.shadow_compression_subset_compression_shadow | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\nu✝ v✝ a u v : Finset α\nhuv : ∀ (x : α), x ∈ u → ∃ y, y ∈ v ∧ IsCompressed (erase u x) (erase v y) 𝒜\n𝒜' : Finset (Finset α) := 𝓒 u v 𝒜\n⊢ (∂ ) 𝒜' ⊆ 𝓒 u v ((∂ ) 𝒜)",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜... | [
426,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.const_smul | [] | [
83,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
8
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_den | [] | [
106,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.comap_singleton_isClosed_of_isIntegral | [] | [
643,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_mul_two_eq_iff | [
{
"state_after": "case zero\na : ZMod Nat.zero\n⊢ valMinAbs a * 2 = ↑Nat.zero ↔ 2 * val a = Nat.zero\n\ncase succ\nn : ℕ\na : ZMod (Nat.succ n)\n⊢ valMinAbs a * 2 = ↑(Nat.succ n) ↔ 2 * val a = Nat.succ n",
"state_before": "n : ℕ\na : ZMod n\n⊢ valMinAbs a * 2 = ↑n ↔ 2 * val a = n",
"tactic": "cases' n w... | [
952,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.coeff_zero_mem_comap_of_root_mem | [] | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_norm_eq_pos_sub_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.110031\nE : Type ?u.110034\nF : Type ?u.110037\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf✝ g : α → E\ns t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ\nhfi : ... | [
444,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
src/lean/Init/Data/List/Basic.lean | List.reverse_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas bs : List α\n⊢ reverse (as ++ bs) = reverse bs ++ reverse as",
"tactic": "induction as generalizing bs with\n| nil => simp\n| cons a as ih => simp [ih]; rw [append_assoc]"
},
{
"state_after": "no goals",
"st... | [
181,
49
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
178,
9
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.not_mem_erase | [] | [
329,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | strictConcaveOn_sqrt_mul_log_Ioi | [
{
"state_after": "⊢ ContinuousOn (fun x => sqrt x * log x) (Ioi 1)\n\nx : ℝ\nhx : x ∈ Ioi 1\n⊢ (deriv^[2]) (fun x => sqrt x * log x) x < 0",
"state_before": "⊢ StrictConcaveOn ℝ (Ioi 1) fun x => sqrt x * log x",
"tactic": "apply strictConcaveOn_of_deriv2_neg' (convex_Ioi 1) _ fun x hx => ?_"
},
{
... | [
163,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableAt.inner | [] | [
135,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_pi_single | [] | [
542,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.const_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.82300\nf g : α → β\nc c₁ c₂ x✝ : α\ninst✝ : AddSemigroup α\nh : Periodic f c\na x : α\n⊢ (fun x => f (a + x)) (x + c) = (fun x => f (a + x)) x",
"tactic": "simpa [add_assoc] using h (a + x)"
}
] | [
183,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.congr_fun | [] | [
158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq'_bounded_by_pos_constant | [
{
"state_after": "case intro\nc : ℝ\nh : ∀ (n : ℕ), c ≤ Real.log (stirlingSeq (succ n))\n⊢ ∃ a, 0 < a ∧ ∀ (n : ℕ), a ≤ stirlingSeq (succ n)",
"state_before": "⊢ ∃ a, 0 < a ∧ ∀ (n : ℕ), a ≤ stirlingSeq (succ n)",
"tactic": "cases' log_stirlingSeq_bounded_by_constant with c h"
},
{
"state_after": ... | [
196,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/List/Basic.lean | List.bind_eq_bind | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_prod_eq_prod | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.154039\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\n⊢ 𝓤 (α × β) = map (fun p => ((p.fst.fst, p.snd.fst), p.fst.snd, p.snd.snd)) (𝓤 α ×ˢ 𝓤 β)",
"tactic": "rw [map_swap4_eq_comap, uniformi... | [
1583,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1581,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_comm | [] | [
354,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.CompleteType.mem_typeOf | [] | [
194,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_div_cancel_left | [
{
"state_after": "no goals",
"state_before": "m n : Nat\nH : 0 < n\n⊢ n * m / n = m",
"tactic": "rw [Nat.mul_comm, Nat.mul_div_cancel _ H]"
}
] | [
593,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
592,
11
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_tfae | [
{
"state_after": "case tfae_1_iff_2\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ Exact f g ↔ f ≫ g = 0 ∧ kernel.ι g ≫ cokernel.π f = 0\n\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\ntfae_1_iff_2 : Exact f g ↔ f ≫ g = 0 ∧ kerne... | [
106,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_neg_of_le_neg | [
{
"state_after": "a b : Int\nh✝ : a ≤ -b\nh : - -b ≤ -a\n⊢ b ≤ -a",
"state_before": "a b : Int\nh : a ≤ -b\n⊢ b ≤ -a",
"tactic": "have h := Int.neg_le_neg h"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : a ≤ -b\nh : - -b ≤ -a\n⊢ b ≤ -a",
"tactic": "rwa [Int.neg_neg] at... | [
904,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
902,
11
] |
Mathlib/Data/List/Basic.lean | List.insertNth_of_length_lt | [
{
"state_after": "case nil\nι : Type ?u.122867\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : List α\nx : α\nn✝ : ℕ\nh✝ : length l < n✝\nn : ℕ\nh : length [] < n\n⊢ insertNth n x [] = []\n\ncase cons\nι : Type ?u.122867\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α... | [
1670,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineMap.homothety_neg_one_apply | [
{
"state_after": "no goals",
"state_before": "k : Type ?u.707847\nP₁ : Type u_1\nP₂ : Type ?u.707853\nP₃ : Type ?u.707856\nP₄ : Type ?u.707859\nV₁ : Type u_2\nV₂ : Type ?u.707865\nV₃ : Type ?u.707868\nV₄ : Type ?u.707871\ninst✝¹⁴ : Ring k\ninst✝¹³ : AddCommGroup V₁\ninst✝¹² : Module k V₁\ninst✝¹¹ : AffineSp... | [
657,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.distribMulActionHom_ext | [] | [
1673,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
] |
Mathlib/Init/Data/Int/Order.lean | Int.lt.elim | [] | [
38,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_empty | [] | [
1015,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one | [
{
"state_after": "case h\nF : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L : IntermediateField F E\nh : ∀ (x : E), finrank F { x_1 // x_1 ∈ F⟮x⟯ } = 1\ny : E\n⊢ y ∈ ⊥ ↔ y ∈ ⊤",
"state_before": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : F... | [
760,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.pow_apply_mem_of_forall_mem | [
{
"state_after": "case zero\nR : Type u_1\nR₁ : Type ?u.246811\nR₂ : Type ?u.246814\nR₃ : Type ?u.246817\nR₄ : Type ?u.246820\nS : Type ?u.246823\nK : Type ?u.246826\nK₂ : Type ?u.246829\nM : Type u_2\nM' : Type ?u.246835\nM₁ : Type ?u.246838\nM₂ : Type ?u.246841\nM₃ : Type ?u.246844\nM₄ : Type ?u.246847\nN : T... | [
411,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.congr_symm_tmul | [] | [
880,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf g : Perm α\nhf : f ∈ cycleFactorsFinset g\n⊢ cycleType (g * f⁻¹) + cycleType f = cycleType g - cycleType f + cycleType f",
"tactic": "rw [← (disjoint_mul_inv_of_mem_cycleFactorsFinset hf).cycleType, ... | [
237,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.smul_le_smul_right | [] | [
1049,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.parallel_bot_iff_eq_bot | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\nh : s ∥ ⊥\n⊢ s = ⊥",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Modul... | [
1757,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1754,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_mul_const' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.946443\nγ : Type ?u.946446\nδ : Type ?u.946449\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\nhr : r ≠ ⊤\n⊢ (∫⁻ (a : α), f a * r ∂μ) = (∫⁻ (a : α), f a ∂μ) * r",
"tactic": "simp_rw [mul_comm, lintegral_const_mul' r... | [
746,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_congr | [] | [
2476,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2474,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_powerset | [] | [
2134,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2134,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.AbsolutelyContinuous.map | [
{
"state_after": "case pos\nα : Type u_2\nβ : Type u_1\nm : MeasurableSpace α\nL : Type ?u.642970\nM : Type u_3\nN : Type u_4\ninst✝⁶ : AddCommMonoid L\ninst✝⁵ : TopologicalSpace L\ninst✝⁴ : AddCommMonoid M\ninst✝³ : TopologicalSpace M\ninst✝² : AddCommMonoid N\ninst✝¹ : TopologicalSpace N\nv : VectorMeasure α ... | [
1152,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.continuous_mul' | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝ : Group α\ng : GroupTopology α\nthis : TopologicalSpace α := g.toTopologicalSpace\n⊢ Continuous fun p => p.fst * p.snd",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝ : Group α\ng : GroupTopology α\n⊢ Continuous... | [
1857,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1852,
1
] |
Mathlib/CategoryTheory/ConnectedComponents.lean | CategoryTheory.inclusion_comp_decomposedTo | [] | [
132,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.and | [] | [
720,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
11
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_of_closed' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.305337\nι : Type ?u.305340\ninst✝ : PseudoMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ\ns✝ s : Set α\nhs : IsClosed s\na : α\n⊢ a ∈ s ↔ ∀ (ε : ℝ), ε > 0 → ∃ b, b ∈ s ∧ dist a b < ε",
"tactic": "simpa only [hs.closure_eq] using @m... | [
1915,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1913,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | Continuous.inv | [] | [
243,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.IccExtend_eq_self | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\ninst✝ : LinearOrder α\na b : α\nh : a ≤ b\nx✝ : α\nf : α → β\nha : ∀ (x : α), x < a → f x = f a\nhb : ∀ (x : α), b < x → f x = f b\nx : α\n⊢ IccExtend h (f ∘ Subtype.val) x = f x",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : LinearOrder α\na b :... | [
152,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_eq | [] | [
984,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.rename_eq | [
{
"state_after": "σ : Type u_1\nτ : Type u_3\nα : Type ?u.245747\nR : Type u_2\nS : Type ?u.245753\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : σ → τ\np : MvPolynomial σ R\n⊢ (sum p fun s a => ↑(monomial (sum s fun a b => Finsupp.single (f a) b)) a) =\n sum p fun a => Finsupp.single (sum a fun a => ... | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_const_mono | [] | [
885,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.denseInducing | [] | [
791,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
11
] |
Mathlib/Order/LiminfLimsup.lean | Filter.OrderIso.apply_bliminf | [] | [
959,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Std/Logic.lean | or_comm | [] | [
263,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
263,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.hasSum_iff_tendsto_nat | [
{
"state_after": "α : Type ?u.312215\nβ : Type ?u.312218\nγ : Type ?u.312221\nf : ℕ → ℝ≥0\nr : ℝ≥0\n⊢ Tendsto (fun n => ∑ i in Finset.range n, ↑(f i)) atTop (𝓝 ↑r) ↔\n Tendsto (fun n => ∑ i in Finset.range n, f i) atTop (𝓝 r)",
"state_before": "α : Type ?u.312215\nβ : Type ?u.312218\nγ : Type ?u.312221... | [
1129,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.measurable_of_not_restrict_le_zero | [] | [
1022,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.self_comp_sort | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\n⊢ graph.proj ∘ (↑(graphEquiv₁ f) ∘ ↑(graphEquiv₁ f).symm) ∘ ↑(graphEquiv₂ f).toEquiv = graph.proj ∘ ↑(graphEquiv₂ f)",
"tactic": "simp"
}
] | [
99,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Order/Lattice.lean | Lattice.ext | [
{
"state_after": "case mk\nα✝ : Type u\nβ : Type v\ninst✝ : Lattice α✝\na b c d : α✝\nα : Type u_1\nB : Lattice α\ntoSemilatticeSup✝ : SemilatticeSup α\ntoInf✝ : Inf α\ninf_le_left✝ : ∀ (a b : α), a ⊓ b ≤ a\ninf_le_right✝ : ∀ (a b : α), a ⊓ b ≤ b\nle_inf✝ : ∀ (a b c : α), a ≤ b → a ≤ c → a ≤ b ⊓ c\nH : ∀ (x y :... | [
726,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_le_snorm_top_mul_snorm | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_4\nF : Type u_2\nG : Type u_3\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\np : ℝ≥0∞\nf : α → E\ng : α → F\nhg : AEStronglyMeasurable g μ\nb : E → F → ... | [
1388,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1347,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | AlternatingMap.eq_smul_basis_det | [
{
"state_after": "R : Type u_1\ninst✝⁶ : CommRing R\nM : Type u_2\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nM' : Type ?u.2583010\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\nι : Type u_3\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\ne : Basis ι R M\nf : AlternatingMap R M R ι\ni : ι → ι\nh : Injective i\... | [
580,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Topology/Sober.lean | genericPoint_specializes | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5792\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : QuasiSober α\ninst✝ : IrreducibleSpace α\nx : α\n⊢ x ∈ closure univ",
"tactic": "simp"
}
] | [
164,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.IntegralClosure.comap_lt_comap | [] | [
343,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_surj | [] | [
490,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Order/SuccPred/Relation.lean | reflTransGen_of_pred_of_ge | [] | [
103,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_X_pow_sub_C | [] | [
404,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_nonneg_iff | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\n⊢ (0 ≤ if val x ≤ n / 2 then ↑(val x) else ↑(val x) - ↑n) ↔ val x ≤ n / 2",
"state_before": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\n⊢ 0 ≤ valMinAbs x ↔ val x ≤ n / 2",
"tactic": "rw [valMinAbs_def_pos]"
},
{
"state_after": "case inl\nn : ℕ\nin... | [
938,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_Ico_mul_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Ring α\nx : α\nm n : ℕ\nhmn : m ≤ n\n⊢ (∑ i in Ico m n, x ^ i) * (1 - x) = x ^ m - x ^ n",
"tactic": "rw [sum_Ico_eq_sub _ hmn, sub_mul, geom_sum_mul_neg, geom_sum_mul_neg, sub_sub_sub_cancel_left]"
}
] | [
340,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.basicOpen_eq_bot_iff | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R\n⊢ zeroLocus {f}ᶜ = ↑⊥ ↔ IsNilpotent f",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R\n⊢ basicOpen f = ⊥ ↔ IsNilpotent f",
"tactic": "rw [← TopologicalSpace.Opens.coe_inj, ... | [
874,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.sup | [] | [
534,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_insert | [] | [
865,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/InformationTheory/Hamming.lean | Hamming.toHamming_neg | [] | [
360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bit1_mod_two | [
{
"state_after": "n : ℕ\n⊢ (bif bodd (bit1 n) then 1 else 0) = 1",
"state_before": "n : ℕ\n⊢ bit1 n % 2 = 1",
"tactic": "rw [Nat.mod_two_of_bodd]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ (bif bodd (bit1 n) then 1 else 0) = 1",
"tactic": "simp"
}
] | [
113,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.IsAdjMatrix.adjMatrix_toGraph_eq | [
{
"state_after": "case a.h\nV : Type u_2\nα : Type u_1\nβ : Type ?u.79711\ninst✝² : MulZeroOneClass α\ninst✝¹ : Nontrivial α\nA : Matrix V V α\nh : IsAdjMatrix A\ninst✝ : DecidableEq α\ni j : V\n⊢ adjMatrix α (toGraph h) i j = A i j",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.79711\ninst✝² : ... | [
297,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_replicate_append_replicate | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\ninst✝ : DecidableEq α\nl : List α\na b : α\nm n : ℕ\nh : a ≠ b\n⊢ (count a l = count a (replicate m a ++ replicate n b) ∧\n (b ≠ a → count b l = count b (replicate m a ++ replicate n b)) ∧\n ∀ (b_1 : α), b_1 ≠ b → b_1 ≠ a → count b_1 l = co... | [
890,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Iic_basis | [] | [
1127,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1125,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.nonneg_total | [
{
"state_after": "case mk'\nb c : ℚ\nn : ℤ\nden✝ : ℕ\nden_nz✝ : den✝ ≠ 0\nreduced✝ : Nat.coprime (Int.natAbs n) den✝\n⊢ Rat.Nonneg (mk' n den✝) ∨ Rat.Nonneg (-mk' n den✝)",
"state_before": "a b c : ℚ\n⊢ Rat.Nonneg a ∨ Rat.Nonneg (-a)",
"tactic": "cases' a with n"
},
{
"state_after": "no goals",
... | [
86,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
11
] |
src/lean/Init/Control/Lawful.lean | ExceptT.run_pure | [] | [
108,
102
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
108,
9
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHom_apply_symm_toNonUnitalRingHom_apply | [] | [
636,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_one | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.comapRight_apply | [] | [
563,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_symm | [] | [
88,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLeast_Ico | [] | [
724,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_eq_length | [
{
"state_after": "case nil\nι : Type ?u.79233\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na : α\n⊢ indexOf a [] = length [] ↔ ¬a ∈ []\n\ncase cons\nι : Type ?u.79233\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : L... | [
1190,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffAt.of_le | [] | [
1349,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | goldConj_irrational | [
{
"state_after": "this : Irrational (sqrt ↑5)\n⊢ Irrational ψ",
"state_before": "⊢ Irrational ψ",
"tactic": "have := Nat.Prime.irrational_sqrt (show Nat.Prime 5 by norm_num)"
},
{
"state_after": "this✝ : Irrational (sqrt ↑5)\nthis : Irrational (↑1 - sqrt ↑5)\n⊢ Irrational ψ",
"state_before":... | [
157,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_liminf_le | [] | [
1019,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1017,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.mem_map | [] | [
360,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/Data/List/NodupEquivFin.lean | List.sublist_iff_exists_fin_orderEmbedding_get_eq | [
{
"state_after": "α : Type u_1\nl l' : List α\n⊢ (∃ f, ∀ (ix : ℕ), get? l ix = get? l' (↑f ix)) ↔ ∃ f, ∀ (ix : Fin (length l)), get l ix = get l' (↑f ix)",
"state_before": "α : Type u_1\nl l' : List α\n⊢ l <+ l' ↔ ∃ f, ∀ (ix : Fin (length l)), get l ix = get l' (↑f ix)",
"tactic": "rw [sublist_iff_exist... | [
209,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.measure_Iic | [
{
"state_after": "f : StieltjesFunction\nl : ℝ\nhf : Tendsto (↑f) atBot (𝓝 l)\nx : ℝ\n⊢ Tendsto (fun x_1 => ↑↑(StieltjesFunction.measure f) (Ioc x_1 x)) atBot (𝓝 (ofReal (↑f x - l)))",
"state_before": "f : StieltjesFunction\nl : ℝ\nhf : Tendsto (↑f) atBot (𝓝 l)\nx : ℝ\n⊢ ↑↑(StieltjesFunction.measure f) (... | [
590,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_nonneg | [] | [
589,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
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