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/Data/Real/Basic.lean | Real.ofCauchy_sub | [
{
"state_after": "x y : ℝ\na b : Cauchy abs\n⊢ { cauchy := a } + -{ cauchy := b } = { cauchy := a } - { cauchy := b }",
"state_before": "x y : ℝ\na b : Cauchy abs\n⊢ { cauchy := a - b } = { cauchy := a } - { cauchy := b }",
"tactic": "rw [sub_eq_add_neg, ofCauchy_add, ofCauchy_neg]"
},
{
"state_... | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_add_int | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.212554\nα : Type u_1\nβ : Type ?u.212560\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na✝ a : α\nz : ℤ\n⊢ ⌈a + ↑z⌉ = ⌈a⌉ + z",
"tactic": "rw [← neg_inj, neg_add', ← floor_neg, ← floor_neg, neg_add', floor_sub_int]"
}
] | [
1145,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.iInf_principal_finite | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.124763\nι✝ : Sort x\nf✝ g : Filter α\ns✝ t : Set α\nι : Type w\nf : ι → Set α\ns : Finset ι\n⊢ (⨅ (i : ι) (_ : i ∈ ↑s), 𝓟 (f i)) = 𝓟 (⋂ (i : ι) (_ : i ∈ ↑s), f i)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?... | [
1049,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_mul_int | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nm : ℤ\nh : Irrational (x * ↑m)\n⊢ Irrational (x * ↑↑m)",
"tactic": "rwa [cast_coe_int]"
}
] | [
356,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.measurePreserving_zpow | [
{
"state_after": "G : Type u_1\ninst✝⁹ : CommGroup G\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : TopologicalGroup G\ninst✝⁶ : T2Space G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\ninst✝³ : SecondCountableTopology G\nμ : Measure G\ninst✝² : IsHaarMeasure μ\ninst✝¹ : CompactSpace G\ninst✝ : RootableBy G ℤ\nn :... | [
857,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ediam_le_of_forall_dist_le | [] | [
2617,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2615,
1
] |
Mathlib/Order/MinMax.lean | min_right_comm | [] | [
227,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_iff_set_range | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\n⊢ p ∈ lifts f ↔ p ∈ Set.range (map f)",
"tactic": "simp only [coe_mapRingHom, lifts, Set.mem_range, RingHom.mem_rangeS]"
}
] | [
69,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_star | [] | [
87,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_injective | [
{
"state_after": "case mk\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.24772\nδ : Type ?u.24775\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf g✝ g : C(α, β)\ntoFun✝ : α → β\ncontinuous_toFun✝ : Continuous toFun✝\nh : ↑(mk toFun✝) = ↑g\n⊢ mk toF... | [
163,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.map_round | [
{
"state_after": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedField α\ninst✝³ : LinearOrderedField β\ninst✝² : FloorRing α\ninst✝¹ : FloorRing β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\nH : ↑f 2 = 2\n⊢ round (↑f a) = round a",
"state_before": "F : Typ... | [
1558,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\n⊢ Tendsto (fun x => eval x P) atTop atBot ↔ 0 < degree P ∧ leadingCoeff P ≤ 0",
"tactic": "simp only [← tendsto_neg_atTop_iff, ← eval_neg, tendsto_atTop_iff_leadingCo... | [
79,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.ite | [] | [
610,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
11
] |
Mathlib/RingTheory/Finiteness.lean | Module.Finite.exists_fin | [] | [
557,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/RingTheory/Polynomial/Tower.lean | Polynomial.aeval_map_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_3\nB : Type u_2\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring A\ninst✝⁴ : Semiring B\ninst✝³ : Algebra R A\ninst✝² : Algebra A B\ninst✝¹ : Algebra R B\ninst✝ : IsScalarTower R A B\nx : B\np : R[X]\n⊢ ↑(aeval x) (map (algebraMap R A) p)... | [
44,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.hasLimitsOfShape_op_of_hasColimitsOfShape | [] | [
258,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Logic/Function/Basic.lean | eq_mp_bijective | [
{
"state_after": "case refl\nα : Sort u_1\n⊢ Bijective (Eq.mp (_ : α = α))",
"state_before": "α β : Sort u_1\nh : α = β\n⊢ Bijective (Eq.mp h)",
"tactic": "cases h"
},
{
"state_after": "no goals",
"state_before": "case refl\nα : Sort u_1\n⊢ Bijective (Eq.mp (_ : α = α))",
"tactic": "refi... | [
1004,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.range_sin | [] | [
656,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_setOf_eq_sep | [] | [
1031,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1030,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformOnFun.isBasis_gen | [] | [
605,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
11
] |
Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.comp_id | [] | [
682,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MeasureTheory.Integrable.intervalIntegrable | [] | [
113,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_zpow_le | [] | [
429,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Multiset/Pi.lean | Multiset.Pi.cons_swap | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nβ : α → Type u\nδ : α → Sort v\na a' : α\nb : δ a\nb' : δ a'\nm : Multiset α\nf : (a : α) → a ∈ m → δ a\nh : a ≠ a'\n⊢ ∀ (a_1 a'_1 : α),\n HEq a_1 a'_1 → HEq (cons (a' ::ₘ m) a b (cons m a' b' f) a_1) (cons (a ::ₘ m) a' b' (cons m a b f) a'_1)",
"sta... | [
61,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_def | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Std/Data/AssocList.lean | Std.AssocList.find?_eq_findEntry? | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\ninst✝ : BEq α\na key✝ : α\nvalue✝ : β\ntail✝ : AssocList α β\ntail_ih✝ : find? a tail✝ = Option.map (fun x => x.snd) (findEntry? a tail✝)\n⊢ (match key✝ == a with\n | true => some value✝\n | false => find? a tail✝) =\n Option.map (fun x => x.snd)... | [
123,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
121,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.Monic.eq_X_add_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhm : Monic p\nhnd : natDegree p = 1\n⊢ p = X + ↑C (coeff p 0)",
"tactic": "rw [← one_mul X, ← C_1, ← hm.coeff_natDegree, hnd, ← eq_X_add_C_of_natDegree_le_one hnd.le]"
}
] | [
464,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.counit_naturality | [] | [
208,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_cons_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b : α\nh : a ≤ b\n⊢ b ::ₘ Ico a b = Icc a b",
"tactic": "classical\n rw [Ico, ← Finset.insert_val_of_not_mem right_not_mem_Ico, Finset.Ico_insert_right h]\n rfl"
},
{
"state_aft... | [
200,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/Complex/AbsMax.lean | Complex.norm_max_aux₃ | [
{
"state_after": "E : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : ℂ → F\nz w : ℂ\nhd : DiffContOnCl ℂ f (ball z (dist w z))\nhz : IsMaxOn (norm ∘ f) (ball z (dist w z)) z\n⊢ ‖f w‖ = ‖f z‖",
"state_before": "E : Type... | [
167,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.mem_infs | [] | [
237,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.add_one_eq_succ | [] | [
376,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_zero_nonneg | [] | [
693,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/CategoryTheory/Subobject/FactorThru.lean | CategoryTheory.Subobject.factors_of_factors_right | [
{
"state_after": "case h\nC : Type u₁\ninst✝¹ : Category C\nX✝ Y✝ Z✝ : C\nD : Type u₂\ninst✝ : Category D\nX Y Z : C\nP✝ : Subobject Z\nf : X ⟶ Y\ng : Y ⟶ Z\nh✝ : Factors P✝ g\nP : MonoOver Z\nh : Factors (Quotient.mk'' P) g\n⊢ Factors (Quotient.mk'' P) (f ≫ g)",
"state_before": "C : Type u₁\ninst✝¹ : Categ... | [
104,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasStrictDerivAt.cexp | [] | [
92,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Topology/Order/Basic.lean | interior_Iic | [] | [
2286,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2285,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_liftAt | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.105226\nP : Type ?u.105229\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn✝ l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\nn n' m : ℕ\... | [
435,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Order/BoundedOrder.lean | OrderDual.ofDual_top | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/SupIndep.lean | CompleteLattice.independent_iff_pairwiseDisjoint | [] | [
408,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | le_of_forall_one_lt_lt_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LinearOrder α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c : α\nh : ∀ (ε : α), 1 < ε → a < b * ε\nh₁ : b < a\n⊢ a < a",
"tactic": "simpa using h _ (lt_inv_mul_iff_lt.mpr h₁)"
}
] | [
1047,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.col_empty | [] | [
169,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.derivative_expand | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np q : ℕ\nf : R[X]\n⊢ ↑derivative (↑(expand R p) f) = ↑(expand R p) (↑derivative f) * (↑p * X ^ (p - 1))",
"tactic": "rw [coe_expand, derivative_eval₂_C, derivative_pow, C_eq_nat_cast, d... | [
98,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Combinatorics/Configuration.lean | Configuration.sum_lineCount_eq_sum_pointCount | [
{
"state_after": "P : Type u_1\nL : Type u_2\ninst✝² : Membership P L\ninst✝¹ : Fintype P\ninst✝ : Fintype L\n⊢ Fintype.card ((a : P) × { l // a ∈ l }) = Fintype.card ((a : L) × { p // p ∈ a })",
"state_before": "P : Type u_1\nL : Type u_2\ninst✝² : Membership P L\ninst✝¹ : Fintype P\ninst✝ : Fintype L\n⊢ ∑... | [
200,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Option/Basic.lean | Option.orElse_eq_some | [
{
"state_after": "case none\nα : Type u_1\nβ : Type ?u.19034\nγ : Type ?u.19037\nδ : Type ?u.19040\no' : Option α\nx : α\n⊢ (HOrElse.hOrElse none fun x => o') = some x ↔ none = some x ∨ none = none ∧ o' = some x\n\ncase some\nα : Type u_1\nβ : Type ?u.19034\nγ : Type ?u.19037\nδ : Type ?u.19040\no' : Option α\n... | [
371,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOn.tendstoUniformlyOn_of_tendsto | [] | [
474,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.zero_mem | [] | [
255,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
11
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.star_add_self' | [] | [
1117,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
8
] |
Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.41707\nγ : Type ?u.41710\nι✝ : Sort ?u.41713\nι'✝ : Sort ?u.41716\nl✝ l' : Filter α\np✝ : ι✝ → Prop\ns✝ : ι✝ → Set α\nt✝ : Set α\ni : ι✝\np' : ι'✝ → Prop\ns' : ι'✝ → Set α\ni' : ι'✝\nι : Sort u_1\nι' : ι → Type u_2\nl : ι → Filter α\np ... | [
605,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/SetTheory/Lists.lean | Lists.isList_toList | [] | [
248,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | nhds_one_symm | [] | [
634,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.ofMultiset_apply | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Algebra/Group/Basic.lean | eq_inv_mul_of_mul_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.50338\nβ : Type ?u.50341\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : b * a = c\n⊢ a = b⁻¹ * c",
"tactic": "simp [h.symm]"
}
] | [
633,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_le_of_ae_bound | [
{
"state_after": "case intro\nα : Type u_1\nE : Type u_2\nF : Type ?u.436188\nG : Type ?u.436191\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : IsFiniteMeasure μ\nf : { x // x ∈ Lp E p }\nC : ℝ≥0\n... | [
430,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.matrix_mul_apply | [
{
"state_after": "k : Type ?u.10982\nl : Type u_3\nm : Type u_1\nn : Type u_2\nα : Type v\ninst✝² : Fintype m\ninst✝¹ : Semiring α\ninst✝ : DecidableEq n\nM : Matrix l m α\nf : m ≃. n\ni : l\nj : n\n⊢ (Finset.sum Finset.univ fun j_1 => M i j_1 * if j ∈ ↑f j_1 then 1 else 0) =\n Option.rec 0 (fun val => M i v... | [
102,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.ext_elem | [
{
"state_after": "case intro\nι : Type u_1\nι' : Type ?u.127186\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝⁴ : AddCommGroup V\ninst✝³ : AffineSpace V P\ninst✝² : Ring k\ninst✝¹ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni j : ι\ne : ι ≃ ι'\ninst✝ : Finite ι\nq₁ q₂ : P\nh : ∀ (i : ι), ↑(coord b i) q... | [
239,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Topology/Algebra/Order/UpperLower.lean | IsLowerSet.closure | [] | [
72,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_sup | [] | [
95,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/List/Basic.lean | List.get_take | [] | [
1993,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1991,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.map_mk | [] | [
429,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.le_close | [] | [
72,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.exp_bound_sq | [
{
"state_after": "case e_a\nz✝ y x✝ : ℝ\nx z : ℂ\nhz : ‖z‖ ≤ 1\n⊢ exp (x + z) - exp x - z * exp x = exp x * (exp z - 1 - z)",
"state_before": "z✝ y x✝ : ℝ\nx z : ℂ\nhz : ‖z‖ ≤ 1\n⊢ ‖exp (x + z) - exp x - z * exp x‖ = ‖exp x * (exp z - 1 - z)‖",
"tactic": "congr"
},
{
"state_after": "case e_a\nz✝... | [
46,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/MeasureTheory/Function/LpOrder.lean | MeasureTheory.Memℒp.inf | [] | [
79,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Erased.lean | Erased.out_inj | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\na b : Erased α\nh : out a = out b\n⊢ a = b",
"tactic": "simpa using congr_arg mk h"
}
] | [
72,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.of_b_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.419811\nF : Type ?u.419814\nK : Type ?u.419817\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\n⊢ toPoly P = ↑C P.c * X + ↑C P.d",
"tactic": "rw [of_a_eq_zero ha, hb, C_0, MulZeroClass.zero_mu... | [
149,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | LinearIsometry.contDiff | [] | [
164,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/GroupTheory/Finiteness.lean | AddMonoid.fg_iff_mul_fg | [] | [
125,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.disjoint_supported_supported_iff | [
{
"state_after": "α : Type u_2\nM : Type u_1\nN : Type ?u.115064\nP : Type ?u.115067\nR : Type u_3\nS : Type ?u.115073\ninst✝⁸ : Semiring R\ninst✝⁷ : Semiring S\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Module R N\ninst✝² : AddCommMonoid P\ninst✝¹ : Module R P\ninst✝ : N... | [
324,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.mk_eq_fun_of_mem_aeSeqSet | [
{
"state_after": "ι : Sort u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.154841\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nf : ι → α → β\nμ : MeasureTheory.Measure α\np : α → (ι → β) → Prop\nhf : ∀ (i : ι), AEMeasurable (f i)\nx : α\nhx : x ∈ aeSeqSet hf p\ni : ι\n⊢ {x | ∀ (i : ι), f i x = AEMeasura... | [
59,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Order/Basic.lean | preimage_neg | [] | [
1944,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1943,
1
] |
Mathlib/Data/List/Basic.lean | List.exists_of_length_succ | [] | [
197,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Order/RelClasses.lean | transitive_of_trans | [] | [
177,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.mono_num | [] | [
142,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/TFAE.lean | exists_maximalIdeal_pow_eq_of_principal | [
{
"state_after": "case mk.intro\nR : Type u_1\ninst✝⁶ : CommRing R\nK : Type ?u.321\ninst✝⁵ : Field K\ninst✝⁴ : Algebra R K\ninst✝³ : IsFractionRing R K\ninst✝² : IsNoetherianRing R\ninst✝¹ : LocalRing R\ninst✝ : IsDomain R\nh : ¬IsField R\nI : Ideal R\nhI : I ≠ ⊥\nx : R\nhx : maximalIdeal R = Ideal.span {x}\n⊢... | [
92,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.isMin_iterate_pred_of_eq_of_ne | [] | [
664,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2.stmts₁_trans | [
{
"state_after": "K : Type u_1\ninst✝ : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nq₁ q₂ : Stmt₂\nh₁₂ : q₁ ∈ stmts₁ q₂\nq₀ : Stmt₂\nh₀₁ : q₀ ∈ stmts₁ q₁\n⊢ q₀ ∈ stmts₁ q₂",
"state_before": "K : Type u_1\ninst✝ : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nq₁ q₂ : Stmt₂\n⊢ ... | [
2211,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2195,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.le_rpow_iff_log_le | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\nhy : 0 < y\n⊢ x ≤ y ^ z ↔ log x ≤ z * log y",
"tactic": "rw [← Real.log_le_log hx (Real.rpow_pos_of_pos hy z), Real.log_rpow hy]"
}
] | [
592,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.filter_fst_eq_antidiagonal | [
{
"state_after": "case a.mk\nn m x y : ℕ\n⊢ (x, y) ∈ filter (fun x => x.fst = m) (antidiagonal n) ↔ (x, y) ∈ if m ≤ n then {(m, n - m)} else ∅",
"state_before": "n m : ℕ\n⊢ filter (fun x => x.fst = m) (antidiagonal n) = if m ≤ n then {(m, n - m)} else ∅",
"tactic": "ext ⟨x, y⟩"
},
{
"state_after... | [
121,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.isIso_inv_app | [
{
"state_after": "case hom_inv_id\nC : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF G : C ⥤ D\nX✝ Y : C\nα : F ⟶ G\ninst✝ : IsIso α\nX : C\n⊢ α.app X ≫ (inv α).app X = 𝟙 (F.obj X)",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝²... | [
207,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.eq_iff_eq | [] | [
367,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/Category/ModuleCat/Algebra.lean | ModuleCat.isScalarTower_of_algebra_moduleCat | [] | [
57,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | mem_rootsOfUnity | [] | [
96,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/Quot.lean | Quotient.hrecOn₂'_mk'' | [] | [
738,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Algebra/Order/SMul.lean | Tactic.smul_nonneg_of_nonneg_of_pos | [] | [
312,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
9
] |
Mathlib/Topology/Basic.lean | Disjoint.frontier_right | [] | [
797,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Algebra/Homology/Augment.lean | CochainComplex.augmentTruncate_hom_f_zero | [] | [
365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/Basic.lean | isOpen_compl_iff | [] | [
202,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
9
] |
Mathlib/Algebra/Module/Basic.lean | CharZero.of_module | [
{
"state_after": "α : Type ?u.280330\nR : Type u_2\nk : Type ?u.280336\nS : Type ?u.280339\nM✝ : Type ?u.280342\nM₂ : Type ?u.280345\nM₃ : Type ?u.280348\nι : Type ?u.280351\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M✝\ninst✝³ : Module R M✝\nM : Type u_1\ninst✝² : AddCommMonoidWithOne M\ninst✝¹ : CharZero M\... | [
659,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Algebra/Free.lean | FreeMagma.traverse_pure' | [] | [
247,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.tendsto_at | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\nhf : TendstoLocallyUniformlyOn F f p s\na : α\nha : a ∈ s\n⊢ 𝓟 {a} ≤ 𝓝[s] a",
"state_before": "α : T... | [
777,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.isRadical_bot_of_noZeroDivisors | [] | [
985,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
984,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithOne.ne_one_iff_exists | [] | [
167,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.and | [] | [
1095,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
11
] |
Std/Data/List/Lemmas.lean | List.eraseP_sublist | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\n⊢ eraseP p l <+ l",
"tactic": "match exists_or_eq_self_of_eraseP p l with\n| .inl h => rw [h]; apply Sublist.refl\n| .inr ⟨c, l₁, l₂, _, _, h₃, h₄⟩ => rw [h₄, h₃]; simp"
},
{
"state_after": "α : Type u_1\np : α... | [
985,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
982,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_subset_smul | [] | [
1359,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.nat_cast_im | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.lift'_smul | [
{
"state_after": "R : Type u_1\ninst✝⁶ : CommRing R\nS : Submonoid R\nM : Type u_2\nM' : Type ?u.503966\nM'' : Type u_3\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\ninst✝¹ : Module R M'\ninst✝ : Module R M''\nf : M →ₗ[R] M'\ng✝ g : M →ₗ[R] M''\nh : ∀ (x ... | [
635,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Data/Set/Semiring.lean | SetSemiring.down_up | [] | [
64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.cells_ssubset_iff | [] | [
111,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | rel_iff_cov | [] | [
132,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_le_of_top | [] | [
243,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
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