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/Finset/Lattice.lean | Finset.le_max | [] | [
1211,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Measurable.comp | [] | [
556,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
11
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.comp_apply | [] | [
194,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.mk_hom_eq_self | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Deprecated/Submonoid.lean | Submonoid.isSubmonoid | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : Monoid M\ns : Set M\nA : Type ?u.82313\ninst✝ : AddMonoid A\nt : Set A\nS : Submonoid M\n⊢ IsSubmonoid ↑S",
"tactic": "refine' ⟨S.2, S.1.2⟩"
}
] | [
431,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_assoc | [
{
"state_after": "no goals",
"state_before": "m : Nat\nb : Int\nk : Nat\n⊢ ↑m + b + ↑k = ↑m + (b + ↑k)",
"tactic": "rw [Int.add_comm, ← aux1, Int.add_comm k, aux1, Int.add_comm b]"
},
{
"state_after": "no goals",
"state_before": "a : Int\nn k : Nat\n⊢ a + ↑n + ↑k = a + (↑n + ↑k)",
"tacti... | [
281,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
261,
11
] |
Mathlib/Logic/Small/Basic.lean | not_small_type | [
{
"state_after": "S : Type u\ne✝ : Type (max u v) ≃ S\na b : Set ((α : S) × ↑e✝.symm α)\ne :\n { fst := ↑e✝ (Set ((α : S) × ↑e✝.symm α)),\n snd := cast (_ : Set ((α : S) × ↑e✝.symm α) = ↑e✝.symm (↑e✝ (Set ((α : S) × ↑e✝.symm α)))) a } =\n { fst := ↑e✝ (Set ((α : S) × ↑e✝.symm α)),\n snd := cast (_... | [
158,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.minpoly.degree_le | [] | [
885,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.natAbs_eq_of_dvd_dvd | [] | [
481,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.orderOf_cycleOf_dvd_orderOf | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\nx : α\nhx : ↑f x = x\n⊢ orderOf (cycleOf f x) ∣ orderOf f\n\ncase neg\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Perm α\nx : α\nhx : ¬↑f x = x\n⊢ orderOf (cycleOf f x) ∣ orderOf f",
"state_bef... | [
194,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.inf_exists | [
{
"state_after": "case empty\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsCofiltered C\nO : Finset C\nH : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))\n⊢ ∃ S T,\n ∀ {X Y : C} (mX : X ∈ O) (mY : Y ∈ O) {f : X ⟶ Y},\n { fst := X, snd := { fst := Y, snd := { fst := mX, snd := { fst :... | [
669,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_csSup_iff | [] | [
476,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Integrable.exists_boundedContinuous_lintegral_sub_le | [
{
"state_after": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : NormalSpace α\ninst✝³ : BorelSpace α\nE : Type u_2\ninst✝² : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\ninst✝¹ : NormedSpace ℝ E\ninst✝ : Measure.WeaklyRegular μ\nf : α → E\nε : ℝ≥0∞\nhε : ε ≠ 0\nhf : Memℒp f 1... | [
314,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/LinearAlgebra/Coevaluation.lean | contractLeft_assoc_coevaluation' | [
{
"state_after": "K : Type u\ninst✝³ : Field K\nV : Type v\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nthis : DecidableEq ↑(Basis.ofVectorSpaceIndex K V) := Classical.decEq ↑(Basis.ofVectorSpaceIndex K V)\n⊢ LinearMap.comp (LinearMap.lTensor V (contractLeft K V))\n (Linear... | [
99,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_ofNat_succ | [] | [
40,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
15
] |
Mathlib/Order/BoundedOrder.lean | isBot_iff_eq_bot | [] | [
346,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.span_singleton_sup_orthogonal_eq_top | [
{
"state_after": "R : Type ?u.260339\nR₁ : Type ?u.260342\nR₂ : Type ?u.260345\nR₃ : Type ?u.260348\nM : Type ?u.260351\nM₁ : Type ?u.260354\nM₂ : Type ?u.260357\nMₗ₁ : Type ?u.260360\nMₗ₁' : Type ?u.260363\nMₗ₂ : Type ?u.260366\nMₗ₂' : Type ?u.260369\nK : Type u_1\nK₁ : Type ?u.260375\nK₂ : Type ?u.260378\nV :... | [
393,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_sq | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, sin x ^ 2) = (sin a * cos a - sin b * cos b + b - a) / 2",
"tactic": "field_simp [integral_sin_pow, add_sub_assoc]"
}
] | [
663,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Algebra/Group/Opposite.lean | SemiconjBy.unop | [] | [
241,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_mul_right' | [] | [
1015,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
21
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.re_eq_add_conj | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.3487608\ninst✝ : IsROrC K\nz : K\n⊢ ↑(↑re z) = (z + ↑(starRingEnd K) z) / 2",
"tactic": "rw [add_conj, mul_div_cancel_left (re z : K) two_ne_zero]"
}
] | [
401,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_inner_eq_zero | [] | [
483,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.lex_fibration | [
{
"state_after": "case mk.mk.intro.intro\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\ninst✝ : (i : ι) → (s : Set ι) → Decidable (i ∈ s)\np : Set ι\nx₁ x₂ x : Π₀ (i : ι), α i\ni : ι\nhr : ∀ (j : ι), r j i → ↑x j = ↑((fun x => piecewise x.snd.fs... | [
100,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_natDegree_eq_zero_of_degree_lt | [] | [
582,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode_unit_succ | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean | CategoryTheory.Pretriangulated.rot_of_dist_triangle | [] | [
110,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.id_apply | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_right_cancel | [
{
"state_after": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.626659\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx y : M\nc : { x // x ∈ S }\nh : ↑(toMap f) ↑c * ↑(toMap f) x = ↑(toMap f) ↑c * ↑(toMap f) y\n⊢ ↑(toMap f) x = ↑(toMap f) y",
"state... | [
686,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_preserving_piFinTwo | [] | [
804,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Eventually.atTop_of_arithmetic | [
{
"state_after": "ι : Type ?u.63705\nι' : Type ?u.63708\nα : Type ?u.63711\nβ : Type ?u.63714\nγ : Type ?u.63717\np : ℕ → Prop\nn : ℕ\nhn : n ≠ 0\nhp : ∀ (k : ℕ), k < n → ∃ a, ∀ (b : ℕ), b ≥ a → p (n * b + k)\n⊢ ∃ a, ∀ (b : ℕ), b ≥ a → p b",
"state_before": "ι : Type ?u.63705\nι' : Type ?u.63708\nα : Type ?... | [
510,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_sub_sinh | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh x - sinh x = exp (-x)",
"tactic": "rw [← mul_right_inj' (two_ne_zero' ℂ), mul_sub, two_cosh, two_sinh, add_sub_sub_cancel, two_mul]"
}
] | [
747,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.imageMonoIsoSource_hom_self | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\nX Y : C\nf : X ⟶ Y\ninst✝ : Mono f\n⊢ (imageMonoIsoSource f).hom ≫ (imageMonoIsoSource f).inv ≫ image.ι f = image.ι f",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y : C\nf : X ⟶ Y\ninst✝ : Mono f\n⊢ (imageMonoIsoSource f).hom ≫ f = image.ι f",
... | [
432,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul | [
{
"state_after": "α : Type u_1\nE : Type ?u.465938\nF : Type ?u.465941\nF' : Type ?u.465944\nG : Type u_2\n𝕜 : Type ?u.465950\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ni... | [
677,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | NormedSpace.isVonNBounded_iff' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\n𝕜' : Type ?u.254043\nE : Type u_1\nE' : Type ?u.254049\nF : Type ?u.254052\nι : Type ?u.254055\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\n⊢ Bornology.IsVonNBounded 𝕜 s ↔ ∃ r, ∀ (... | [
302,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Ioo | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\nthis : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)\n⊢ (fun x => a - x) '' Ioo b c = Ioo (a - c) (a - b)",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : ... | [
365,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_ofReal | [] | [
108,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nδ : Type ?u.31281\na : α\ns t : Multiset α\nf✝ g : α → Multiset β\nm : Multiset α\nn : β → Multiset γ\nf : α → β\n⊢ bind (map f 0) n = bind 0 fun a => n (f a)",
"tactic": "simp"
},
{
"state_after": "no goals"... | [
169,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/CategoryTheory/Preadditive/Generator.lean | CategoryTheory.Preadditive.isCoseparator_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nG : C\nhG : IsCoseparator G\nX Y : C\nf : X ⟶ Y\nhf : ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (h : Y ⟶ G), f ≫ h = 0 ≫ h",
"tactic": "simpa only [Limits.zero_comp] using hf"
},
{
"state_after": "no goals"... | [
54,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_le_factorization_mul_right | [
{
"state_after": "a b : ℕ\nha : a ≠ 0\n⊢ factorization b ≤ factorization (b * a)",
"state_before": "a b : ℕ\nha : a ≠ 0\n⊢ factorization b ≤ factorization (a * b)",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "a b : ℕ\nha : a ≠ 0\n⊢ factorization b ≤ factorizati... | [
487,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/CategoryTheory/Category/Grpd.lean | CategoryTheory.Grpd.piIsoPi_hom_π | [
{
"state_after": "J : Type u\nf : J → Grpd\nj : J\n⊢ (piLimitFan f).π.app { as := j } = Pi.eval (fun i => ↑(f i)) j",
"state_before": "J : Type u\nf : J → Grpd\nj : J\n⊢ (piIsoPi J f).hom ≫ Limits.Pi.π f j = Pi.eval (fun i => ↑(f i)) j",
"tactic": "simp [piIsoPi]"
},
{
"state_after": "no goals",... | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integrable_prod_iff' | [
{
"state_after": "case h.e'_1.a\nα : Type u_1\nα' : Type ?u.2403525\nβ : Type u_2\nβ' : Type ?u.2403531\nγ : Type ?u.2403534\nE : Type u_3\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measu... | [
290,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_left_surjective₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.29573\nM₀ : Type ?u.29576\nG₀ : Type u_1\nM₀' : Type ?u.29582\nG₀' : Type ?u.29585\nF : Type ?u.29588\nF' : Type ?u.29591\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\nh : a ≠ 0\ng : G₀\n⊢ (fun g => a * g) (a⁻¹ * g) = g",
"tactic": "simp [← mul_assoc... | [
425,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eq_interpolate_iff | [
{
"state_after": "case mp\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\nf : F[X]\nhvs : Set.InjOn v ↑s\nh : degree f < ↑(card s) ∧ ∀ (i : ι), i ∈ s → eval (v i) f = r i\n⊢ f = ↑(interpolate s v) r\n\ncase mpr\nF : Type u_1\ninst✝¹ : Field F\nι : T... | [
394,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Order/Bounds/Basic.lean | Monotone.mem_lowerBounds_image | [] | [
1269,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.IsSymm.ext_iff | [] | [
45,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_eq_bot_of_cancel | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.1573042\nR₂ : Type u_2\nR₃ : Type ?u.1573048\nR₄ : Type ?u.1573051\nS : Type ?u.1573054\nK : Type ?u.1573057\nK₂ : Type ?u.1573060\nM : Type u_3\nM' : Type ?u.1573066\nM₁ : Type ?u.1573069\nM₂ : Type u_4\nM₃ : Type ?u.1573075\nM₄ : Type ?u.1573078\nN : Type ?u.157308... | [
1713,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousLinearMap.smul_compLpL | [
{
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1057,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset | [
{
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"state_before": "ι : Type ?u.2757665\nα : Ty... | [
1485,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1477,
1
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_lt_bit0 | [
{
"state_after": "no goals",
"state_before": "h : 0 ≠ 0\n⊢ 1 < bit0 0",
"tactic": "contradiction"
},
{
"state_after": "n : ℕ\nx✝ : succ n ≠ 0\n⊢ 1 < succ (succ (bit0 n))",
"state_before": "n : ℕ\nx✝ : succ n ≠ 0\n⊢ 1 < bit0 (succ n)",
"tactic": "rw [Nat.bit0_succ_eq]"
},
{
"state... | [
174,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
11
] |
Mathlib/Topology/Basic.lean | all_mem_nhds | [
{
"state_after": "no goals",
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... | [
1017,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
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Mathlib/Deprecated/Group.lean | IsMonoidHom.inv | [] | [
185,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/LinearAlgebra/Multilinear/TensorProduct.lean | MultilinearMap.domCoprod'_apply | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.monomial_def | [
{
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"state_before": "σ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\ninst✝ : DecidableEq σ\nn : σ →₀ ℕ\n⊢ monomial R n = LinearMap.... | [
150,
14
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146,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_eq_succ_iff_of_not_isMax | [
{
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"tactic": "rw [eq_iff_le_not_lt, eq_iff_le_not_lt, succ_le_succ_iff_of_not_isMax ha hb,\n succ_lt_succ_iff_of_not_isMax ha hb]"
... | [
414,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
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Mathlib/GroupTheory/Commutator.lean | Subgroup.commutator_le_left | [] | [
155,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.add_quot | [
{
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"state_before... | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.sub_apply | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.len_le_of_epi | [
{
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"state_before": "x y : SimplexCategory\nf : x ⟶ y\n⊢ Epi f → len y ≤ len x",
"tactic": "intro hyp_f_epi"
},
{
"state_after": "x y : SimplexCategory\nf : x ⟶ y\nhyp_f_epi : Epi f\nf_surj : Function.Surjective... | [
512,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.equiv_def₃ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf g : CauSeq β abv\nh : f ≈ g\nε : α\nε0 : 0 < ε\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → abv (↑(f - g) j) < ε / 2 ∧ ∀ (k : ℕ), k ≥ j → abv (↑f k - ↑f j) < ε / 2\nj : ℕ\nij : j ≥ i\nk : ... | [
491,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | DirectSum.decompose_mul_add_right | [] | [
163,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | Antitone.covariant_of_const | [] | [
275,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.mk_eq_zero | [] | [
122,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Topology/Separation.lean | exists_mem_nhds_isClosed_subset | [
{
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"state_before": "α : Type u\nβ... | [
1534,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_fiberwise_le_prod_of_one_le_prod_fiber' | [] | [
247,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.of_apply | [] | [
644,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.card_support_eq_two | [
{
"state_after": "case mp\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : card (support f) = 2\n⊢ IsSwap f\n\ncase mpr\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nh : IsSwap f\n⊢ card (support f) = 2",
"state_before": "α : Type u_1\ninst✝¹ : Deci... | [
637,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.set_integral_eq_subtype | [
{
"state_after": "α✝ : Type ?u.1476210\nE : Type u_2\nF : Type ?u.1476216\n𝕜 : Type ?u.1476219\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace ℝ E\ninst✝⁹ : CompleteSpace E\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : SMulCommClass ℝ 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst... | [
1581,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1577,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_bit1 | [] | [
369,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_embDomain | [
{
"state_after": "α : Type u_3\nι : Type ?u.531151\nγ : Type ?u.531154\nA : Type ?u.531157\nB : Type ?u.531160\nC : Type ?u.531163\ninst✝⁴ : AddCommMonoid A\ninst✝³ : AddCommMonoid B\ninst✝² : AddCommMonoid C\nt : ι → A → C\nh0 : ∀ (i : ι), t i 0 = 0\nh1 : ∀ (i : ι) (x y : A), t i (x + y) = t i x + t i y\ns : F... | [
517,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.ofEquiv_σ | [] | [
203,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.dim_pos | [] | [
127,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
src/lean/Init/SimpLemmas.lean | Bool.true_or | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (true || b) = true",
"tactic": "cases b <;> rfl"
}
] | [
105,
83
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
105,
9
] |
Mathlib/Combinatorics/Colex.lean | Colex.sdiff_le_sdiff_iff_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\nA B : Finset α\n⊢ toColex (A \\ B) ≤ toColex (B \\ A) ↔ toColex A ≤ toColex B",
"tactic": "rw [le_iff_le_iff_lt_iff_lt, sdiff_lt_sdiff_iff_lt]"
}
] | [
334,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_smul_real_left | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1383018\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\nr : ℝ\n⊢ ↑r * inner x y = ↑(algebraMap ℝ 𝕜) r * inner x y",
"... | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/List/Func.lean | List.Func.get_neg | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : AddGroup α\nk : ℕ\nas : List α\n⊢ get k (map (fun a => -a) as) = -get k as",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝ : AddGroup α\nk : ℕ\nas : List α\n⊢ get k (neg as) = -get k as",
"tactic": "unfold neg"
},
{
"stat... | [
266,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.add_equiv_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf1 f2 g1 g2 : CauSeq β abv\nhf : f1 ≈ f2\nhg : g1 ≈ g2\n⊢ f1 + g1 ≈ f2 + g2",
"tactic": "simpa only [← add_sub_add_comm] using add_limZero h... | [
475,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.head_iterate | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_bot | [] | [
2165,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2165,
9
] |
Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_def | [] | [
1992,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1991,
1
] |
Mathlib/Order/RelClasses.lean | IsOrderConnected.neg_trans | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nr✝ : α → α → Prop\ns : β → β → Prop\nr : α → α → Prop\ninst✝ : IsOrderConnected α r\na b c : α\nh₁ : ¬r a b\nh₂ : ¬r b c\n⊢ ¬(r a b ∨ r b c)",
"tactic": "simp [h₁, h₂]"
}
] | [
249,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.dist_triangle | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx y z : Completion α\n⊢ IsClosed {x | dist x.fst x.snd.snd ≤ dist x.fst x.snd.fst + dist x.snd.fst x.snd.snd}\n\ncase refine'_2\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx y z : Completion α\n⊢ ∀ (a b c : α), dist... | [
84,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
11
] |
Mathlib/Order/Filter/Basic.lean | Filter.forall_mem_nonempty_iff_neBot | [] | [
768,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.ext_ring_iff | [] | [
405,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | IsScalarTower.coe_toAlgHom | [] | [
130,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bit_add' | [] | [
99,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.to_comma_map_right | [] | [
153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_singleton | [] | [
210,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/NormedSpace/MazurUlam.lean | IsometryEquiv.toRealLinearIsometryEquiv_symm_apply | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovary_toDual_left | [] | [
249,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.div_add_mod' | [
{
"state_after": "m k : ℕ+\n⊢ ↑k * div m k + ↑(mod m k) = ↑m",
"state_before": "m k : ℕ+\n⊢ div m k * ↑k + ↑(mod m k) = ↑m",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m k : ℕ+\n⊢ ↑k * div m k + ↑(mod m k) = ↑m",
"tactic": "exact div_add_mod _ _"
}
] | [
376,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Order/MinMax.lean | max_cases | [] | [
170,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | RingEquiv.ofLeftInverseS_apply | [] | [
1295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mk_smul | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : Monoid γ\ninst✝¹ : (i : ι) → AddMonoid (β i)\ninst✝ : (i : ι) → DistribMulAction γ (β i)\ns : Finset ι\nc : γ\nx : (i : ↑↑s) → β ↑i\ni : ι\n⊢ (if H : i ∈ s then (c • x) { val := i, propert... | [
1074,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/RingTheory/Nakayama.lean | Submodule.smul_sup_eq_smul_sup_of_le_smul_of_le_jacobson | [
{
"state_after": "R : Type u_1\nM : Type u_2\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI J : Ideal R\nN N' : Submodule R M\nhN' : FG N'\nhIJ : I ≤ jacobson J\nhNN : N ⊔ N' ≤ N ⊔ I • N'\nhNN' : N ⊔ N' = N ⊔ I • N'\n⊢ N ⊔ I • N' = N ⊔ J • N'",
"state_before": "R : Type u_1\nM : Type u... | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_mono | [] | [
1322,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inlCokernelCofork_π | [] | [
1715,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1714,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.HasColimit.isoOfNatIso_ι_hom | [] | [
914,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/Combinatorics/Young/SemistandardTableau.lean | Ssyt.col_weak | [
{
"state_after": "case inl\nμ : YoungDiagram\nT : Ssyt μ\ni1 i2 j : ℕ\nhi : i1 ≤ i2\ncell : (i2, j) ∈ μ\nh : i1 = i2\n⊢ ↑T i1 j ≤ ↑T i2 j\n\ncase inr\nμ : YoungDiagram\nT : Ssyt μ\ni1 i2 j : ℕ\nhi : i1 ≤ i2\ncell : (i2, j) ∈ μ\nh : i1 < i2\n⊢ ↑T i1 j ≤ ↑T i2 j",
"state_before": "μ : YoungDiagram\nT : Ssyt μ... | [
139,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.sq_mul_squarefree | [
{
"state_after": "case zero\n\n⊢ ∃ a b, b ^ 2 * a = zero ∧ Squarefree a\n\ncase succ\nn : ℕ\n⊢ ∃ a b, b ^ 2 * a = succ n ∧ Squarefree a",
"state_before": "n : ℕ\n⊢ ∃ a b, b ^ 2 * a = n ∧ Squarefree a",
"tactic": "cases' n with n"
},
{
"state_after": "no goals",
"state_before": "case zero\n\n... | [
365,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.mk_Icc_real | [] | [
285,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
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