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/SetTheory/ZFC/Basic.lean | Class.not_mem_empty | [] | [
1505,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1505,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_sup | [] | [
330,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Order/Chain.lean | Flag.coe_mk | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Data/Set/Function.lean | Set.image_eq_iff_surjOn_mapsTo | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.48017\nι : Sort ?u.48020\nπ : α → Type ?u.48025\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\n⊢ f '' s = t → SurjOn f s t ∧ MapsTo f s t",
"state_before": "α : Type u_... | [
871,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_div_iff_smul_subset | [
{
"state_after": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : CommSemiring A\ninst✝ : Algebra R A\nM N : Submodule R A\nm n x : A\nI J : Submodule R A\nh : x ∈ I / J\ny : A\nx✝ : y ∈ x • ↑J\ny' : A\nhy' : y' ∈ ↑J\nxy'_eq_y : (fun x_1 => x • x_1) y' = y\n⊢ (fun x_1 => x • x_1) y' ∈ ↑I"... | [
697,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | differentiableOn_neg | [] | [
285,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.fuzzy_congr | [
{
"state_after": "no goals",
"state_before": "x₁ y₁ x₂ y₂ : PGame\nhx : x₁ ≈ x₂\nhy : y₁ ≈ y₂\n⊢ x₁ ⧏ y₁ ∧ y₁ ⧏ x₁ ↔ x₂ ⧏ y₂ ∧ y₂ ⧏ x₂",
"tactic": "rw [lf_congr hx hy, lf_congr hy hx]"
}
] | [
959,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.comap_quotient_eq_uniformity | [] | [
327,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.continuousAt_symm | [] | [
240,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_nil | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mem_span_singleton_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.228713\ninst✝ : CommSemiring R\nI✝ J K L : Ideal R\nx y : R\nI : Ideal R\n⊢ x ∈ span {y} * I ↔ ∃ z, z ∈ I ∧ y * z = x",
"tactic": "simp only [mul_comm, mem_mul_span_singleton]"
}
] | [
543,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.lt_of_st_lt | [] | [
424,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Order/Bounds/Basic.lean | not_bddBelow_univ | [] | [
855,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/Data/Part.lean | Part.bind_some_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.49896\nγ : Type ?u.49899\nx : Part α\n⊢ map (fun a => a) x = x",
"state_before": "α : Type u_1\nβ : Type ?u.49896\nγ : Type ?u.49899\nx : Part α\n⊢ Part.bind x some = x",
"tactic": "erw [bind_some_eq_map]"
},
{
"state_after": "no goals",
"state_bef... | [
598,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Finset.prod_mulIndicator_eq_prod_filter | [
{
"state_after": "α : Type u_2\nβ : Type ?u.106435\nι : Type u_1\nM : Type u_3\nN : Type ?u.106444\ninst✝¹ : CommMonoid M\ns : Finset ι\nf : ι → α → M\nt : ι → Set α\ng : ι → α\ninst✝ : DecidablePred fun i => g i ∈ t i\n⊢ (∏ x in Finset.filter (fun i => g i ∈ t i) s, mulIndicator (t x) (f x) (g x)) *\n ∏ x... | [
630,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.infDist_inter_closedBall_of_mem | [
{
"state_after": "ι : Sort ?u.67810\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nh : y ∈ s ∩ closedBall x (dist y x)\n⊢ infDist x (s ∩ closedBall x (dist y x)) = infDist x s",
"state_before": "ι : Sort ?u.67810\nα : Type u\nβ : Type v... | [
630,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9191\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\n⊢ chainHeight s = 0 ↔ s = ∅",
"tactic": "rw [← not_iff_not, ← Ne.def, ← ENat.one_le_iff_ne_zero, one_le_chainHeight_iff,\n nonempty_iff_ne_empty]"
}
] | [
147,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.toNonneg_le | [
{
"state_after": "case mk\nα : Type u_1\ninst✝¹ : Zero α\ninst✝ : LinearOrder α\na b : α\nhb : 0 ≤ b\n⊢ toNonneg a ≤ { val := b, property := hb } ↔ a ≤ ↑{ val := b, property := hb }",
"state_before": "α : Type u_1\ninst✝¹ : Zero α\ninst✝ : LinearOrder α\na : α\nb : { x // 0 ≤ x }\n⊢ toNonneg a ≤ b ↔ a ≤ ↑b"... | [
376,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mk_mem_col_iff | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\ni j : ℕ\n⊢ (i, j) ∈ col μ j ↔ (i, j) ∈ μ",
"tactic": "simp [col]"
}
] | [
355,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.mk_eq_mk | [] | [
133,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Multiset.toFinset_sum_count_nsmul_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.936659\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝ : DecidableEq α\ns : Multiset α\n⊢ ∑ a in toFinset s, count a s • {a} = s",
"tactic": "rw [← Finset.sum_multiset_map_count, Multiset.sum_map_singleton]"
... | [
2153,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2151,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isGLB_csInf | [] | [
499,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mapDomain_mul | [
{
"state_after": "k : Type u₁\nG : Type u₂\nR : Type ?u.1957244\ninst✝⁴ : Semiring k\nα : Type u_1\nβ : Type u_2\nα₂ : Type u_3\ninst✝³ : Semiring β\ninst✝² : Add α\ninst✝¹ : Add α₂\nF : Type u_4\ninst✝ : AddHomClass F α α₂\nf : F\nx y : AddMonoidAlgebra β α\n⊢ (sum x fun a b => sum y fun a_1 b_1 => single (↑f ... | [
1565,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLinearEquiv.lean | Matrix.exists_mulVec_eq_zero_iff | [] | [
175,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.transitive | [] | [
81,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.prod_apply | [] | [
2002,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2000,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.succ_log_def | [
{
"state_after": "b x : Ordinal\nhb : 1 < b\nhx : x ≠ 0\nt : Ordinal := sInf {o | x < b ^ o}\n⊢ succ (log b x) = sInf {o | x < b ^ o}",
"state_before": "b x : Ordinal\nhb : 1 < b\nhx : x ≠ 0\n⊢ succ (log b x) = sInf {o | x < b ^ o}",
"tactic": "let t := sInf { o | x < (b^o) }"
},
{
"state_after"... | [
308,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_lt_mul_iff_left | [] | [
821,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.inf_eq_div_pos_div | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b : α\n⊢ a ⊓ b = a * 1 ⊓ a * (b / a)",
"tactic": "rw [mul_one a, div_eq_mul_inv, mul_comm b, mul_inv_cancel_left]"
},
{
"s... | [
329,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.set_walk_length_zero_eq_of_ne | [
{
"state_after": "case h\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nh : u ≠ v\np : Walk G u v\n⊢ p ∈ {p | Walk.length p = 0} ↔ p ∈ ∅",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : Si... | [
2308,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2304,
1
] |
Mathlib/Data/Quot.lean | Quotient.mk_out' | [] | [
796,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/List/Basic.lean | List.foldl_join | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.231477\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β → α\na : α\nl : List β\nL : List (List β)\n⊢ foldl f a (join (l :: L)) = foldl (foldl f) a (l :: L)",
"tactic": "simp only [join, foldl_append, foldl_cons, foldl_jo... | [
2443,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2440,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuousAt_pow | [] | [
592,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finsum_smul | [
{
"state_after": "case inl\nG : Type ?u.140761\nM✝ : Type ?u.140764\nN : Type ?u.140767\nα : Sort ?u.140770\nβ : Sort ?u.140773\nι : Sort u_3\ninst✝⁵ : CommMonoid M✝\ninst✝⁴ : CommMonoid N\nR : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : NoZeroSMulDivisors R M\... | [
338,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | nonempty_measurable_superset | [] | [
251,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_def | [] | [
74,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.lsub_lt_ord_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.157734\nr : α → α → Prop\nι : Type (max u_1 u_2)\nf : ι → Ordinal\nc : Cardinal\nhc : IsRegular c\nhι : (#ι) < c\n⊢ (#ι) < Ordinal.cof (ord c)",
"tactic": "rwa [hc.cof_eq]"
}
] | [
1068,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_inter_compl | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.150973\ns✝ s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\ns : Set ι\n⊢ pi s t ∩ pi (sᶜ) t = pi univ t",
"tactic": "rw [← union_pi, union_compl_self]"
}
] | [
767,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | toMatrix_dualTensorHom | [
{
"state_after": "case a.h\nι : Type w\nR : Type u\nM : Type v₁\nN : Type v₂\nP : Type v₃\nQ : Type v₄\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : AddCommMonoid N\ninst✝¹¹ : AddCommMonoid P\ninst✝¹⁰ : AddCommMonoid Q\ninst✝⁹ : Module R M\ninst✝⁸ : Module R N\ninst✝⁷ : Module R P\ninst✝⁶ : Mo... | [
144,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.map_smul₂ | [] | [
175,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.disjoint_diag_offDiag | [] | [
370,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff_eq_or_lt_of_not_isMin | [] | [
801,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.map_ne | [] | [
1007,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.integral_pos | [
{
"state_after": "E : Type u_1\nX : Type ?u.1741316\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup X\ninst✝⁶ : NormedSpace ℝ X\ninst✝⁵ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\ninst✝⁴ : MeasurableSpace E\nμ : MeasureTheory.Measure E\ninst✝³ : BorelSpac... | [
527,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.X_sub_C_mul_divByMonic_eq_sub_modByMonic | [
{
"state_after": "case _hq\nR : Type u\nS : Type v\nk : Type y\nA : Type z\na✝ b : R\nn : ℕ\ninst✝¹ : Field R\np q : R[X]\nK : Type u_1\ninst✝ : Field K\nf : K[X]\na : K\n⊢ Monic (X - ↑C a)",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na✝ b : R\nn : ℕ\ninst✝¹ : Field R\np q : R[X]\nK : ... | [
506,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.int_cast_toProd | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_top | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns : Set P\nh : affineSpan k s = ⊤\n⊢ vectorSpan k s = ⊤",
"tactic": "rw [← direction_affineSpan, h, direction_top]"
}
] | [
789,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | mul_left_bijective_of_finite₀ | [] | [
48,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.one_sub_K_pos' | [
{
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54,
89
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54,
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Mathlib/Logic/Basic.lean | iff_iff_and_or_not_and_not | [] | [
443,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
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Mathlib/Analysis/Convex/Gauge.lean | mul_gauge_le_norm | [
{
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471,
49
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Mathlib/Order/LiminfLimsup.lean | Filter.eventually_lt_of_lt_liminf | [
{
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1127,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_union_Ioi | [
{
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Mathlib/Order/Monotone/Monovary.lean | Monotone.monovary | [] | [
321,
43
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.choose_exists_companion | [
{
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360,
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Mathlib/Algebra/Algebra/Prod.lean | Prod.algebraMap_apply | [] | [
55,
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.supports_union | [
{
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}
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1926,
38
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1925,
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Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.apply_eq_coe_toFun | [] | [
95,
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Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback_lift_map_isPullback | [
{
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443,
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436,
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Mathlib/Topology/UniformSpace/Basic.lean | swap_idRel | [
{
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] | [
163,
77
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162,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_X | [] | [
1448,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
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Mathlib/MeasureTheory/CardMeasurableSpace.lean | MeasurableSpace.compl_mem_generateMeasurableRec | [
{
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74,
81
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Mathlib/Data/Subtype.lean | Subtype.restrict_apply | [
{
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160,
6
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158,
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Mathlib/Topology/Basic.lean | interior_interior | [] | [
344,
30
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343,
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.symmetry | [] | [
1014,
33
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1012,
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Mathlib/Logic/Basic.lean | forall₂_true_iff | [
{
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}
] | [
723,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
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Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsTerminal.mono_from | [
{
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"tactic": "haveI := t.isSplitMono_from f"
},
{
"state_after": "no goals",
... | [
184,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_add | [
{
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}
] | [
168,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
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Mathlib/Algebra/Quandle.lean | Rack.involutory_invAct_eq_act | [
{
"state_after": "no goals",
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}
] | [
342,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.subtype_comp_codRestrict | [] | [
221,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.image_iff | [
{
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857,
23
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849,
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Mathlib/Topology/Basic.lean | interior_eq_nhds | [
{
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}
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1209,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
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Mathlib/Order/Hom/Lattice.lean | InfHom.coe_inf | [] | [
671,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.floor_map_map_zero_le | [] | [
474,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
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Mathlib/Tactic/NormNum/NatSqrt.lean | Tactic.NormNum.isNat_sqrt | [] | [
27,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
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Mathlib/Topology/Maps.lean | OpenEmbedding.of_comp_iff | [
{
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"tactic": "simp only [... | [
626,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
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Mathlib/Data/Nat/Log.lean | Nat.pow_le_of_le_log | [
{
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"state_before": "b x y : ℕ\nhy : y ≠ 0\nh : x ≤ log b y\n⊢ b ^ x ≤ y",
"tactic": "refine' (le_or_lt b 1).elim (fun hb => _) fun hb => (pow_le_iff_le_log hb hy).2 h"
},
{
"state_after": "b x y : ℕ\nhy : y ≠ 0\nh :... | [
114,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.X_pow_card_pow_sub_X_natDegree_eq | [] | [
244,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
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Mathlib/Data/Int/Bitwise.lean | Int.shiftr_neg | [
{
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}
] | [
376,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | Ring.inverse_exp | [] | [
485,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
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Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.range_log | [] | [
93,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Combinatorics/Catalan.lean | Tree.mem_treesOfNumNodesEq | [
{
"state_after": "case base.succ\nn✝ : ℕ\n⊢ ¬0 = n✝ + 1",
"state_before": "x : Tree Unit\nn : ℕ\n⊢ x ∈ treesOfNumNodesEq n ↔ numNodes x = n",
"tactic": "induction x using Tree.unitRecOn generalizing n <;> cases n <;>\n simp [treesOfNumNodesEq_succ, Nat.succ_eq_add_one, *]"
},
{
"state_after": "... | [
199,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isDetector_unop_iff | [
{
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"tactic": "rw [IsDetector, IsCodetector, ← isDetecting_unop_iff, Set.singleton_unop]"
}
] | [
435,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
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Mathlib/Logic/Equiv/Fin.lean | finSuccEquivLast_last | [
{
"state_after": "no goals",
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"tactic": "simp [finSuccEquivLast]"
}
] | [
279,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
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Mathlib/Deprecated/Group.lean | IsMulHom.id | [] | [
63,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
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Mathlib/Data/List/Basic.lean | List.get_attach | [
{
"state_after": "no goals",
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"tactic": "simpa using i.2"
},
{
"state_after": "no goals",
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4322,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4317,
1
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Mathlib/Data/Matrix/Basis.lean | Matrix.smul_stdBasisMatrix | [
{
"state_after": "l : Type ?u.855\nm : Type u_1\nn : Type u_2\nR : Type ?u.864\nα : Type u_3\ninst✝³ : DecidableEq l\ninst✝² : DecidableEq m\ninst✝¹ : DecidableEq n\ninst✝ : Semiring α\ni : m\nj : n\na b : α\n⊢ (b • fun i' j' => if i = i' ∧ j = j' then a else 0) = fun i' j' => if i = i' ∧ j = j' then b • a else... | [
48,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
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Mathlib/GroupTheory/Congruence.lean | Con.symm | [] | [
150,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
11
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Mathlib/Topology/LocalExtr.lean | IsLocalMin.comp_continuous | [] | [
306,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_add | [
{
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764,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
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Mathlib/Algebra/Order/WithZero.lean | div_le_div_left₀ | [
{
"state_after": "no goals",
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"tactic": "simp only [div_eq_mul_inv, mul_le_mul_left₀ ha, inv_le_inv₀ hb hc]"
}
] | [
245,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.subseq_mem | [] | [
1427,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1424,
1
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Mathlib/Combinatorics/SimpleGraph/Matching.lean | SimpleGraph.Subgraph.IsPerfectMatching.even_card | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\nM✝ M : Subgraph G\ninst✝ : Fintype V\nh : IsPerfectMatching M\n⊢ Even (Fintype.card V)",
"tactic": "classical\nsimpa only [h.2.card_verts] using IsMatching.even_card h.1"
},
{
"state_after": "no goals",
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133,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.Forall₂.prod_le_prod' | [
{
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269,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
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] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | isPrimitiveRoot_of_mem_primitiveRoots | [
{
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"state_before": "M : Type ?u.1452815\nN : Type ?u.1452818\nG : Type ?u.1452821\nR : Type u_1\nS : Type ?u.1452827\nF : Type ?u.1452830\ninst✝⁴ : CommMonoid M\ninst✝³ : CommMonoid N\ninst✝² : DivisionCommMonoid G\nk : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nζ : R\nh : ζ ∈ pri... | [
330,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
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] |
Mathlib/Topology/Sequences.lean | FrechetUrysohnSpace.of_seq_tendsto_imp_tendsto | [
{
"state_after": "X : Type u_1\nY : Type ?u.4450\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh :\n ∀ (f : X → Prop) (a : X), (∀ (u : ℕ → X), Tendsto u atTop (𝓝 a) → Tendsto (f ∘ u) atTop (𝓝 (f a))) → ContinuousAt f a\ns : Set X\nx : X\nhcx : x ∈ closure s\n⊢ x ∈ seqClosure s",
"state_before... | [
171,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivWithinAt.union | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.239899\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.239994\... | [
490,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
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] |
Mathlib/Order/PropInstances.lean | Prop.top_eq_true | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_mul_le' | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.63293\n𝕜 : Type ?u.63296\nα : Type ?u.63299\nι : Type ?u.63302\nκ : Type ?u.63305\nE : Type u_1\nF : Type ?u.63311\nG : Type ?u.63314\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na✝ a₁ a₂ b✝ b₁ b₂ :... | [
470,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Complex/Exponential.lean | Complex.ofReal_tanh_ofReal_re | [
{
"state_after": "no goals",
"state_before": "x✝ y : ℂ\nx : ℝ\n⊢ ↑(starRingEnd ℂ) (tanh ↑x) = tanh ↑x",
"tactic": "rw [← tanh_conj, conj_ofReal]"
}
] | [
710,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
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