file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.mem_sSup_of_mem | [
{
"state_after": "R : Type u_2\nS✝ : Type ?u.168464\nM : Type u_1\ninst✝⁶ : Semiring R\ninst✝⁵ : Semiring S✝\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : Module S✝ M\ninst✝¹ : SMul S✝ R\ninst✝ : IsScalarTower S✝ R M\np q : Submodule R M\nS : Set (Submodule R M)\ns : Submodule R M\nhs : s ∈ S\nthis :... | [
324,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | TopologicalGroup.tendstoUniformly_iff | [] | [
618,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.image_smul_product | [] | [
1275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
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Mathlib/Topology/Order.lean | isClosed_induced_iff' | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nt✝ : TopologicalSpace β\nf✝ : α → β\nt : TopologicalSpace β\nf : α → β\ns : Set α\nthis : TopologicalSpace α := induced f t\n⊢ IsClosed s ↔ ∀ (a : α), f a ∈ closure (f '' s) → a ∈ s",
"state_before": "α : Type u_2\nβ : Type u_1\nt✝ : TopologicalSpace β\nf✝ : α →... | [
891,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.differentiable | [] | [
1477,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
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Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_apply | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\n⊢ (sum f fun n r => ↑(monomial (n - k)) (choose n k • r)) = sum f fun i r => ↑(monomial (i - k)) (↑(choose i k) * r)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\n⊢ ↑(hasseDeriv k) f = sum f fun i r => ↑(monomial (i... | [
69,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.mkQ_apply | [] | [
327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
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Mathlib/Dynamics/FixedPoints/Topology.lean | isFixedPt_of_tendsto_iterate | [
{
"state_after": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : T2Space α\nf : α → α\nx y : α\nhy : Tendsto (fun n => (f^[n]) x) atTop (𝓝 y)\nhf : ContinuousAt f y\n⊢ Tendsto (fun n => (f^[n + 1]) x) atTop (𝓝 (f y))",
"state_before": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : T2Space α\nf : ... | [
40,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.update_eq_sub_add_single | [
{
"state_after": "no goals",
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1318,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_pow_length_eq_one_of_nodup | [
{
"state_after": "case H\nα : Type u_1\nβ : Type ?u.842481\ninst✝ : DecidableEq α\nl : List α\nx✝ : α\nhl : Nodup l\nx : α\n⊢ ↑(formPerm l ^ length l) x = ↑1 x",
"state_before": "α : Type u_1\nβ : Type ?u.842481\ninst✝ : DecidableEq α\nl : List α\nx : α\nhl : Nodup l\n⊢ formPerm l ^ length l = 1",
"tact... | [
468,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
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Mathlib/Data/ULift.lean | PLift.up_bijective | [] | [
53,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/Algebra/Order/Field/Basic.lean | mul_sub_mul_div_mul_nonpos_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.193207\nα : Type u_1\nβ : Type ?u.193213\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhc : c ≠ 0\nhd : d ≠ 0\n⊢ (a * d - b * c) / (c * d) ≤ 0 ↔ a / c ≤ b / d",
"tactic": "rw [mul_comm b c, ← div_sub_div _ _ hc hd, sub_nonpos]"
}
] | [
962,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | AddMonoidAlgebra.toDirectSum_add | [] | [
131,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.as_factorThruImage | [] | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.congr_fun | [] | [
92,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Lattice.lean | inf_comm | [] | [
496,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
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Mathlib/Order/CompleteLattice.lean | iSup_const | [
{
"state_after": "no goals",
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"tactic... | [
1044,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
1
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.exists_disjoint_cylinder | [
{
"state_after": "case inl\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), DiscreteTopology (E n)\nx : (n : ℕ) → E n\nhs : IsClosed ∅\nhx : ¬x ∈ ∅\n⊢ ∃ n, Disjoint ∅ (cylinder x n)\n\ncase inr\nE : ℕ → Type u_1\ninst✝¹ : (n : ℕ) → TopologicalSpace (E n)\ninst✝ : ∀ (n : ℕ), Discr... | [
503,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | CauchySeq.eventually_eventually | [] | [
250,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.isDomain_of_prime | [] | [
375,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | deriv.lhopital_zero_atTop_on_Ioi | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhdf✝ : DifferentiableOn ℝ f (Ioi a)\nhg' : ∀ (x : ℝ), x ∈ Ioi a → deriv g x ≠ 0\nhftop : Tendsto f atTop (𝓝 0)\nhgtop : Tendsto g atTop (𝓝 0)\nhdiv : Tendsto (fun x => deriv f x / deriv g x) atTop l\nhdf : ∀ (x : ℝ), x ∈ Ioi a → Differen... | [
257,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.continuous_snd | [] | [
66,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
8
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lt_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ y < -x ↔ x < -y",
"tactic": "rw [← neg_neg x, neg_lt_neg_iff, neg_neg]"
}
] | [
1368,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1368,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.FinitaryExtensive.mono_inl_of_isColimit | [] | [
251,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_zero | [] | [
147,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Data/Rat/NNRat.lean | Rat.toNNRat_lt_toNNRat_iff | [] | [
370,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/Calculus/Deriv/Pow.lean | differentiableAt_pow | [] | [
75,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.lift_fst | [] | [
1365,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.comap_mul_comap_le | [] | [
628,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.ext | [] | [
173,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.pow_one | [] | [
461,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.acc | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.41887\nδ : Type ?u.41890\nr : α →... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/NFA.lean | NFA.evalFrom_nil | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_iff_openSegment_subset | [] | [
57,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\n⊢ sinh x < 0 ↔ x < 0",
"tactic": "simpa only [sinh_zero] using @sinh_lt_sinh x 0"
}
] | [
713,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_surjective | [] | [
102,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.mk_mem_interedges_iff | [] | [
335,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_incidenceSet | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.137668\n𝕜 : Type ?u.137671\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\nv w : V\n⊢ Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ incidenceSet G v ↔ Adj G v w",
"tactic": "simp [incidenceSe... | [
959,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/LinearAlgebra/FreeModule/Basic.lean | Module.Free.of_basis | [] | [
72,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_comp_val_Ioi_atTop | [
{
"state_after": "ι : Type ?u.337904\nι' : Type ?u.337907\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.337916\ninst✝¹ : SemilatticeSup α\ninst✝ : NoMaxOrder α\na : α\nf : α → β\nl : Filter β\n⊢ Tendsto (fun x => f ↑x) atTop l ↔ Tendsto (f ∘ Subtype.val) atTop l",
"state_before": "ι : Type ?u.337904\nι' : Type ?... | [
1618,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
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Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_factorial_div_pow_self_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.482700\nβ : Type ?u.482703\nι : Type ?u.482706\nn : ℕ\n⊢ 0 ≤ ↑n !",
"tactic": "exact_mod_cast n.factorial_pos.le"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.482700\nβ : Type ?u.482703\nι : Type ?u.482706\nn : ℕ\n⊢ 0 ... | [
562,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.ωSup_def | [] | [
841,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
840,
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Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_nonneg | [] | [
540,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.ofLists_moveRight | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.piCongrRight_trans | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Order/Basic.lean | LT.lt.gt | [] | [
304,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
11
] |
Mathlib/Analysis/Complex/Liouville.lean | Differentiable.apply_eq_apply_of_bounded | [
{
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"state_before": "E :... | [
123,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
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] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.smul_ae_eq_self_of_mem_zpowers | [
{
"state_after": "case intro\nG : Type u_2\nM : Type ?u.82889\nα : Type u_1\ns : Set α\nm : MeasurableSpace α\ninst✝⁴ : Group G\ninst✝³ : MulAction G α\ninst✝² : MeasurableSpace G\ninst✝¹ : MeasurableSMul G α\nc : G\nμ : Measure α\ninst✝ : SMulInvariantMeasure G α μ\nx : G\nhs : x • s =ᶠ[ae μ] s\nk : ℤ\nhy : x ... | [
274,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Logic/Basic.lean | Decidable.not_ball | [] | [
1090,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
11
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.restrict_apply_mk | [] | [
378,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_zero | [] | [
250,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
11
] |
Mathlib/Data/Real/Sqrt.lean | Real.continuous_sqrt | [] | [
189,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_self | [] | [
200,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.one_le_coe | [] | [
509,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.zero_divByMonic | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Ring R\np✝ q p : R[X]\n⊢ (if h : Monic p then\n (if h_1 : degree p ≤ degree 0 ∧ 0 ≠ 0 then\n let z := ↑C (leadingCoeff 0) * X ^ (natDegree 0 - natDegree p);\n let_fun _wf := (_ : degree (0 - ↑C (lead... | [
187,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.rescale_neg_one_X | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.3551663\nA : Type u_1\ninst✝ : CommRing A\n⊢ ↑(rescale (-1)) X = -X",
"tactic": "rw [rescale_X, map_neg, map_one, neg_one_mul]"
}
] | [
1964,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1963,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Equicontinuous.closure' | [] | [
410,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.exists_measure_inter_spanningSets_pos | [
{
"state_after": "α : Type u_1\nβ : Type ?u.733391\nγ : Type ?u.733394\nδ : Type ?u.733397\nι : Type ?u.733400\nR : Type ?u.733403\nR' : Type ?u.733406\nm0 : MeasurableSpace α\ninst✝³ : MeasurableSpace β\ninst✝² : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝¹ : MeasurableSpace α... | [
3569,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3565,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.odd_eq | [] | [
461,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_natTrailingDegree | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : p ≠ 0\nhn : ∀ (m : ℕ), m < n → coeff p m = 0\n⊢ n ≤ min' (support p) (_ : Finset.Nonempty (support p))",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nhp : p ≠ 0\... | [
335,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_wf | [] | [
1189,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/Order/RelClasses.lean | antisymm_of' | [] | [
61,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Holor.lean | Holor.cprankMax_nil | [
{
"state_after": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝¹ : Monoid α\ninst✝ : AddMonoid α\nx : Holor α []\nh : CPRankMax (0 + 1) (x + 0)\n⊢ CPRankMax 1 x",
"state_before": "α : Type\nd : ℕ\nds ds₁ ds₂ ds₃ : List ℕ\ninst✝¹ : Monoid α\ninst✝ : AddMonoid α\nx : Holor α []\n⊢ CPRankMax 1 x",
"tacti... | [
329,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.succ_top | [
{
"state_after": "case hml\nn m : ℕ\nh : n ≤ m\n⊢ m ≤ m + 1",
"state_before": "n m : ℕ\nh : n ≤ m\n⊢ Ico n (m + 1) = Ico n m ++ [m]",
"tactic": "rwa [← succ_singleton, append_consecutive]"
},
{
"state_after": "no goals",
"state_before": "case hml\nn m : ℕ\nh : n ≤ m\n⊢ m ≤ m + 1",
"tacti... | [
129,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_le_iff_le_right | [] | [
109,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.smul_mem | [] | [
145,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.inv_lt_inv | [] | [
911,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.trunc_c | [
{
"state_after": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn✝ n : σ →₀ ℕ\nhnn : n ≠ 0\na : R\nm : σ →₀ ℕ\n⊢ (if m < n then if m = 0 then a else 0 else 0) = if 0 = m then a else 0",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn✝ n : σ →₀ ℕ\nhnn : n ≠ 0\na : R\nm : σ →₀ ℕ\n... | [
730,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.mapRange.linearMap_toAddMonoidHom | [] | [
844,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
src/lean/Init/Control/StateCps.lean | StateCpsT.runK_bind_pure | [] | [
64,
166
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
64,
9
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq | [] | [
101,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformity_translate_mul | [] | [
178,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.neighborSet_subgraphOfAdj_of_ne_of_ne | [
{
"state_after": "case h\nι : Sort ?u.223995\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nu v w : V\nhvw : Adj G v w\nhv : u ≠ v\nhw : u ≠ w\nx✝ : V\n⊢ x✝ ∈ Subgraph.neighborSet (subgraphOfAdj G hvw) u ↔ x✝ ∈ ∅",
"state_before": "ι : Sort ?u.223995\nV : Type u\nW : Type v\nG : SimpleGraph... | [
960,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Data/List/AList.lean | AList.lookup_to_alist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : List (Sigma β)\n⊢ lookup a (toAList s) = dlookup a s",
"tactic": "rw [List.toAList, lookup, dlookup_dedupKeys]"
}
] | [
316,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_comp | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_iff | [
{
"state_after": "case mp\na b : ℤ\nn : ℕ\n⊢ gcd a b ∣ n → ∃ x y, ↑n = a * x + b * y\n\ncase mpr\na b : ℤ\nn : ℕ\n⊢ (∃ x y, ↑n = a * x + b * y) → gcd a b ∣ n",
"state_before": "a b : ℤ\nn : ℕ\n⊢ gcd a b ∣ n ↔ ∃ x y, ↑n = a * x + b * y",
"tactic": "constructor"
},
{
"state_after": "case mp\na b :... | [
399,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | ofBoolRing_toBoolRing | [] | [
419,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.eventually_mul_right_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.492377\nG : Type u_1\nH : Type ?u.492383\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableSpace H\ninst✝² : Group G\ninst✝¹ : MeasurableMul G\nμ : Measure G\ninst✝ : IsMulRightInvariant μ\nt : G\np : G → Prop\n⊢ (∀ᵐ (x : G) ∂μ, p (x * t)) ↔ ∀ᵐ (x : G... | [
329,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_interleave_right | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns₁ s₂ : Stream' α\n⊢ nth (s₁ ⋈ s₂) (succ (succ (2 * n + 1))) = nth s₂ (succ n)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\ns₁ s₂ : Stream' α\n⊢ nth (s₁ ⋈ s₂) (2 * (n + 1) + 1) = nth s₂ (n + 1)",
"tactic": "change nth (s₁ ⋈ s₂... | [
449,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/Instances/Matrix.lean | continuous_matrix_diag | [] | [
187,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot | [] | [
370,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Vector.lean | Vector.head_cons | [] | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean | Matrix.nondegenerate_of_det_ne_zero | [
{
"state_after": "m : Type u_1\nR : Type ?u.4064\nA : Type u_2\ninst✝⁴ : Fintype m\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : IsDomain A\ninst✝ : DecidableEq m\nM : Matrix m m A\nhM : det M ≠ 0\nv : m → A\nhv : ∀ (w : m → A), v ⬝ᵥ mulVec M w = 0\n⊢ v = 0",
"state_before": "m : Type u_1\nR : Type ?u... | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.b_pos | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhb : 1 < b\n⊢ 0 < b",
"tactic": "linarith"
}
] | [
142,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
9
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.measurablySeparable_range_of_disjoint | [
{
"state_after": "α : Type u_1\ninst✝³ : TopologicalSpace α\nι : Type ?u.68523\ninst✝² : T2Space α\ninst✝¹ : MeasurableSpace α\ninst✝ : BorelSpace α\nf g : (ℕ → ℕ) → α\nhf : Continuous f\nhg : Continuous g\nh : Disjoint (range f) (range g)\nhfg : ¬MeasurablySeparable (range f) (range g)\n⊢ False",
"state_be... | [
402,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Topology/Basic.lean | frontier_closure_subset | [] | [
723,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Topology/Perfect.lean | Preperfect.open_inter | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : TopologicalSpace α\nC U : Set α\nhC : Preperfect C\nhU : IsOpen U\nx : α\nxU : x ∈ U\nxC : x ∈ C\n⊢ AccPt x (𝓟 (U ∩ C))",
"state_before": "α : Type u_1\ninst✝ : TopologicalSpace α\nC U : Set α\nhC : Preperfect C\nhU : IsOpen U\n⊢ Preperfect (U ∩ C)",
... | [
98,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/WellFoundedSet.lean | IsAntichain.finite_of_partiallyWellOrderedOn | [
{
"state_after": "ι : Type ?u.49249\nα : Type u_1\nβ : Type ?u.49255\nr : α → α → Prop\nr' : β → β → Prop\nf : α → β\ns t : Set α\na : α\nha : IsAntichain r s\nhp : PartiallyWellOrderedOn s r\nhi : Set.Infinite s\n⊢ False",
"state_before": "ι : Type ?u.49249\nα : Type u_1\nβ : Type ?u.49255\nr : α → α → Pro... | [
287,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_unitBall_of_pos | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.198360\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y z : E\nδ ε r : ℝ\nhr : 0 < r\n⊢ r • ball 0 1 = ball 0 r",
"tactic": "rw [smul_unitBall hr.ne', Real.norm_of... | [
152,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_re | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_norm_norm | [] | [
809,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_const_left | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.609377\nE : Type ?u.609380\nF : Type ?u.609383\nG : Type ?u.609386\nE' : Type ?u.609389\nF' : Type ?u.609392\nG' : Type ?u.609395\nE'' : Type u_2\nF'' : Type u_3\nG'' : Type ?u.609404\nR : Type ?u.609407\nR' : Type ?u.609410\n𝕜 : Type ?u.609413\n𝕜' : Type ... | [
1860,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1856,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.num_div_den | [
{
"state_after": "case a\np q✝ q : ℚ≥0\n⊢ ↑(↑(num q) / ↑(den q)) = ↑q",
"state_before": "p q✝ q : ℚ≥0\n⊢ ↑(num q) / ↑(den q) = q",
"tactic": "ext1"
},
{
"state_after": "case a\np q✝ q : ℚ≥0\n⊢ ↑(↑q).num / ↑(den q) = ↑q",
"state_before": "case a\np q✝ q : ℚ≥0\n⊢ ↑(↑(num q) / ↑(den q)) = ↑q",
... | [
489,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Order/Basic.lean | le_of_eq_of_le' | [] | [
195,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Std/Data/List/Lemmas.lean | List.head!_of_head? | [] | [
439,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
438,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.coprodᵢ_neBot_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : ι → Type u_1\nf f₁ f₂ : (i : ι) → Filter (α i)\ns : (i : ι) → Set (α i)\n⊢ NeBot (Filter.coprodᵢ f) ↔ (∀ (i : ι), Nonempty (α i)) ∧ ∃ d, NeBot (f d)",
"tactic": "simp only [Filter.coprodᵢ, iSup_neBot, ← exists_and_left, ← comap_eval_neBot_i... | [
215,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf✝ : α ↪ β\ns✝ : Finset α\nf : α ↪ β\ng : β ↪ γ\ns : Finset α\n⊢ Multiset.map ((fun x => ↑g x) ∘ fun x => ↑f x) s.val = Multiset.map (fun x => ↑(Embedding.trans f g) x) s.val",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf✝ : α ↪ β\n... | [
138,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | MeasurableSpace.measurableSpace_iSup_eq | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.36119\nγ : Type ?u.36122\nδ : Type ?u.36125\nδ' : Type ?u.36128\nι : Sort u_2\ns✝ t u : Set α\nm : ι → MeasurableSpace α\ns : Set α\n⊢ MeasurableSet s ↔ MeasurableSet s",
"state_before": "α : Type u_1\nβ : Type ?u.36119\nγ : Type ?u.36122\nδ : Type ?u.3612... | [
517,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.IsSatisfiable.isFinitelySatisfiable | [] | [
105,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/Directed.lean | directedOn_singleton | [] | [
243,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
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