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/Topology/PathConnected.lean | Path.coe_mk_mk | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Data/List/Func.lean | List.Func.nil_sub | [
{
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"tactic": "rw [sub, @nil_pointwise _ _ _... | [
387,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.uniformContinuous | [] | [
191,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
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Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.lipschitz | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type ?u.49416\ninst✝⁴ : NormedAddCommGroup G\ninst✝³ : NormedS... | [
169,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
11
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.mul_factorial_pred | [] | [
66,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_mul_inl | [] | [
399,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.not_eq_false_eq_eq_true | [
{
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"state_before": "a : Bool\n⊢ ((!a) = false) = (a = true)",
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}
] | [
109,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.inclusion_inclusion | [] | [
1068,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.disjoint_ball_infDist | [] | [
538,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Data/Set/Basic.lean | Set.sep_union | [] | [
1464,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
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Mathlib/Topology/UniformSpace/Cauchy.lean | totallyBounded_empty | [] | [
505,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.union | [] | [
1573,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
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Mathlib/Algebra/GradedMonoid.lean | List.dProdIndex_eq_map_sum | [
{
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"tactic": "match l with\n| [] => simp\n| head::tail => simp [List.dProdIndex_eq_map_sum tail... | [
380,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_of_is_cokernel | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nh : IsColimit (CokernelCofork.ofπ g w)\n⊢ kernel.ι g ≫ cokernel.π f = 0",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = ... | [
232,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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Mathlib/Data/Part.lean | Part.mul_get_eq | [] | [
735,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.pow_mem | [] | [
240,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
11
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.continuousLinearMapOfBilin_apply | [
{
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"tactic": "simp [continuousLinearMapOfBilin]"
}
] | [
180,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Order/Hom/Bounded.lean | BoundedOrderHom.symm_dual_id | [] | [
821,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
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Std/Logic.lean | or_right_comm | [
{
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}
] | [
278,
92
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
278,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | StrictMono.const_mul | [] | [
594,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.size_eq_realSize | [
{
"state_after": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\nh₁ : s = size l + size r + 1\nh₂ : Sized l\nh₃ : Sized r\n⊢ realSize l + realSize r + 1 = realSize (node (realSize l + realSize r + 1) l x r)",
"state_before": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\nh₁ : s = size... | [
138,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.tailings_succ | [
{
"state_after": "no goals",
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970,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffWithinAt.rpow_const_of_le | [] | [
543,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_left_self_sup | [] | [
502,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_dvd | [] | [
160,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/String/Lemmas.lean | String.next_of_valid' | [
{
"state_after": "cs cs' : List Char\n⊢ { byteIdx := utf8Len cs } + List.headD cs' default = { byteIdx := utf8Len cs + csize (List.headD cs' default) }",
"state_before": "cs cs' : List Char\n⊢ next { data := cs ++ cs' } { byteIdx := utf8Len cs } = { byteIdx := utf8Len cs + csize (List.headD cs' default) }",... | [
255,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
253,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_arctan | [] | [
124,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Sigma/Basic.lean | Prod.toSigma_mk | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/MeasureTheory/Group/MeasurableEquiv.lean | measurableEmbedding_mulLeft | [] | [
127,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Lp.lean | MeasureTheory.Memℒp.aefinStronglyMeasurable | [] | [
67,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.comp_add | [] | [
896,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.toFun_eq_coe_aux | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_comm | [] | [
1393,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Coplanar.finiteDimensional_direction_affineSpan | [] | [
620,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
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] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.subtypePerm_zpow | [
{
"state_after": "case ofNat\nα : Type u\nβ : Type v\np : α → Prop\nf✝ f : Perm α\nhf : ∀ (x : α), p x ↔ p (↑f x)\nn : ℕ\n⊢ subtypePerm f hf ^ Int.ofNat n = subtypePerm (f ^ Int.ofNat n) (_ : ∀ (x : α), p x ↔ p (↑(f ^ Int.ofNat n) x))\n\ncase negSucc\nα : Type u\nβ : Type v\np : α → Prop\nf✝ f : Perm α\nhf : ∀ ... | [
424,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
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Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.ker_toContinuousLinearMap | [] | [
324,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
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] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_iff_card_roots | [
{
"state_after": "case mp\nF : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\np : K[X]\n⊢ Splits (RingHom.id K) p → ↑Multiset.card (roots p) = natDegree p\n\ncase mpr\nF : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : ... | [
448,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | GCongr.prod_le_prod' | [] | [
132,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.comap_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.4517\nι : Sort ?u.4520\ns : Set α\nt : Set β\nf✝ : Filter α\ng : Filter β\nf : α → β × γ\nb : Filter β\nc : Filter γ\n⊢ comap f (b ×ˢ c) = comap (Prod.fst ∘ f) b ⊓ comap (Prod.snd ∘ f) c",
"tactic": "erw ... | [
114,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.sub_left | [] | [
235,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
11
] |
Mathlib/Algebra/Ring/BooleanRing.lean | add_eq_zero' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3681\nγ : Type ?u.3684\ninst✝ : BooleanRing α\na b : α\n⊢ a = -b ↔ a = b",
"tactic": "rw [neg_eq]"
}
] | [
91,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.top_coe | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_mem_prod_iff | [] | [
87,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/InformationTheory/Hamming.lean | hammingDist_smul | [] | [
153,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | AlgHom.coe_to_lieHom | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.one_moveLeft | [] | [
366,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.sub_one_lt_iff | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\nk : Fin (n + 1)\n⊢ ¬k - 1 < k ↔ ¬0 < k",
"tactic": "simp only [not_lt, le_sub_one_iff, le_zero_iff]"
}
] | [
2005,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2004,
1
] |
Mathlib/Data/Set/Basic.lean | Set.not_mem_compl_iff | [] | [
1645,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1644,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | left_eq_midpoint_iff | [
{
"state_after": "no goals",
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169,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Order/Heyting/Basic.lean | PUnit.sdiff_eq | [] | [
1360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1359,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.toGlueR_isometry | [] | [
524,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.iSup_lt_succ' | [
{
"state_after": "α : Type u_1\ninst✝ : CompleteLattice α\nu : ℕ → α\nn : ℕ\n⊢ ((⨆ (_ : 0 < n + 1), u 0) ⊔ ⨆ (i : ℕ) (_ : i + 1 < n + 1), u (i + 1)) = u 0 ⊔ ⨆ (k : ℕ) (_ : k < n), u (k + 1)",
"state_before": "α : Type u_1\ninst✝ : CompleteLattice α\nu : ℕ → α\nn : ℕ\n⊢ (⨆ (k : ℕ) (_ : k < n + 1), u k) = u 0... | [
186,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.map_sum₂ | [] | [
184,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_coprime_fib_succ | [
{
"state_after": "case zero\n\n⊢ coprime (fib zero) (fib (zero + 1))\n\ncase succ\nn : ℕ\nih : coprime (fib n) (fib (n + 1))\n⊢ coprime (fib (succ n)) (fib (succ n + 1))",
"state_before": "n : ℕ\n⊢ coprime (fib n) (fib (n + 1))",
"tactic": "induction' n with n ih"
},
{
"state_after": "no goals",... | [
146,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_distrib_subset_right | [
{
"state_after": "α : Type u_4\nα' : Type u_6\nβ : Type u_5\nβ' : Type u_7\nγ✝ : Type ?u.89133\nγ' : Type ?u.89136\nδ : Type u_3\nδ' : Type ?u.89142\nε : Type u_2\nε' : Type ?u.89148\nζ : Type ?u.89151\nζ' : Type ?u.89154\nν : Type ?u.89157\ninst✝⁷ : DecidableEq α'\ninst✝⁶ : DecidableEq β'\ninst✝⁵ : DecidableEq... | [
466,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_assoc | [] | [
350,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | pow_nonneg | [
{
"state_after": "α : Type u\nβ : Type ?u.13277\ninst✝ : OrderedSemiring α\na b c d : α\nH : 0 ≤ a\n⊢ 0 ≤ 1",
"state_before": "α : Type u\nβ : Type ?u.13277\ninst✝ : OrderedSemiring α\na b c d : α\nH : 0 ≤ a\n⊢ 0 ≤ a ^ 0",
"tactic": "rw [pow_zero]"
},
{
"state_after": "no goals",
"state_befo... | [
250,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/AlgebraicTopology/AlternatingFaceMapComplex.lean | AlgebraicTopology.AlternatingFaceMapComplex.d_squared | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nn : ℕ\n⊢ (∑ i : Fin (n + 1 + 2), (-1) ^ ↑i • SimplicialObject.δ X i) ≫ ∑ i : Fin (n + 2), (-1) ^ ↑i • SimplicialObject.δ X i =\n 0",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditiv... | [
119,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.is_id | [] | [
479,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.toMeasure_bindOnSupport_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.156387\np : Pmf α\nf : (a : α) → a ∈ support p → Pmf β\ns : Set β\ninst✝ : MeasurableSpace β\nhs : MeasurableSet s\n⊢ ↑↑(toMeasure (bindOnSupport p f)) s = ∑' (a : α), ↑p a * if h : ↑p a = 0 then 0 else ↑↑(toMeasure (f a h... | [
335,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.lt_map_of_nat_lt_translationNumber | [] | [
887,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_abs_left | [] | [
796,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Std/Data/Option/Lemmas.lean | Option.none_orElse | [] | [
170,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
170,
9
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | sInf_sup_eq | [] | [
199,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.image_emetric_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.725615\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nh : α ≃ᵢ β\nx : α\nr : ℝ≥0∞\n⊢ ↑h '' EMetric.ball x r = EMetric.ball (↑h x) r",
"tactic": "rw [← h.preimage_sy... | [
493,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/ModelTheory/Definability.lean | Set.Definable.image_comp_sum_inl_fin | [
{
"state_after": "case intro\nM : Type w\nA : Set M\nL : Language\ninst✝ : Structure L M\nα : Type u₁\nβ : Type ?u.18147\nB : Set M\ns : Set (α → M)\nm : ℕ\nφ : Formula (L[[↑A]]) (α ⊕ Fin m)\n⊢ Definable A L ((fun g => g ∘ Sum.inl) '' setOf (Formula.Realize φ))",
"state_before": "M : Type w\nA : Set M\nL : ... | [
187,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Logic/Function/Basic.lean | Function.Injective.extend_apply | [] | [
728,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.nat_add | [] | [
255,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | MonoidHomClass.uniformContinuous_of_bound | [] | [
851,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
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Mathlib/Analysis/Convex/Basic.lean | Convex.mem_smul_of_zero_mem | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.256081\nβ : Type ?u.256084\ninst✝⁴ : LinearOrderedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nh : Convex 𝕜 s\nx : E\nzero_mem : 0 ∈ s\nhx : x ∈ s\nt : 𝕜\nht : 1 ≤ t\n⊢ t⁻¹ • x ∈ s",... | [
538,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | AddSubmonoid.toSubmonoid_closure | [] | [
157,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_sup_of_normal_left | [] | [
324,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.nilpotentOfNilpotentQuotient | [
{
"state_after": "case mk.intro\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk✝ : ℕ\nN✝ N : LieSubmodule R L M\nh₁ : N ≤ maxTrivSubmodule R L M\nk : ℕ\nhk ... | [
250,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_le_card_width | [
{
"state_after": "l : Type ?u.15349\nm : Type u_2\nn : Type u_3\no : Type ?u.15358\nR : Type u_1\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : CommRing R\ninst✝ : StrongRankCondition R\nA : Matrix m n R\nthis : Module.Finite R (n → R)\n⊢ rank A ≤ Fintype.card n",
"state_before": "l : ... | [
68,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.exists_mem_Ico | [] | [
298,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasDerivWithinAt | [] | [
95,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
11
] |
Mathlib/Order/Filter/Bases.lean | Filter.inf_neBot_iff_frequently_right | [
{
"state_after": "α : Type u_1\nβ : Type ?u.61014\nγ : Type ?u.61017\nι : Sort ?u.61020\nι' : Sort ?u.61023\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nf g : Filter α\n⊢ NeBot (g ⊓ f) ↔ ∀ {p : α → Prop}, (∀ᶠ (x : α) in g, p x) → ∃ᶠ (x : α) in f, p x... | [
750,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_attach_biUnion | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nR₂ : Type ?u.43659\nK : Type ?u.43662\nM : Type u_1\nM₂ : Type ?u.43668\nV : Type ?u.43671\nS : Type ?u.43674\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nx : M\np p' : Submodule R M\ninst✝³ : Semiring R₂\nσ₁₂ : R →+* R₂\nin... | [
251,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.sizeUpTo_strict_mono | [
{
"state_after": "n : ℕ\nc : Composition n\ni : ℕ\nh : i < length c\n⊢ sizeUpTo c i < sizeUpTo c i + nthLe c.blocks i h",
"state_before": "n : ℕ\nc : Composition n\ni : ℕ\nh : i < length c\n⊢ sizeUpTo c i < sizeUpTo c (i + 1)",
"tactic": "rw [c.sizeUpTo_succ h]"
},
{
"state_after": "no goals",
... | [
250,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.frequently_high_scores | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.75677\nι' : Type ?u.75680\nα : Type ?u.75683\nβ : Type u_1\nγ : Type ?u.75689\ninst✝¹ : LinearOrder β\ninst✝ : NoMaxOrder β\nu : ℕ → β\nhu : Tendsto u atTop atTop\n⊢ ∃ᶠ (n : ℕ) in atTop, ∀ (k : ℕ), k < n → u k < u n",
"tactic": "simpa [frequently... | [
579,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_map | [] | [
1384,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1382,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_cond_ne | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.190903\nι : Type ?u.190906\nG : Type ?u.190909\nM : Type u_2\nN : Type ?u.190915\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\nf : α → M\na : α\ninst✝ : DecidableEq α\nhf : Set.Finite (mulSupport f)\n⊢ ∀ {x : α}, f x ≠ 1 → (x ≠ a ↔ x ∈ Finset.erase (Finite.to... | [
462,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_bound' | [
{
"state_after": "x : ℝ\nh1 : 0 ≤ x\nh2 : x ≤ 1\nn : ℕ\nhn : 0 < n\nh3 : abs' x = x\n⊢ exp x ≤ ∑ m in range n, x ^ m / ↑(Nat.factorial m) + x ^ n * (↑n + 1) / (↑(Nat.factorial n) * ↑n)",
"state_before": "x : ℝ\nh1 : 0 ≤ x\nh2 : x ≤ 1\nn : ℕ\nhn : 0 < n\n⊢ exp x ≤ ∑ m in range n, x ^ m / ↑(Nat.factorial m) +... | [
1721,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1712,
1
] |
Mathlib/RingTheory/Localization/LocalizationLocalization.lean | IsLocalization.localization_isScalarTower_of_submonoid_le | [] | [
197,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_mono | [] | [
389,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
11
] |
Mathlib/Order/Monotone/Basic.lean | strictAnti_of_le_iff_le | [] | [
548,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.iUnion_eq | [] | [
1468,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1467,
1
] |
Mathlib/Order/Cover.lean | Prod.mk_covby_mk_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PartialOrder β\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α × β\n⊢ (a, b₁) ⋖ (a, b₂) ↔ b₁ ⋖ b₂",
"tactic": "simp_rw [covby_iff_wcovby_and_lt, mk_wcovby_mk_iff_right, mk_lt_mk_iff_right]"
}
] | [
533,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.TendstoInMeasure.congr | [] | [
89,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.const_smul | [] | [
88,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | ENNReal.lintegral_rpow_funMulInvSnorm_eq_one | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np : ℝ\nhp0_lt : 0 < p\nf : α → ℝ≥0∞\nhf_nonzero : (∫⁻ (a : α), f a ^ p ∂μ) ≠ 0\nhf_top : (∫⁻ (a : α), f a ^ p ∂μ) ≠ ⊤\n⊢ (∫⁻ (c : α), f c ^ p * (∫⁻ (c : α), f c ^ p ∂μ)⁻¹ ∂μ) = 1",
"state_before": "α : Type u_1\ninst✝ : ... | [
104,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.continuousOn_primitive | [
{
"state_after": "case pos\nι : Type ?u.18234336\n𝕜 : Type ?u.18234339\nE : Type u_1\nF : Type ?u.18234345\nA : Type ?u.18234348\ninst✝³ : NormedAddCommGroup E\ninst✝² : CompleteSpace E\ninst✝¹ : NormedSpace ℝ E\na b b₀ b₁ b₂ : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → E\ninst✝ : NoAtoms μ\nh_int : IntegrableO... | [
1207,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basisDivisor_add_symm | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝¹ : Field F\nι : Type ?u.84878\ninst✝ : DecidableEq ι\ns : Finset ι\nv : ι → F\ni j : ι\nx y : F\nhxy : x ≠ y\n⊢ basisDivisor x y + basisDivisor y x = 1",
"tactic": "classical rw [\n ← sum_basis (Set.injOn_of_injective Function.injective_... | [
280,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_ofReal_norm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1684989\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 : E\n⊢ ↑(↑re (inner x x)) = inner x x",
"state_before": "𝕜 : Type u_... | [
604,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.openToLocalization_apply | [] | [
524,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.comp_inj | [
{
"state_after": "V : Type u\ninst✝ : Quiver V\na b c d : V\np₁ p₂ : Path a b\nq₁ q₂ : Path b c\nhq : length q₁ = length q₂\nh : comp p₁ q₁ = comp p₂ q₂\n⊢ p₁ = p₂ ∧ q₁ = q₂",
"state_before": "V : Type u\ninst✝ : Quiver V\na b c d : V\np₁ p₂ : Path a b\nq₁ q₂ : Path b c\nhq : length q₁ = length q₂\n⊢ comp p... | [
138,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_ne_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.217228\nβ : Type ?u.217231\nγ : Type ?u.217234\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\n⊢ a ≠ 0 → b ≠ 0 → a * b ≠ 0",
"tactic": "simpa only [Ordinal.pos_iff_ne_zero] using mul_pos"
}
] | [
837,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_testAgainstNN_of_le_const | [] | [
648,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_abs | [
{
"state_after": "x : ℝ\n⊢ ↑↑(↑Real.nnabs x) = ↑↑(↑Real.nnabs x)",
"state_before": "x : ℝ\n⊢ ↑(EReal.abs ↑x) = ↑(abs x)",
"tactic": "rw [abs_def, ← Real.coe_nnabs, ENNReal.ofReal_coe_nnreal]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑↑(↑Real.nnabs x) = ↑↑(↑Real.nnabs x)",
... | [
1083,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.multiset_sum_mem | [] | [
222,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
11
] |
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