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/Order/Basic.lean | closure_le_eq | [] | [
209,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | IsUnit.aemeasurable_const_smul_iff | [] | [
752,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
8
] |
Mathlib/LinearAlgebra/Finrank.lean | FiniteDimensional.finrank_le_of_rank_le | [
{
"state_after": "case hc\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nn : ℕ\nh : Module.rank K V ≤ ↑n\n⊢ Module.rank K V < ℵ₀\n\ncase hd\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\nins... | [
74,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/Data/Real/Irrational.lean | Irrational.of_add_nat | [] | [
251,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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Mathlib/Data/Nat/Order/Basic.lean | Nat.mul_div_mul_comm_of_dvd_dvd | [
{
"state_after": "case inl\nm n l : ℕ\nhnl : l ∣ n\nhmk : 0 ∣ m\n⊢ m * n / (0 * l) = m / 0 * (n / l)\n\ncase inr\nm n k l : ℕ\nhmk : k ∣ m\nhnl : l ∣ n\nhk0 : k > 0\n⊢ m * n / (k * l) = m / k * (n / l)",
"state_before": "m n k l : ℕ\nhmk : k ∣ m\nhnl : l ∣ n\n⊢ m * n / (k * l) = m / k * (n / l)",
"tacti... | [
434,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | differentiableWithinAt_of_derivWithin_ne_zero | [] | [
238,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
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Mathlib/Combinatorics/Composition.lean | Composition.sizeUpTo_ofLength_le | [
{
"state_after": "n : ℕ\nc : Composition n\ni : ℕ\nh : length c ≤ i\n⊢ sum (take i c.blocks) = n",
"state_before": "n : ℕ\nc : Composition n\ni : ℕ\nh : length c ≤ i\n⊢ sizeUpTo c i = n",
"tactic": "dsimp [sizeUpTo]"
},
{
"state_after": "case h.e'_2.h.e'_4\nn : ℕ\nc : Composition n\ni : ℕ\nh : l... | [
224,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.vanishingIdeal_anti_mono | [] | [
250,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Int/Cast/Basic.lean | Int.cast_subNatNat | [
{
"state_after": "R : Type u\ninst✝ : AddGroupWithOne R\nm n : ℕ\n⊢ ↑(match n - m with\n | 0 => ofNat (m - n)\n | succ k => -[k+1]) =\n ↑m - ↑n",
"state_before": "R : Type u\ninst✝ : AddGroupWithOne R\nm n : ℕ\n⊢ ↑(subNatNat m n) = ↑m - ↑n",
"tactic": "unfold subNatNat"
},
{
"state_... | [
99,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_top | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
440,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_add_emod' | [
{
"state_after": "m k : Int\n⊢ k * (m / k) + m % k = m",
"state_before": "m k : Int\n⊢ m / k * k + m % k = m",
"tactic": "rw [Int.mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m k : Int\n⊢ k * (m / k) + m % k = m",
"tactic": "apply ediv_add_emod"
}
] | [
402,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
401,
1
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_eq_span_mul_set | [] | [
354,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Computability/DFA.lean | DFA.evalFrom_of_append | [] | [
94,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.zpow_sub_one | [
{
"state_after": "no goals",
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"tactic": "rw [mul_assoc, mul_eq_mul A, mul_nonsing_inv _ h, mul_one]"
},
{
"stat... | [
167,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_pos_iff | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type ?u.247460\nn : ℕ\nx : α\ninst✝ : LinearOrderedRing α\nhn : n ≠ 0\nh : 0 < ∑ i in range n, x ^ i\n⊢ Odd n ∨ 0 < x + 1\n\ncase refine'_2\nα : Type u\nβ : Type ?u.247460\nn : ℕ\nx : α\ninst✝ : LinearOrderedRing α\nhn : n ≠ 0\n⊢ Odd n ∨ 0 < x + 1 → 0 < ∑ i in r... | [
540,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.74500\nγ : Type ?u.74503\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf : Filter α\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha : a ≠ ⊤\n⊢ Tendsto u f (𝓝 a) ↔ ∀ (ε : ℝ≥0∞), ε > 0 → ∀ᶠ (x : α) in f, u x ∈ Icc (a - ε) (a + ε)",
... | [
279,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
11
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_blockDiagonal | [] | [
256,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin'Aux_eq | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | LocalHomeomorph.singletonChartedSpace_mem_atlas_eq | [] | [
1005,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Std/Data/List/Lemmas.lean | List.filterMap_join | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → Option β\nL : List (List α)\n⊢ filterMap f (join L) = join (map (filterMap f) L)",
"tactic": "induction L <;> simp [*, filterMap_append]"
}
] | [
1213,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1211,
9
] |
Mathlib/Init/Algebra/Order.lean | ne_of_gt | [] | [
108,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | mul_mem_cancel_right | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.12139\ninst✝⁶ : Group G\ninst✝⁵ : Group G'\nA : Type ?u.12148\ninst✝⁴ : AddGroup A\nM : Type ?u.12154\nS : Type u_2\ninst✝³ : DivInvMonoid M\ninst✝² : SetLike S M\nhSM : SubgroupClass S M\nH K : S\ninst✝¹ : SetLike S G\ninst✝ : Subgrou... | [
184,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.comap_lift'_eq | [] | [
311,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | continuousOn_of_locally_uniform_approx_of_continuousWithinAt | [] | [
846,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_comp_lattice_hom' | [] | [
1307,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.epimorphisms | [
{
"state_after": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.61126\ninst✝ : Category D\nX Y Z : C\ne : Y ≅ Z\nf : X ⟶ Y\n⊢ MorphismProperty.epimorphisms C f → MorphismProperty.epimorphisms C (f ≫ e.hom)",
"state_before": "case right\nC : Type u\ninst✝¹ : Category C\nD : Type ?u.61126\ninst✝ : ... | [
442,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | nnnorm_pow_le' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.126931\nγ : Type ?u.126934\nι : Type ?u.126937\ninst✝ : SeminormedRing α\na : α\nx✝ : 0 < 1\n⊢ ‖a ^ 1‖₊ ≤ ‖a‖₊ ^ 1",
"tactic": "simp only [pow_one, le_rfl]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\n... | [
365,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.map_sup | [] | [
788,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_top_of_surjective | [
{
"state_after": "no goals",
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"tactic": "rw [map_top, hf.range_eq, restrict_univ]"
}
] | [
646,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Data/List/Basic.lean | List.takeD_left | [
{
"state_after": "no goals",
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"tactic": "simp only [length_append, Nat.le_add_right]"
}
] | [
2368,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2367,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.left_of_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1130\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhn : IsFixedPt (f^[n] ∘ f^[m]) x\nhm : IsPeriodicPt f m x\n⊢ IsPeriodicPt f n x",
"state_before": "α : Type u_1\nβ : Type ?u.1130\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhn : IsPeriodicPt f (n + m) x\nhm : IsP... | [
107,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_blsub_le_lift | [
{
"state_after": "α : Type ?u.38775\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\n⊢ cof (blsub o f) ≤ Cardinal.lift (#(Quotient.out o).α)",
"state_before": "α : Type ?u.38775\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\n⊢ cof (blsub o f) ≤ Cardinal.lift (card o... | [
435,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.mem_map | [] | [
857,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_dvd_iff_zpow_eq_one | [
{
"state_after": "case intro.inl\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Group G\ninst✝ : AddGroup A\ni : ℕ\n⊢ ↑(orderOf x) ∣ ↑i ↔ x ^ ↑i = 1\n\ncase intro.inr\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Group G\ninst✝ : AddGroup A\ni : ℕ\n⊢ ↑(orderOf x) ∣ -↑i ↔ x ^ (-↑i) =... | [
560,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Data/Part.lean | Part.bind_defined | [] | [
664,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.inv_unique | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b c u u₁ u₂ : αˣ\nh : ↑u₁ = ↑u₂\n⊢ ↑u₁ * ↑u₂⁻¹ = 1",
"tactic": "rw [h, u₂.mul_inv]"
}
] | [
401,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Topology/LocallyFinite.lean | locallyFinite_sum | [] | [
213,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.mul_lt_one | [] | [
858,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.isGreatest_image2 | [] | [
1491,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_prod' | [
{
"state_after": "no goals",
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995,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
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] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.mem_leadingCoeffNth | [
{
"state_after": "R : Type u\nS : Type ?u.130378\ninst✝¹ : CommSemiring R\ninst✝ : Semiring S\nI : Ideal R[X]\nn : ℕ\nx : R\n⊢ (∃ y, (degree y ≤ ↑n ∧ y ∈ ofPolynomial I) ∧ coeff y n = x) ↔\n ∃ p, p ∈ I ∧ degree p ≤ ↑n ∧ Polynomial.leadingCoeff p = x",
"state_before": "R : Type u\nS : Type ?u.130378\ninst... | [
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80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
] |
Std/Data/List/Lemmas.lean | List.isSuffix.subset | [] | [
1616,
20
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1615,
11
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Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_spec | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\n⊢ x = ↑(valMinAbs x) ∧ valMinAbs x * 2 ∈ Set.Ioc (-↑n) ↑n",
"state_before": "n : ℕ\ninst✝ : NeZero n\nx : ZMod n\ny : ℤ\n⊢ valMinAbs x = y → x = ↑y ∧ y * 2 ∈ Set.Ioc (-↑n) ↑n",
"tactic": "rintro rfl"
},
{
"state_after": "no goals",
"stat... | [
978,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.det_reindexLinearEquiv_self | [] | [
163,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.coe_transferFunction | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝ : Group G\nH : Subgroup G\ng : G\nq : G ⧸ H\n⊢ ↑(transferFunction H g q) = q",
"tactic": "rw [transferFunction_apply, ← smul_eq_mul, Quotient.coe_smul_out',\n ← quotientEquivSigmaZMod_symm_apply, Sigma.eta, symm_apply_apply]"
}
] | [
610,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
608,
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Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.comap_comap | [
{
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"state_before": "α✝ : Type ua\nβ✝ : Type ub\nγ✝ : Type uc\nδ : Type ud\nι : Sort ?u.137464\nα : Type u_1\n... | [
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70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.basisRepr_eq_of_iIsOrtho | [
{
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Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Functor.sum_obj_inr | [] | [
202,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.ne_zero_of_coe_le_degree | [] | [
1125,
73
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Mathlib/Algebra/GeomSum.lean | geom_sum_pos | [
{
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] | [
457,
76
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455,
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Mathlib/Computability/Partrec.lean | Partrec.option_casesOn_right | [
{
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777,
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_sdiff_left | [
{
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628,
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624,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vadd_right_mem_affineSpan_pair | [
{
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1349,
25
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_mono_nnnorm_ae | [
{
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355,
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350,
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Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.nonempty_of_nonempty_constants | [] | [
383,
12
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382,
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.union | [] | [
414,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_map | [
{
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456,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.left_of_add_measure | [] | [
679,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
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Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_mul_eq_sum_mul_comp_perm_iff | [] | [
414,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.pi_ne_zero | [] | [
170,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
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Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_Ioo | [] | [
514,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.max_eq_zero_iff | [
{
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},
{
"state_after": "case mp\nm n k l : ℕ\nh : max m n = 0\n⊢ m = 0 ∧ n = 0",
... | [
137,
9
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128,
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Mathlib/Topology/UniformSpace/Separation.lean | isClosed_range_of_spaced_out | [
{
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246,
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242,
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Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.isDomain | [] | [
113,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
11
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Mathlib/Data/List/Nodup.lean | List.Nodup.insert | [
{
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377,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_eq_lintegral | [
{
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530,
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528,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow_of_exponent_ge' | [
{
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583,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/Analysis/Calculus/Darboux.lean | deriv_forall_lt_or_forall_gt_of_forall_ne | [
{
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110,
65
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104,
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_attach | [] | [
1563,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1562,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.smul_def | [] | [
1252,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
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Mathlib/Order/JordanHolder.lean | CompositionSeries.total | [
{
"state_after": "case intro\nX : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\ny : X\nhy : y ∈ s\ni : Fin (s.length + 1)\nhx : series s i ∈ s\n⊢ series s i ≤ y ∨ y ≤ series s i",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : Compos... | [
199,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.mul_const | [] | [
424,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
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Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eqToIso.hom | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.algebraMap_eq' | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.min_succ_succ | [
{
"state_after": "x y : Nat\n⊢ (if x ≤ y then succ x else succ y) = succ (if x ≤ y then x else y)",
"state_before": "x y : Nat\n⊢ min (succ x) (succ y) = succ (min x y)",
"tactic": "simp [Nat.min_def, succ_le_succ_iff]"
},
{
"state_after": "no goals",
"state_before": "x y : Nat\n⊢ (if x ≤ y ... | [
218,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
217,
1
] |
Mathlib/Data/List/OfFn.lean | List.map_ofFn | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nn : ℕ\nf : Fin n → α\ng : α → β\ni : ℕ\nh :... | [
89,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.alephIdx.initialSeg_coe | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.of_exists_unique_irreducible_factors | [
{
"state_after": "case h.h'.h.e'_2.h.h.e'_1.h.h'.a\nα : Type u_1\ninst✝ : CancelCommMonoidWithZero α\neif : ∀ (a : α), a ≠ 0 → ∃ f, (∀ (b : α), b ∈ f → Irreducible b) ∧ Multiset.prod f ~ᵤ a\nuif :\n ∀ (f g : Multiset α),\n (∀ (x : α), x ∈ f → Irreducible x) →\n (∀ (x : α), x ∈ g → Irreducible x) → Mult... | [
434,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_neg_neg | [] | [
141,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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Mathlib/Topology/Constructions.lean | Prod.tendsto_iff | [
{
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564,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
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Mathlib/GroupTheory/Index.lean | Subgroup.relindex_ne_zero_trans | [] | [
415,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
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Mathlib/RingTheory/Int/Basic.lean | Int.gcd_ne_one_iff_gcd_mul_right_ne_one | [
{
"state_after": "no goals",
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"tactic": "simp only [gcd_eq_one_iff_coprime, ← not_and_or, not_iff_not, IsCoprime.mul_right_iff]"
}
] | [
212,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | ContinuousLinearMap.inCoordinates_eq | [
{
"state_after": "case h\nR : Type ?u.523106\nB : Type u_5\nF : Type u_6\nE : B → Type u_3\ninst✝²² : NontriviallyNormedField R\ninst✝²¹ : (x : B) → AddCommMonoid (E x)\ninst✝²⁰ : (x : B) → Module R (E x)\ninst✝¹⁹ : NormedAddCommGroup F\ninst✝¹⁸ : NormedSpace R F\ninst✝¹⁷ : TopologicalSpace B\ninst✝¹⁶ : (x : B)... | [
1048,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1040,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.bddBelow_coe | [] | [
485,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
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Mathlib/Data/Rat/Defs.lean | Rat.coe_int_den | [] | [
58,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yz_sub | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\n⊢ yz a1 (m - n) = xz a1 m * -yz a1 n + yz a1 m * xz a1 n",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\n⊢ yz a1 (m - n) = xz a1 n * yz a1 m - xz a1 m * yz a1 n",
"tactic": "rw [sub_eq_add_neg, ← mul_neg, mul_comm, add_comm]"
},
{
... | [
394,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicator_one_of_mem_closure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nδ_pos : 0 < δ\nE : Set α\nx : α\nx_mem : x ∈ closure E\n⊢ ↑(thickenedIndicator δ_pos E) x = 1",
"tactic": "rw [thickenedIndicator_apply, thickenedIndicatorAux_one_of_mem_closure δ E x_mem, one_toNNReal]"
}... | [
199,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | LipschitzWith.coeFn_compLp | [] | [
905,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.map_pure | [] | [
208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.Fix.rec_unique | [
{
"state_after": "case h\nn : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nβ : Type u\ng : F (α ::: β) → β\nh : Fix F α → β\nhyp : ∀ (x : F (α ::: Fix F α)), h (mk x) = g ((TypeVec.id ::: h) <$$> x)\nx : Fix F α\n⊢ rec g x = h x",
"state_before": "n : ℕ\nF : TypeVec (n +... | [
287,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_of_not_mem_support | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.166602\nγ : Type ?u.166605\nι : Type ?u.166608\nM : Type u_2\nM' : Type ?u.166614\nN : Type ?u.166617\nP : Type ?u.166620\nG : Type ?u.166623\nH : Type ?u.166626\nR : Type ?u.166629\nS : Type ?u.166632\ninst✝ : Zero M\nf : α →₀ M\na : α\nhaf : ¬a ∈ f.support\n... | [
671,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.coe_pnatDen | [] | [
331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Set/Function.lean | Set.eqOn_range | [] | [
240,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.coe_mk | [] | [
90,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.finset_sup_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\nδ : Type ?u.804933\ninst✝² : MeasurableSpace α\nK : Type ?u.804939\ninst✝¹ : SemilatticeSup β\ninst✝ : OrderBot β\nf : γ → α →ₛ β\ns : Finset γ\na : α\n⊢ ∀ ⦃a_1 : γ⦄ {s : Finset γ},\n ¬a_1 ∈ s →\n (↑(Finset.sup s f) a = Finset.sup s fun c => ↑(... | [
733,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.inf | [] | [
496,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_nsmul | [] | [
306,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/CategoryTheory/Adjunction/FullyFaithful.lean | CategoryTheory.inv_counit_map | [] | [
112,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.castSucc_inj | [] | [
1267,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.dirac_apply | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.327267\nγ : Type ?u.327270\nδ : Type ?u.327273\nι : Type ?u.327276\nR : Type ?u.327279\nR' : Type ?u.327282\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 : Measurab... | [
2000,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1994,
1
] |
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