file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | continuous_circleMap_inv | [
{
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"state_before": "E : Type ?u.59862\ninst✝ : NormedAddCommGroup E\nR : ℝ\nz w : ℂ\nhw : w ∈ ball z R\n⊢ Continuous f... | [
222,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/Data/Sym/Basic.lean | Sym.cast_cast | [] | [
480,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Data/Finset/Basic.lean | Finset.nonempty_iff_ne_empty | [] | [
608,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
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Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_union | [] | [
183,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.sin_eq_tsum | [] | [
101,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/Quiver/Path.lean | Quiver.Path.length_comp | [] | [
124,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.differentiableAt_cosh | [] | [
158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.types_id | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Instances/NNReal.lean | NNReal.summable_nat_add | [] | [
209,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Data/UnionFind.lean | UnionFind.lt_rankMax | [
{
"state_after": "α : Type u_1\nself : UnionFind α\ni : ℕ\n⊢ (if h : i < size self then self.arr[i].rank else 0) < rankMax self",
"state_before": "α : Type u_1\nself : UnionFind α\ni : ℕ\n⊢ rank self i < rankMax self",
"tactic": "simp [rank]"
},
{
"state_after": "case inl\nα : Type u_1\nself : U... | [
195,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_iff_injective_total | [] | [
479,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_finset_sum' | [
{
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Mathlib/Order/WithBot.lean | WithBot.exists | [] | [
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16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
11
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Mathlib/Data/Set/Basic.lean | Set.insert_comm | [] | [
1182,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
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Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.iInter_compactOpen_gen_subset_compactConvNhd | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nhK : IsCompact K\nhV : V ∈ 𝓤 β\nW : Set (β × β)\nhW₁ : W ∈ 𝓤 β\nhW₄ : IsOpen W\nhW₂ : SymmetricRel W\nhW₃ : W ○ W ⊆ V\n⊢ ∃ ι x C _hC U _hU,\n ... | [
267,
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Mathlib/FieldTheory/PerfectClosure.lean | coe_frobeniusEquiv | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cos_mul_complex | [
{
"state_after": "case hderiv\na✝ b✝ : ℝ\nn : ℕ\nz : ℂ\nhz : z ≠ 0\na b : ℝ\n⊢ ∀ (x : ℝ), x ∈ [[a, b]] → HasDerivAt (fun b => Complex.sin (z * ↑b) / z) (Complex.cos (z * ↑x)) x\n\ncase hint\na✝ b✝ : ℝ\nn : ℕ\nz : ℂ\nhz : z ≠ 0\na b : ℝ\n⊢ IntervalIntegrable (fun y => Complex.cos (z * ↑y)) MeasureTheory.volume a... | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.le_logb_iff_rpow_le | [
{
"state_after": "no goals",
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}
] | [
172,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_symm_apply | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.iterate | [] | [
136,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
11
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Mathlib/Algebra/Support.lean | Function.support_inv | [] | [
385,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.rotate_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.222353\nP : Type u_3\nP' : Type ?u.222359\ninst✝⁷ : OrderedRing R\ninst✝⁶ : AddCommGroup V\ninst✝⁵ : Module R V\ninst✝⁴ : AddTorsor V P\ninst✝³ : AddCommGroup V'\ninst✝² : Module R V'\ninst✝¹ : AddTorsor V' P'\ninst✝ : No... | [
400,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Chain.lean | chainClosure_succ_total | [
{
"state_after": "case succ\nα : Type u_1\nβ : Type ?u.11677\nr : α → α → Prop\nc c₂ c₃ s t : Set α\na b x y : α\ns✝ : Set α\na✝ : ChainClosure r s✝\na_ih✝ : ∀ {c₁ : Set α}, ChainClosure r c₁ → c₁ ⊆ s✝ → s✝ = c₁ ∨ SuccChain r c₁ ⊆ s✝\nc₁ : Set α\nhc₁ : ChainClosure r c₁\nh : c₁ ⊆ SuccChain r s✝\n⊢ SuccChain r s... | [
243,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Data/Set/Sups.lean | Set.sups_subset_right | [] | [
94,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.pointwise_smul_le_pointwise_smul_iff₀ | [] | [
466,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Set/Function.lean | Set.BijOn.image_eq | [] | [
970,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Std/Data/Int/DivMod.lean | Int.eq_div_of_mul_eq_right | [] | [
749,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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11
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Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.isSymm_zero | [] | [
78,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_pos | [
{
"state_after": "no goals",
"state_before": "⊢ 0 < 0 → 0 < φ 0",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "⊢ 0 < 1 → 0 < φ 1",
"tactic": "simp [totient]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nx✝ : 0 < n + 2\n⊢ 1 < n + 2",
"tact... | [
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96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.le_sub_of_add_le_right | [] | [
1165,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_insert_insert_of_mem_affineSpan_pair | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.323622\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ : P\nh₁ : p₁ ∈ affineSpan k {p₃, p₄}\nh₂ : p₂ ∈ affineSpan k {p₃, p₄}\n⊢ Collinear k {p₃, p₄}",
"state_before": "k : Typ... | [
568,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sign_coe_neg_pi_div_two | [
{
"state_after": "no goals",
"state_before": "⊢ sign ↑(-π / 2) = -1",
"tactic": "rw [sign, sin_coe, neg_div, Real.sin_neg, sin_pi_div_two, Left.sign_neg, sign_one]"
}
] | [
976,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.add_lt_add_right_coe | [] | [
689,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
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Mathlib/Data/Finset/Image.lean | Finset.map_disjiUnion | [] | [
281,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
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] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.coe_copy | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_left_pure_ceil | [] | [
83,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.algebraMap₀_eq_smul_one | [
{
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"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nr : R\n⊢ ... | [
237,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_mul_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : CanonicallyOrderedMonoid α\na b c d : α\nh : a ≤ b\n⊢ a = a * 1",
"tactic": "simp"
}
] | [
283,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_eq_zero_of_hasDerivWithinAt | [] | [
487,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.id_hcomp_app | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G H✝ I : C ⥤ D\nH : E ⥤ C\nα : F ⟶ G\nX : E\n⊢ (𝟙 H ◫ α).app X = α.app (H.obj X)",
"tactic": "simp"
}
] | [
124,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.IsImage.iff_symm_preimage_eq | [] | [
519,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Topology/Category/Profinite/Basic.lean | FintypeCat.discreteTopology | [] | [
235,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushout.inr_desc | [] | [
1194,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Order/RelClasses.lean | WellFoundedGT.induction | [] | [
440,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | ModuleCat.Free.ε_apply | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.comap' | [] | [
162,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_prod | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_2\nτ : Type ?u.166872\nr : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\nι : Type u_1\ninst✝ : DecidableEq σ\ns : Finset ι\nf : ι → MvPolynomial σ R\n⊢ vars (∏ i in s, f i) ⊆ Finset.biUnion s ... | [
392,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
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Mathlib/Order/Concept.lean | intentClosure_empty | [] | [
87,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | rotationOf_rotation | [
{
"state_after": "no goals",
"state_before": "a : { x // x ∈ circle }\n⊢ ↑(rotationOf (↑rotation a)) = ↑a",
"tactic": "simp"
}
] | [
86,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/RingTheory/Algebraic.lean | Algebra.isAlgebraic_iff_isIntegral | [] | [
200,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Topology/LocalAtTarget.lean | Set.restrictPreimage_openEmbedding | [] | [
55,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition | [] | [
273,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.cast_refl | [] | [
764,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
11
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Mathlib/Algebra/Group/Units.lean | IsUnit.mul_val_inv | [
{
"state_after": "α : Type u\nM : Type u_1\nN : Type ?u.65932\ninst✝ : Monoid M\na b c : M\nh : IsUnit a\n⊢ a * ↑(IsUnit.unit h)⁻¹ = ↑(IsUnit.unit h) * ↑(IsUnit.unit h)⁻¹",
"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.65932\ninst✝ : Monoid M\na b c : M\nh : IsUnit a\n⊢ a * ↑(IsUnit.unit h)⁻¹ = 1",... | [
756,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
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Mathlib/CategoryTheory/Products/Bifunctor.lean | CategoryTheory.Bifunctor.map_id_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝² : Category C\ninst✝¹ : Category D\ninst✝ : Category E\nF : C × D ⥤ E\nW : C\nX Y Z : D\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ F.map (𝟙 W, f ≫ g) = F.map (𝟙 W, f) ≫ F.map (𝟙 W, g)",
"tactic": "rw [← Functor.map_comp, prod_co... | [
38,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineMap.span_eq_top_of_surjective | [
{
"state_after": "no goals",
"state_before": "k : Type u_5\nV₁ : Type u_3\nP₁ : Type u_1\nV₂ : Type u_4\nP₂ : Type u_2\nV₃ : Type ?u.579305\nP₃ : Type ?u.579308\ninst✝⁹ : Ring k\ninst✝⁸ : AddCommGroup V₁\ninst✝⁷ : Module k V₁\ninst✝⁶ : AffineSpace V₁ P₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module k V₂\ninst✝... | [
1586,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_lf_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ -x ⧏ 0 ↔ 0 ⧏ x",
"tactic": "rw [neg_lf_iff, neg_zero]"
}
] | [
1380,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1380,
1
] |
Mathlib/Data/List/Duplicate.lean | List.duplicate_cons_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nl : List α\nx y : α\nh : x ∈+ y :: l\n⊢ y = x ∧ x ∈ l ∨ x ∈+ l\n\ncase refine'_2\nα : Type u_1\nl : List α\nx y : α\nh : y = x ∧ x ∈ l ∨ x ∈+ l\n⊢ x ∈+ y :: l",
"state_before": "α : Type u_1\nl : List α\nx y : α\n⊢ x ∈+ y :: l ↔ y = x ∧ x ∈ l ∨ x ∈+ l",
"t... | [
99,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_biInter_finset | [] | [
270,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Std/Data/List/Lemmas.lean | List.next?_cons | [] | [
457,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
457,
9
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_iff_not_exists_st | [] | [
342,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.derivBFamily_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.167917\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal → Ordinal\nc : Cardinal\nhc : IsRegular c\nhι : card o < c\nhc' : c ≠ ℵ₀\nhf : ∀ (i : Ordinal) (hi : i < o) (b : Ordinal), b < ord c → f i hi b < ord c\na : Ordinal\n⊢ lift (c... | [
1198,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.submodule_span_le_lieSpan | [
{
"state_after": "R : 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\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\ns : Set M\n⊢ s ⊆ ↑↑(lieSpan R L s)",
"stat... | [
624,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Algebra/Associated.lean | Associates.quot_mk_eq_mk | [] | [
758,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.sum_degrees_eq_twice_card_edges | [] | [
116,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.quot_mk_eq_mk | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Computability/Partrec.lean | Computable.fin_app | [] | [
399,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | maximal_orthonormal_iff_orthogonalComplement_eq_bot | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1095350\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nv : Set E\nhv : Orthonormal 𝕜 Subtype.val\n⊢ (∀ (u : Set E), u ⊇ v → Orthonor... | [
1328,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1269,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.dvd_term_of_isRoot_of_dvd_terms | [] | [
469,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_le_of_le_sub_right | [
{
"state_after": "a b c : Int\nh✝ : a ≤ c - b\nh : a + b ≤ c - b + b\n⊢ a + b ≤ c",
"state_before": "a b c : Int\nh : a ≤ c - b\n⊢ a + b ≤ c",
"tactic": "have h := Int.add_le_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a ≤ c - b\nh : a + b ≤ c - b + b\n⊢... | [
968,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
966,
11
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_pos_iff_exists_ne_zero | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.253674\nR : Type u\nM : Type v\ninst✝⁴ : Ring R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : NoZeroSMulDivisors R M\ninst✝ : Nontrivial R\n⊢ ¬0 < Module.rank R ... | [
522,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.coeff_restriction | [
{
"state_after": "R : Type u\nS : Type ?u.66016\ninst✝ : Ring R\np : R[X]\nn : ℕ\n⊢ ↑(if coeff p n = 0 then 0 else { val := coeff p n, property := (_ : coeff p n ∈ Subring.closure ↑(frange p)) }) =\n coeff p n",
"state_before": "R : Type u\nS : Type ?u.66016\ninst✝ : Ring R\np : R[X]\nn : ℕ\n⊢ ↑(coeff (r... | [
283,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.sum_incMatrix_apply_of_mem_edgeSet | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nα : Type u_1\nG : SimpleGraph α\ninst✝¹ : Fintype α\ninst✝ : NonAssocSemiring R\na b : α\ne : Sym2 α\n⊢ e ∈ edgeSet G → ∑ a : α, incMatrix R G a e = 2",
"tactic": "classical\n refine' e.ind _\n intro a b h\n rw [mem_edgeSet] at h\n rw [← Na... | [
145,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.mem_reverse_iff | [] | [
558,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.eval₂_gcd_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Field R\np q : R[X]\ninst✝ : CommSemiring k\nϕ : R →+* k\nf g : R[X]\nα : k\nhf : eval₂ ϕ α f = 0\nhg : eval₂ ϕ α g = 0\n⊢ eval₂ ϕ α (EuclideanDomain.gcd f g) = 0",
"tactic": "rw [Eucli... | [
329,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.mk_ne_zero_of_natDegree_lt | [] | [
224,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.coe_iSup_of_directed | [
{
"state_after": "no goals",
"state_before": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\nι : Sort u_1\nhι : Nonempty ι\nS : ι → Subfield K\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : K\n⊢ x ∈ ↑(⨆ (i : ι), S i) ↔ x ∈ ⋃ (i : ι), ↑(S i)",
"tactic": "simp [mem_... | [
839,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_smul | [] | [
82,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.convergent_eq_conts_a_div_conts_b | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.Equalizer.norm_map_le | [] | [
1003,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMaxOn.fderivWithin_eq_zero | [
{
"state_after": "E : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\na : E\nf' : E →L[ℝ] ℝ\ns : Set E\nh : IsLocalMaxOn f s a\ny : E\nhy : y ∈ posTangentConeAt s a\nhy' : -y ∈ posTangentConeAt s a\nhf : ¬DifferentiableWithinAt ℝ f s a\n⊢ ↑0 y = 0",
"state_before": "E : Type u\nin... | [
152,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measure_preimage_smul | [] | [
180,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_C_mul_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na✝ b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\na : R\nf : R[X]\n⊢ natDegree (↑C a) + natDegree f = 0 + natDegree f",
"tactic": "rw [natDegree_C a]"
}
] | [
97,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.sup_direction_le | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\np₁ p₂ : P\ns1 s2 : AffineSubspace k P\n⊢ Submodule.span k (↑s1 -ᵥ ↑s1) ⊔ Submodule.span k (↑s2 -ᵥ ↑s2) ≤ Submodule.span k (↑(s1 ⊔ s2) -ᵥ ↑(s1 ⊔ s2))",
"state_before"... | [
951,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.val_apply | [] | [
446,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coord_equivFun_symm | [] | [
1009,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_multiset_of_isEmpty | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : IsEmpty α\n⊢ (#α →₀ ℕ) = 1",
"tactic": "simp"
}
] | [
1081,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1080,
1
] |
Mathlib/MeasureTheory/Measure/Complex.lean | MeasureTheory.SignedMeasure.toComplexMeasure_apply | [] | [
74,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.angle_zero_left | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x : V\n⊢ arccos (inner 0 x / (‖0‖ * ‖x‖)) = π / 2",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y x : V\n⊢ angle 0 x = π / 2",
"tactic": "unfold angle"
... | [
122,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_subset | [] | [
2653,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2652,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_top_bot | [] | [
176,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Order/CompleteLattice.lean | inf_eq_iInf | [] | [
1527,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_range | [] | [
169,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.neg_of_le_one | [] | [
507,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.exists_pow_eq | [
{
"state_after": "case pos\nι : Type ?u.2618181\nα : Type u_1\nβ : Type ?u.2618187\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx y : α\nf : Perm α\nh : SameCycle f x y\nhx : x ∈ support f\n⊢ ∃ i x_1 x_2, ↑(f ^ i) x = y\n\ncase neg\nι : Type ?u.2618181\nα : Type u_1\nβ : Type ?u.2618187\ninst✝¹ : ... | [
1221,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Topology/Inseparable.lean | specializes_iff_nhds | [] | [
102,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.range_sin | [] | [
203,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PullbackCone.op_inr | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nc : PullbackCone f g\n⊢ PushoutCocone.inr (op c) = (snd c).op",
"tactic": "aesop_cat"
}
] | [
546,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.exists | [] | [
117,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
11
] |
Mathlib/Logic/Basic.lean | exists_apply_eq_apply' | [] | [
774,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
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