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/Analysis/Convex/Slope.lean | StrictConvexOn.secant_strict_mono_aux3 | [
{
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"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜... | [
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319,
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Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl | [
{
"state_after": "V : Type u\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nn k ℓ μ : ℕ\nh : IsSRGWith G n k ℓ μ\nv w : V\nha : Adj (Gᶜ) v w\n⊢ Finset.card (neighborFinset G vᶜ \\ {v} ∩ (neighborFinset G wᶜ \\ {w})) = n - (2 * k - μ) - 2",
"state_before": "V : Ty... | [
156,
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144,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_le_rpow | [] | [
145,
30
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144,
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_fin_succ | [
{
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"state_before": "ι : Type u'\nι' : Type ?u.1249118\nR : Type ?u.1249121\nK : Type u_1\nM : Type ?u.1249127\nM' : Type ?u.1249130\nM'' : Type ?u.1249133\nV : Type u\nV' : Type ?u.1249138\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module ... | [
1255,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Count.lean | List.countp_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\np q : α → Bool\n⊢ 0 < countp p l ↔ ∃ a, a ∈ l ∧ p a = true",
"tactic": "simp only [countp_eq_length_filter, length_pos_iff_exists_mem, mem_filter, exists_prop]"
}
] | [
102,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.binomial_eq_choose | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : a ≠ b\n⊢ multinomial {a, b} f = choose (f a + f b) (f a)",
"tactic": "simp [binomial_eq _ h, choose_eq_factorial_div_factorial (Nat.le_add_right _ _)]"
}
] | [
113,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Data/Bool/Count.lean | List.Chain'.two_mul_count_bool_of_even | [
{
"state_after": "no goals",
"state_before": "l : List Bool\nhl : Chain' (fun x x_1 => x ≠ x_1) l\nh2 : Even (length l)\nb : Bool\n⊢ 2 * count b l = length l",
"tactic": "rw [← count_not_add_count l b, hl.count_not_eq_count h2, two_mul]"
}
] | [
105,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.image_ι_eq | [
{
"state_after": "Δ Δ'' : SimplexCategory\nφ : Δ ⟶ Δ''\ne : Δ ⟶ image φ\ninst✝¹ : Epi e\ni : image φ ⟶ Δ''\ninst✝ : Mono i\nfac : e ≫ i = φ\nthis : StrongEpi e\n⊢ image.ι φ = i",
"state_before": "Δ Δ'' : SimplexCategory\nφ : Δ ⟶ Δ''\ne : Δ ⟶ image φ\ninst✝¹ : Epi e\ni : image φ ⟶ Δ''\ninst✝ : Mono i\nfac : ... | [
793,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousInv.of_nhds_one | [
{
"state_after": "α : Type u\nβ : Type v\nG✝ : Type w\nH : Type x\ninst✝⁵ : TopologicalSpace G✝\ninst✝⁴ : Group G✝\ninst✝³ : TopologicalGroup G✝\ninst✝² : TopologicalSpace α\nf : α → G✝\ns : Set α\nx : α\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nhinv : Tendsto (fun x => x⁻¹) (𝓝 1) (𝓝 1)\nhl... | [
915,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
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Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.mk_eq_zero' | [] | [
199,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_nonneg | [] | [
137,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_injective | [] | [
131,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Std/Data/List/Lemmas.lean | List.Pairwise.imp | [] | [
1298,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1295,
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_refl | [] | [
565,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.nondegenerateRestrictOfDisjointOrthogonal | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.581487\nR₂ : Type ?u.581490\nR₃ : Type ?u.581493\nM : Type u_2\nM₁ : Type ?u.581499\nM₂ : Type ?u.581502\nMₗ₁ : Type ?u.581505\nMₗ₁' : Type ?u.581508\nMₗ₂ : Type ?u.581511\nMₗ₂' : Type ?u.581514\nK : Type ?u.581517\nK₁ : Type ?u.581520\nK₂ : Type ?u.581523\nV : Type ... | [
761,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.closure_singleton_one | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nA : Type ?u.72862\nB : Type ?u.72865\ninst✝ : Monoid M\n⊢ closure {1} = ⊥",
"tactic": "simp [eq_bot_iff_forall, mem_closure_singleton]"
}
] | [
345,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Stream.next?_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : RBNode.Stream α\n⊢ Option.map\n (fun x =>\n match x with\n | (a, b) => (a, toList b))\n (next? s) =\n List.next? (toList s)",
"tactic": "cases s <;> simp [next?, toStream_toList']"
}
] | [
399,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
397,
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Mathlib/Order/Filter/Extr.lean | isExtrFilter_dual_iff | [] | [
218,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.inv_ext' | [] | [
518,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
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Mathlib/Analysis/Convex/Star.lean | starConvex_iff_div | [
{
"state_after": "case a\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.140518\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx : E\ns : Set E\nh : StarConvex 𝕜 x s\ny : E\nhy : y ∈ s\na b : 𝕜\nha : 0 ≤ a\nhb : 0 ≤ b\nhab : 0 < a + b\n⊢ 0 ≤ a / (a + b)\n\ncase a\n𝕜 : Type u_1\nE : ... | [
405,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Mathlib/Topology/Separation.lean | closure_singleton | [] | [
627,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_mk' | [] | [
279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
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] |
Std/Logic.lean | imp_intro | [] | [
109,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
109,
1
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Mathlib/RingTheory/PrincipalIdealDomain.lean | gcd_isUnit_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : GCDMonoid R\nx y : R\n⊢ IsUnit (gcd x y) ↔ IsCoprime x y",
"tactic": "rw [IsCoprime, ← Ideal.mem_span_pair, ← span_gcd, ← span_singleton_eq_top, eq_top... | [
388,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/RingTheory/AlgebraTower.lean | Basis.coe_algebraMapCoeffs | [] | [
100,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
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] |
Mathlib/GroupTheory/Abelianization.lean | commutator_eq_normalClosure | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝ : Group G\n⊢ commutator G = Subgroup.normalClosure (commutatorSet G)",
"tactic": "simp [commutator, Subgroup.commutator_def', commutatorSet]"
}
] | [
55,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/Algebra/AddTorsor.lean | vadd_vsub | [] | [
96,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
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] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.norm_toSpanSingleton | [
{
"state_after": "case refine'_1\n𝕜 : Type u_1\n𝕜₂ : Type ?u.2121574\n𝕜₃ : Type ?u.2121577\nE : Type u_2\nEₗ : Type ?u.2121583\nF : Type ?u.2121586\nFₗ : Type ?u.2121589\nG : Type ?u.2121592\nGₗ : Type ?u.2121595\n𝓕 : Type ?u.2121598\ninst✝²² : SeminormedAddCommGroup E\ninst✝²¹ : SeminormedAddCommGroup Eₗ\n... | [
1214,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
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Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Presieve.singleton_eq_iff_domain | [
{
"state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf✝ f g : Y ⟶ X\n⊢ singleton f g → f = g\n\ncase mpr\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf✝ f g : Y ⟶ X\n⊢ f = g → singleton f g",
"state_b... | [
104,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.constantCoeff_wittAdd | [
{
"state_after": "p : ℕ\nR : Type ?u.75316\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (X 0 + X 1) = 0",
"state_before": "p : ℕ\nR : Type ?u.75316\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (wittAdd p n) = 0",
"tactic": "apply constantCoeff_wittStruct... | [
296,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Order/Basic.lean | Prod.mk_lt_mk_iff_right | [] | [
1233,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | ContinuousAt.log | [] | [
394,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
8
] |
Mathlib/Algebra/Group/Units.lean | Units.val_mk | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | nhds_eq_uniformity_prod | [
{
"state_after": "case hg₁\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.78723\ninst✝ : UniformSpace α\na b : α\n⊢ ∀ (s : Set (α × α)), Monotone fun t => {y | (y, a) ∈ s} ×ˢ {y | (b, y) ∈ t}\n\ncase hg₂\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.78723\ninst✝ : UniformSpa... | [
892,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
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Mathlib/Topology/Constructions.lean | continuous_apply | [] | [
1199,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1198,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_one_mul | [
{
"state_after": "no goals",
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649,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
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] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | Polynomial.coe_basisMonomials | [] | [
142,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Topology/Algebra/Module/WeakDual.lean | WeakDual.eval_continuous | [] | [
284,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/FieldTheory/AxGrothendieck.lean | ax_grothendieck_of_locally_finite | [
{
"state_after": "ι : Type u_1\nK : Type u_2\nR : Type u_3\ninst✝⁴ : Field K\ninst✝³ : Finite K\ninst✝² : CommRing R\ninst✝¹ : Finite ι\ninst✝ : Algebra K R\nalg : Algebra.IsAlgebraic K R\nps : ι → MvPolynomial ι R\nhinj : Injective fun v i => ↑(MvPolynomial.eval v) (ps i)\nis_int : ∀ (x : R), IsIntegral K x\n⊢... | [
70,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
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Mathlib/LinearAlgebra/Finrank.lean | finrank_range_le_card | [
{
"state_after": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\nι : Type u_1\ninst✝ : Fintype ι\nb : ι → V\n⊢ Finset.card (Finset.image b Finset.univ) ≤ Fintype.card ι",
"state_before": "K : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V... | [
328,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_iUnion_le | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.tendsto_polynomial_inv_mul_zero | [
{
"state_after": "p : ℝ[X]\n⊢ Tendsto (fun x => if x ≤ 0 then 0 else Polynomial.eval x⁻¹ p * exp (-x⁻¹)) (𝓝 0) (𝓝 0)",
"state_before": "p : ℝ[X]\n⊢ Tendsto (fun x => Polynomial.eval x⁻¹ p * expNegInvGlue x) (𝓝 0) (𝓝 0)",
"tactic": "simp only [expNegInvGlue, mul_ite, mul_zero]"
},
{
"state_af... | [
120,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/Topology/Instances/ENNReal.lean | Real.ediam_Ioc | [] | [
1552,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1550,
1
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Mathlib/MeasureTheory/Function/LpOrder.lean | MeasureTheory.Lp.coeFn_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\np : ℝ≥0∞\ninst✝ : NormedLatticeAddCommGroup E\nf g : { x // x ∈ Lp E p }\n⊢ ↑↑f ≤ᵐ[μ] ↑↑g ↔ f ≤ g",
"tactic": "rw [← Subtype.coe_le_coe, ← AEEqFun.coeFn_le]"
}
] | [
46,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/Data/Finset/Fold.lean | Finset.fold_min_lt | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.67307\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns : Finset α\na : α\ninst✝ : LinearOrder β\nc : β\n⊢ c > fold min b f s ↔ b < c ∨ ∃ x, x ∈ s ∧ f x < c",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ... | [
239,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Data/Opposite.lean | Opposite.equivToOpposite_coe | [] | [
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | FDerivMeasurableAux.isOpen_a | [
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Mathlib/Algebra/Lie/Nilpotent.lean | LieIdeal.lowerCentralSeries_map_eq | [
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Mathlib/Data/List/Palindrome.lean | List.Palindrome.append_reverse | [
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Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.contDiffAt | [] | [
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Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.list_prod_ofFn_eq_dProd | [
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_neg | [
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Mathlib/Logic/Basic.lean | forall_prop_congr | [] | [
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Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_smul_right | [
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Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | strictConcaveOn_log_Iio | [
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Mathlib/Algebra/Algebra/Operations.lean | Submodule.mem_span_mul_finite_of_mem_span_mul | [
{
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Mathlib/LinearAlgebra/Determinant.lean | LinearMap.associated_det_comp_equiv | [
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Mathlib/Topology/Order/Basic.lean | Ioc_mem_nhdsWithin_Ioi | [] | [
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Mathlib/CategoryTheory/Abelian/Homology.lean | homology.map_eq_lift_desc'_left | [
{
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276,
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Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.zeroth_continuant_aux_eq_one_zero | [] | [
123,
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_tensorUnit | [] | [
215,
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214,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cofork.app_zero_eq_comp_π_right | [
{
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] | [
356,
61
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Mathlib/Data/Set/UnionLift.lean | Set.preimage_iUnionLift | [
{
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_iSup | [
{
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703,
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Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.symm_symm | [] | [
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19
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268,
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Mathlib/Data/Fin/Basic.lean | Fin.cast_addNat_left | [
{
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... | [
1381,
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Mathlib/RingTheory/IntegralClosure.lean | RingHom.is_integral_mul | [] | [
524,
100
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521,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_le_atBot | [] | [
190,
14
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189,
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_neg | [
{
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Mathlib/Order/Basic.lean | min_rec' | [] | [
949,
34
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Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAtFilter.sub | [
{
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.zero_apply | [] | [
408,
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407,
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Mathlib/Logic/Equiv/Fin.lean | finCongr_symm_apply_coe | [] | [
126,
6
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Mathlib/LinearAlgebra/Basis.lean | Basis.constr_apply | [
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Mathlib/Analysis/NormedSpace/Exponential.lean | exp_sum_of_commute | [
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509,
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Mathlib/RingTheory/FreeRing.lean | FreeRing.lift_comp_of | [] | [
93,
19
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.sub_apply | [] | [
522,
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Mathlib/Analysis/Normed/Group/Basic.lean | Subgroup.norm_coe | [] | [
2674,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.prod_filter_index | [
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Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.MonoidalFunctor.map_leftUnitor | [
{
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214,
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Mathlib/Data/Finset/Slice.lean | Set.Sized.univ_mem_iff | [] | [
94,
29
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Mathlib/Order/Filter/Pointwise.lean | Filter.smul_eq_bot_iff | [] | [
989,
18
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988,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_zsmul | [] | [
336,
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335,
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Mathlib/Computability/Primrec.lean | Primrec.fin_succ | [
{
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... | [
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47
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Mathlib/Analysis/MeanInequalitiesPow.lean | Real.rpow_arith_mean_le_arith_mean_rpow | [] | [
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42
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Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.deriv | [] | [
70,
21
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11
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Mathlib/Data/Real/CauSeq.lean | CauSeq.cauchy | [] | [
160,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_monotone | [] | [
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Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.linearMapAt_eq_zero | [] | [
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13
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Mathlib/Topology/UniformSpace/Basic.lean | uniformSpace_eq | [
{
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369,
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Mathlib/Topology/PathConnected.lean | JoinedIn.joined | [] | [
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15
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858,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoMod_apply_right | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ a < a + p ∧ ∃ z, a + p = a + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b c : α\nn : ℤ\na : α\n⊢ ... | [
226,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | quotient_nhd_basis | [
{
"state_after": "case this\nM : Type u_1\nN : Type ?u.386793\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\n⊢ ∀ (ε : ℝ), mk '' ball 0 ε = {x | ‖x‖ < ε}\n\nM : Type u_1\nN : Type ?u.386793\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubg... | [
239,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.mul_self_le_mul_self_iff | [] | [
294,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_lt_toNNReal_iff | [] | [
646,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousOn | [] | [
102,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
11
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.Disjoint.orderOf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nσ τ : Perm α\nhστ : Disjoint σ τ\nn : ℕ\n⊢ (σ * τ) ^ n = 1 ↔ σ ^ n = 1 ∧ τ ^ n = 1",
"tactic": "rw [hστ.commute.mul_pow, Disjoint.mul_eq_one_iff (hστ.pow_disjoint_pow n n)]"
}
] | [
180,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
8
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.card_roots_of_disc_ne_zero | [
{
"state_after": "R : Type ?u.1301913\nS : Type ?u.1301916\nF : Type u_2\nK : Type u_1\nP : Cubic F\ninst✝² : Field F\ninst✝¹ : Field K\nφ : F →+* K\nx y z : K\ninst✝ : DecidableEq K\nha : P.a ≠ 0\nh3 : roots (map φ P) = {x, y, z}\nhd : disc P ≠ 0\n⊢ ∃ x y z, roots (map φ P) = {x, y, z}",
"state_before": "R... | [
601,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_eq_left_iff_subset | [] | [
800,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.erase_ne | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np✝ q p : R[X]\nn i : ℕ\nh : i ≠ n\n⊢ coeff (erase n p) i = coeff p i",
"tactic": "simp [coeff_erase, h]"
}
] | [
1072,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
] |
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