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/Data/Finset/LocallyFinite.lean | Finset.eq_of_mem_uIcc_of_mem_uIcc | [
{
"state_after": "ι : Type ?u.190771\nα : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ b ⊓ c ≤ a ∧ a ≤ b ⊔ c → a ⊓ c ≤ b ∧ b ≤ a ⊔ c → a = b",
"state_before": "ι : Type ?u.190771\nα : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ ... | [
968,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/Data/List/Forall2.lean | List.rel_bind | [] | [
278,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | coprime_sq_sub_mul_of_even_odd | [
{
"state_after": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 0\nhn : n % 2 = 1\nH : ¬Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1\n⊢ False",
"state_before": "m n : ℤ\nh : Int.gcd m n = 1\nhm : m % 2 = 0\nhn : n % 2 = 1\n⊢ Int.gcd (m ^ 2 - n ^ 2) (2 * m * n) = 1",
"tactic": "by_contra H"
},
{
"state_a... | [
390,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
9
] |
Mathlib/Analysis/LocallyConvex/WeakDual.lean | LinearMap.toSeminorm_apply | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_mem_smul_set_iff₀ | [] | [
1014,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.IsRegular.eq | [] | [
50,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Data/Set/Basic.lean | Membership.mem.out | [] | [
268,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | List.norm_prod_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.113892\nγ : Type ?u.113895\nι : Type ?u.113898\ninst✝¹ : SeminormedRing α\ninst✝ : NormOneClass α\n⊢ ‖prod []‖ ≤ prod (map norm [])",
"tactic": "simp"
}
] | [
329,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_div_mul_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.69162\nβ : Type ?u.69165\nG : Type u_1\ninst✝ : CommGroup G\na✝ b✝ c✝ d a b c : G\n⊢ a / b = c / b * (a / c)",
"tactic": "simp [mul_left_comm c]"
}
] | [
937,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.lift_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.70086\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\n⊢ lift q 1 = 1",
"tactic": "simp [lift]"
}
] | [
121,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_le_self | [] | [
1574,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1571,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.lintegral_coe_le_coe_iff_integral_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.1088155\nF : Type ?u.1088158\n𝕜 : Type ?u.1088161\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝... | [
1198,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1195,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_incl | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.id_comp | [] | [
154,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.combo_interior_closure_mem_interior | [] | [
160,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | SymmetricRel.eq | [] | [
236,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.rel_mk | [] | [
168,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.sigma_mono | [] | [
75,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_source_at | [
{
"state_after": "ι : Type u_3\nB : Type u_1\nF : Type u_2\nX : Type ?u.46750\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nZ : FiberBundleCore ι B F\ni : ι\nb : B\na : F\n⊢ { fst := b, snd := a }.fst ∈ (localTriv Z (indexAt Z b)).baseSet",
"state_before": "ι : Type ... | [
716,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_pow' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.681610\n⊢ leadingCoeff p ^ Nat.zero ≠ 0 → leadingCoeff (p ^ Nat.zero) = leadingCoeff p ^ Nat.zero",
"tactic": "simp"
},
{
"state_after": "R : Type u\nS : Type v... | [
975,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | dvd_abs | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Ring α\ninst✝ : LinearOrder α\na✝ b✝ a b : α\n⊢ a ∣ abs b ↔ a ∣ b",
"tactic": "cases' abs_choice b with h h <;> simp only [h, dvd_neg]"
}
] | [
134,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulHom.coe_prodMap | [] | [
398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_map | [] | [
454,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Logic/Nonempty.lean | nonempty_plift | [] | [
106,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.incl_range | [
{
"state_after": "case h\nV : Type ?u.489284\nW : Type ?u.489287\nV₁ : Type u_1\nV₂ : Type ?u.489293\nV₃ : Type ?u.489296\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : SeminormedAddCommGroup W\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf : NormedAd... | [
809,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.rfl | [] | [
2384,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2384,
11
] |
Mathlib/MeasureTheory/Integral/MeanInequalities.lean | NNReal.lintegral_mul_le_Lp_mul_Lq | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\np q : ℝ\nhpq : Real.IsConjugateExponent p q\nf g : α → ℝ≥0\nhf : AEMeasurable f\nhg : AEMeasurable g\n⊢ (∫⁻ (a : α), ↑(f a) * ↑(g a) ∂μ) ≤ (∫⁻ (a : α), ↑(f a) ^ p ∂μ) ^ (1 / p) * (∫⁻ (a : α), ↑(g a) ^ q ∂μ) ^ (1 / q)",
"... | [
407,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_zero | [] | [
138,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pi_div_four | [
{
"state_after": "⊢ sqrt 2 / 2 / (sqrt 2 / 2) = 1",
"state_before": "⊢ tan (π / 4) = 1",
"tactic": "rw [tan_eq_sin_div_cos, cos_pi_div_four, sin_pi_div_four]"
},
{
"state_after": "h : sqrt 2 / 2 > 0\n⊢ sqrt 2 / 2 / (sqrt 2 / 2) = 1",
"state_before": "⊢ sqrt 2 / 2 / (sqrt 2 / 2) = 1",
"ta... | [
932,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Data/List/Basic.lean | List.take_left | [] | [
1943,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1941,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ioc_iff | [] | [
570,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | List.norm_prod | [] | [
557,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
11
] |
Mathlib/Data/List/Basic.lean | List.reduceOption_get?_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.369711\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nl : List (Option α)\nx : α\n⊢ (∃ i, get? l i = some (some x)) ↔ ∃ i, get? (reduceOption l) i = some x",
"tactic": "rw [← mem_iff_get?, ← mem_iff_get?, reduceOption_mem_iff]"
... | [
3502,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3500,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.coe_zero | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean | Ideal.adic_module_basis | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nI : Ideal R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nm : M\ni : ℕ\n⊢ ↑(I ^ i • ⊤) = ↑((fun i => toAddSubgroup (I ^ i • ⊤)) i)",
"tactic": "simp"
},
{
"state_after": "R : Type u_1\ninst✝² : CommRin... | [
130,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.edgeSet_singletonSubgraph | [] | [
877,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.dvd_add_right | [] | [
730,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
11
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X_pow_eq_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\nn k : ℕ\n⊢ (↑derivative^[k]) (X ^ n) = ↑(Nat.descFactorial n k) • X ^ (n - k)",
"tactic": "rw [iterate_derivative_X_pow_eq_C_mul n k, smul_eq_C_mul]"
}
] | [
520,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.dualRestrict_ker_eq_dualAnnihilator | [] | [
816,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
813,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.cos_surjective | [
{
"state_after": "x : ℂ\n⊢ ∃ a, cos a = x",
"state_before": "⊢ Function.Surjective cos",
"tactic": "intro x"
},
{
"state_after": "case intro.intro\nx w : ℂ\nw₀ : w ≠ 0\nhw : 1 * w * w + -2 * x * w + 1 = 0\n⊢ ∃ a, cos a = x",
"state_before": "x : ℂ\n⊢ ∃ a, cos a = x",
"tactic": "obtain ⟨w... | [
187,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.mem_pure_self | [] | [
168,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.le_of_mem_factorization | [] | [
149,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_of_memℒp_trim | [] | [
1006,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Topology/Algebra/Algebra.lean | Subalgebra.isClosed_topologicalClosure | [
{
"state_after": "no goals",
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"tactic": "convert @isClosed_closure A _ s"
}... | [
121,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_monic_mul | [
{
"state_after": "case inl\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q : R[X]\nι : Type ?u.691467\np : R[X]\nhp : Monic p\n⊢ leadingCoeff (p * 0) = leadingCoeff 0\n\ncase inr\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\nι : Type ?u.691467\np q : R[... | [
1007,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_ofRepr | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.quotientMapSubgroupOfOfLe_mk | [] | [
469,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Geometry/Manifold/ChartedSpace.lean | StructureGroupoid.compatible | [] | [
872,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.closure_mul_closure | [
{
"state_after": "case a\nα : Type ?u.244690\nG : Type ?u.244693\nM : Type ?u.244696\nR : Type u_1\nA : Type ?u.244702\ninst✝² : Monoid M\ninst✝¹ : AddMonoid A\ninst✝ : NonUnitalNonAssocSemiring R\nS T : Set R\n⊢ closure S * closure T ≤ closure (S * T)\n\ncase a\nα : Type ?u.244690\nG : Type ?u.244693\nM : Type... | [
565,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Combinatorics/Hall/Finite.lean | HallMarriageTheorem.hall_hard_inductive_step_B | [
{
"state_after": "ι : Type u\nα : Type v\ninst✝¹ : DecidableEq α\nt : ι → Finset α\ninst✝ : Fintype ι\nn : ℕ\nhn : Fintype.card ι = n + 1\nht : ∀ (s : Finset ι), card s ≤ card (Finset.biUnion s t)\nih :\n ∀ {ι' : Type u} [inst : Fintype ι'] (t' : ι' → Finset α),\n Fintype.card ι' ≤ n →\n (∀ (s' : Finse... | [
219,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.abs_tendsto_atTop | [
{
"state_after": "case inl\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhdeg : 0 < degree P\nhP : 0 ≤ leadingCoeff P\n⊢ Tendsto (fun x => abs (eval x P)) atTop atTop\n\ncase inr\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopolo... | [
91,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousOn.zpow | [] | [
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Mathlib/RingTheory/ClassGroup.lean | toPrincipalIdeal_eq_iff | [
{
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | derivWithin_sin | [] | [
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841,
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Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.sheaf_for_finestTopology | [
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Std/Data/List/Init/Lemmas.lean | List.headD_cons | [] | [
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_sum | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.iUnion_Ico_coe_nat | [
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.comap_incl_self | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_union' | [] | [
133,
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Mathlib/Analysis/Convex/Segment.lean | insert_endpoints_openSegment | [
{
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Mathlib/Analysis/Convex/Between.lean | Sbtw.ne_right | [] | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.subset_div | [] | [
703,
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701,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_lt_type | [] | [
442,
31
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Mathlib/Data/Seq/Computation.lean | Computation.not_terminates_empty | [] | [
405,
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Mathlib/Logic/Basic.lean | BAll.imp_left | [] | [
1055,
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Mathlib/Topology/Maps.lean | inducing_iff_nhds | [] | [
92,
49
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.coe_pi | [] | [
264,
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Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.ext | [] | [
437,
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437,
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Mathlib/Topology/IsLocallyHomeomorph.lean | isLocallyHomeomorph_iff_isLocallyHomeomorphOn_univ | [
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Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.pow_inv_comm' | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.sum_centroidWeightsIndicator | [] | [
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant | [
{
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.diag_map_fst_snd_comp | [
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87
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813,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_self_tail | [
{
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Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDerivWithin_eq_equiv_comp | [
{
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Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.IsSpanning.card_verts | [
{
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Mathlib/Order/Max.lean | IsTop.prod_mk | [] | [
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Mathlib/Topology/Algebra/Affine.lean | AffineMap.lineMap_continuous | [] | [
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_δ | [
{
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485,
55
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482,
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Mathlib/Topology/Maps.lean | OpenEmbedding.tendsto_nhds_iff' | [
{
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575,
47
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573,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.intDegree_mul | [
{
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1610,
27
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1600,
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Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | Asymptotics.IsLittleO.rpow | [
{
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}
] | [
240,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
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Mathlib/Order/Lattice.lean | Monotone.max | [] | [
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1084,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_congr | [] | [
582,
65
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580,
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Mathlib/Data/List/MinMax.lean | List.not_lt_minimum_of_mem' | [] | [
338,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.succ | [
{
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591,
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586,
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Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.ae_eventually_measure_pos | [
{
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119,
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Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_re_gt | [] | [
31,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Logic.lean | and_imp | [] | [
314,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.exists_ball_inter_eq_singleton_of_mem_discrete | [] | [
1122,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1120,
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Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.Nondegenerate.toBilin' | [
{
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Mathlib/Data/List/BigOperators/Basic.lean | List.length_pos_of_one_lt_prod | [] | [
200,
36
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199,
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.mem_wf_aux | [
{
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321,
26
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314,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pos_of_mem_Ioo | [
{
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"tactic": "linarith [hx.1]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : x ∈ Ioo (-(π / 2)) (π / 2)\n⊢ x + π / 2 < π",
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}
] | [
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85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
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Mathlib/Order/CompleteLattice.lean | monotone_sInf_of_monotone | [] | [
1814,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1813,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.set_eventuallyEq_iff_inf_principal | [
{
"state_after": "no goals",
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"tactic": "simp only [eventuallyLE_antisymm_iff, le_antisymm_iff, set_eventuallyLE_iff_inf_principal_le]"
}
] | [
1749,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1747,
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Mathlib/Topology/Homotopy/Equiv.lean | ContinuousMap.HomotopyEquiv.symm_trans | [] | [
162,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
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Mathlib/Topology/Separation.lean | IsCompact.inter | [] | [
1297,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
1
] |
Mathlib/Order/BoundedOrder.lean | Monotone.ball | [] | [
588,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
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