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/Sigma.lean | Finset.sup_sigma | [
{
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107,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_pos_iff_ne_top | [] | [
2308,
64
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Mathlib/NumberTheory/Padics/Hensel.lean | soln_spec | [] | [
393,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
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Mathlib/Analysis/NormedSpace/CompactOperator.lean | isCompactOperator_iff_isCompact_closure_image_closedBall | [] | [
197,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.order_neg | [
{
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481,
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478,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_comp_cast_add | [
{
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496,
51
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Mathlib/Data/List/Range.lean | List.nthLe_range' | [] | [
61,
65
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Mathlib/Algebra/BigOperators/Associated.lean | Prime.exists_mem_finset_dvd | [] | [
51,
33
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_filter | [] | [
602,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
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Mathlib/Order/Filter/Lift.lean | Filter.le_lift' | [] | [
333,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
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Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.isNat_lcm | [] | [
80,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
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Mathlib/Topology/Semicontinuous.lean | ContinuousAt.comp_lowerSemicontinuousWithinAt | [
{
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325,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
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Mathlib/Order/Filter/Basic.lean | Filter.mem_inf_of_right | [] | [
430,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.sigmaUncurry_apply | [] | [
1550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1546,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lift_apply | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
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Mathlib/CategoryTheory/Limits/Shapes/RegularMono.lean | CategoryTheory.isIso_of_regularEpi_of_mono | [] | [
292,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_mul_self | [] | [
1446,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
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Mathlib/Order/Disjoint.lean | disjoint_assoc | [
{
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"tactic": "rw [disjoint_iff_inf_le, disjoint_iff_inf_le, inf_assoc]"
}
] | [
141,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/Algebra/Hom/Group.lean | map_zpow | [] | [
467,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | stronglyMeasurableAt_bot | [
{
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"tactic": "... | [
47,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.ccos | [] | [
327,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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Mathlib/Data/PFun.lean | PFun.fixInduction'_fwd | [
{
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394,
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Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.id_apply | [] | [
141,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_eq | [] | [
84,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Star/Basic.lean | Units.coe_star_inv | [] | [
549,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/GroupTheory/OrderOfElement.lean | addOrderOf_ofMul_eq_orderOf | [] | [
142,
6
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141,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_trunc | [
{
"state_after": "no goals",
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"tactic": "simp [trunc, Polynomial.coeff_sum, Polynomial.coeff_monomial, Nat.lt_succ_iff]"
}
] | [
1811,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/ZFC/Basic.lean | PSet.nonempty_of_nonempty_type | [] | [
377,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
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Mathlib/Algebra/Group/Units.lean | IsUnit.mul_inv_cancel | [
{
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"state_before": "α : Type u\nM : Type u_1\nN : Type ?u.68821\ninst✝ : DivisionMonoid M\na : M\n⊢ IsUnit a → a * a⁻¹ = 1",
"tactic": "rintro ⟨u, rfl⟩"
},
{
"state_after... | [
818,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Basic.lean | Nat.find_le_iff | [
{
"state_after": "no goals",
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"tactic": "simp only [exists_prop, ← lt_succ_iff, find_lt_iff]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.succ_pos | [] | [
809,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/AbsoluteValue.lean | Matrix.det_le | [
{
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.mem_bot | [] | [
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22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_inter_of_mem | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_neg | [
{
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61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.pow_right | [
{
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199,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.ext' | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dite_irrel | [
{
"state_after": "no goals",
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Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.lift_of | [] | [
164,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
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Mathlib/LinearAlgebra/Dimension.lean | Basis.mk_eq_rank' | [] | [
837,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Quotient.lean | Submodule.quotEquivOfEqBot_apply_mk | [] | [
624,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
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Mathlib/CategoryTheory/Adjunction/Mates.lean | CategoryTheory.unit_transferNatTransSelf | [
{
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181,
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173,
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Mathlib/Algebra/Order/Field/Basic.lean | div_lt_self | [
{
"state_after": "no goals",
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"tactic": "simpa only [div_one] using div_lt_div_of_lt_left ha zero_lt_one hb"
}
] | [
417,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | zero_cpow_eq_nhds | [
{
"state_after": "α : Type ?u.1960\nb : ℂ\nhb : b ≠ 0\nthis : ∀ᶠ (x : ℂ) in 𝓝 b, x ≠ 0\n⊢ (fun x => 0 ^ x) =ᶠ[𝓝 b] 0\n\ncase this\nα : Type ?u.1960\nb : ℂ\nhb : b ≠ 0\n⊢ ∀ᶠ (x : ℂ) in 𝓝 b, x ≠ 0",
"state_before": "α : Type ?u.1960\nb : ℂ\nhb : b ≠ 0\n⊢ (fun x => 0 ^ x) =ᶠ[𝓝 b] 0",
"tactic": "suffice... | [
46,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/Pointwise.lean | Real.smul_iSup_of_nonneg | [] | [
68,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_map | [
{
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"state_before": "... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.clear_ok | [
{
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1440,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
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Mathlib/Analysis/Calculus/Monotone.lean | Monotone.ae_hasDerivAt | [
{
"state_after": "case h\nf : ℝ → ℝ\nhf : Monotone f\nx : ℝ\nhx :\n HasDerivAt (↑(stieltjesFunction hf))\n (ENNReal.toReal (rnDeriv (StieltjesFunction.measure (stieltjesFunction hf)) volume x)) x\nh'x : ¬¬ContinuousAt f x\n⊢ HasDerivAt f (ENNReal.toReal (rnDeriv (StieltjesFunction.measure (stieltjesFunction... | [
217,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongMono_of_mono | [] | [
225,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
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Mathlib/Analysis/BoxIntegral/Integrability.lean | MeasureTheory.IntegrableOn.hasBoxIntegral | [
{
"state_after": "ι : Type u\nE : Type v\ninst✝⁴ : Fintype ι\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nf : (ι → ℝ) → E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nI : Box ι\nhf : IntegrableOn f ↑I\nl : IntegrationParams\nhl : l.bRiemann = false\nthis✝¹ : Mea... | [
304,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_ne_zero_iff_ne | [] | [
278,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.hasSum_iff | [] | [
624,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.destruct_think | [] | [
151,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1461\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Ico a b = ∅ ↔ ¬a < b",
"tactic": "rw [← coe_eq_empty, coe_Ico, Set.Ico_eq_empty_iff]"
}
] | [
75,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Separation.lean | limUnder_nhds_id | [] | [
1078,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.WF_iff | [] | [
477,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
476,
9
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | UniformSpace.complete_of_cauchySeq_tendsto | [] | [
739,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.dist_self | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nG : SimpleGraph V\nv : V\n⊢ dist G v v = 0",
"tactic": "simp"
}
] | [
77,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.fun_comp | [] | [
1508,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.exists_pos_left | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : LinearOrderedField R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y v₁ v₂ : M\nh✝ : SameRay R x y\nhx : x ≠ 0\nhy : y ≠ 0\nr₁ r₂ : R\nhr₁ : 0 < r₁\nhr₂ : 0 < r₂\nh : r₁ • x = r₂ • y\n⊢ (r₂⁻¹ * r₁) • x = y",
"tactic": "... | [
657,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_mul_right | [
{
"state_after": "i j k : ℤ\n⊢ Nat.gcd (natAbs i * natAbs j) (natAbs k * natAbs j) = Nat.gcd (natAbs i) (natAbs k) * natAbs j",
"state_before": "i j k : ℤ\n⊢ gcd (i * j) (k * j) = gcd i k * natAbs j",
"tactic": "rw [Int.gcd, Int.gcd, natAbs_mul, natAbs_mul]"
},
{
"state_after": "no goals",
"... | [
308,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.equivOfInverse_apply | [] | [
2170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2168,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.dom_of_le_of_dom | [] | [
213,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithTop.succ_coe | [] | [
1153,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_pos_of_neg | [] | [
555,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Deprecated/Subfield.lean | IsSubfield.div_mem | [
{
"state_after": "F : Type u_1\ninst✝ : Field F\nS✝ S : Set F\nhS : IsSubfield S\nx y : F\nhx : x ∈ S\nhy : y ∈ S\n⊢ x * y⁻¹ ∈ S",
"state_before": "F : Type u_1\ninst✝ : Field F\nS✝ S : Set F\nhS : IsSubfield S\nx y : F\nhx : x ∈ S\nhy : y ∈ S\n⊢ x / y ∈ S",
"tactic": "rw [div_eq_mul_inv]"
},
{
... | [
45,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_zero | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝ : DecidableEq (Associates α)\np : Associates α\nhp : Irreducible p\n⊢ dite (Irreducible p) (fun hp => bcount { val := p, property := hp }) (fun hp => 0) 0 = 0",
"state_before"... | [
1304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
1
] |
Mathlib/CategoryTheory/Functor/Flat.lean | CategoryTheory.flat_iff_lan_flat | [
{
"state_after": "C D : Type u₁\ninst✝⁹ : SmallCategory C\ninst✝⁸ : SmallCategory D\nE : Type u₂\ninst✝⁷ : Category E\ninst✝⁶ : ConcreteCategory E\ninst✝⁵ : HasLimits E\ninst✝⁴ : HasColimits E\ninst✝³ : ReflectsLimits (forget E)\ninst✝² : PreservesFilteredColimits (forget E)\ninst✝¹ : PreservesLimits (forget E)... | [
428,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/CategoryTheory/Core.lean | CategoryTheory.Core.id_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX : C\n⊢ (𝟙 X).hom = 𝟙 X",
"tactic": "rfl"
}
] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_mk' | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.mem_properDivisors_prime_pow | [
{
"state_after": "n p : ℕ\npp : Prime p\nk x : ℕ\n⊢ (∃ x_1, (x_1 ≤ k ∧ x = p ^ x_1) ∧ x < p ^ k) ↔ ∃ j x_1, x = p ^ j",
"state_before": "n p : ℕ\npp : Prime p\nk x : ℕ\n⊢ x ∈ properDivisors (p ^ k) ↔ ∃ j x_1, x = p ^ j",
"tactic": "rw [mem_properDivisors, Nat.dvd_prime_pow pp, ← exists_and_right]"
},
... | [
437,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Order/Hom/Set.lean | StrictMono.coe_orderIsoOfSurjective | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_sSup | [] | [
1221,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_add_bdd_below_right | [] | [
758,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | PseudoMetricSpace.ext | [
{
"state_after": "case mk\nα✝ : Type u\nβ : Type v\nX : Type ?u.6808\nι : Type ?u.6811\nα : Type u_1\nm' : PseudoMetricSpace α\nd : Dist α\ndist_self✝ : ∀ (x : α), dist x x = 0\ndist_comm✝ : ∀ (x y : α), dist x y = dist y x\ndist_triangle✝ : ∀ (x y z : α), dist x z ≤ dist x y + dist y z\ned : α → α → ℝ≥0∞\nhed ... | [
151,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balance_eq_balance' | [
{
"state_after": "case nil\nα : Type u_1\nx : α\nr : Ordnode α\nhr : Balanced r\nsr : Sized r\nhl : Balanced nil\nsl : Sized nil\n⊢ balance nil x r = balance' nil x r\n\ncase node\nα : Type u_1\nx : α\nr : Ordnode α\nhr : Balanced r\nsr : Sized r\nls : ℕ\nll : Ordnode α\nlx : α\nlr : Ordnode α\nhl : Balanced (n... | [
758,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | weightedVSub_mem_vectorSpan | [
{
"state_after": "case inl\nk : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_1\ns : Finset ι\nw : ι → k\nh : ∑ i in s, w i = 0\np : ι → P\nhι : IsEmpty ι\n⊢ ↑(Finset.weightedVSub s p) w ∈ vectorSpan k (Set.range p)\n\nca... | [
1012,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
996,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.isCoprime_map | [
{
"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✝ : Field k\nf : R →+* k\n⊢ IsCoprime (map f p) (map f q) ↔ IsCoprime p q",
"tactic": "rw [← EuclideanDomain.gcd_isUnit_iff, ← EuclideanDomain.gcd_isUnit_iff, g... | [
360,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_one_add_measure | [
{
"state_after": "α : Type u_1\nE : Type ?u.2308880\nF : Type u_2\nG : Type ?u.2308886\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ✝ ν✝ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nμ ν : Measure α\n⊢ (∫⁻ (x : α), ↑‖f x‖₊ ∂μ + ν) = (∫⁻ (x : ... | [
665,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_lt_cos_of_nonneg_of_le_pi_div_two | [
{
"state_after": "x y : ℝ\nhx₁ : 0 ≤ x\nhy₂ : y ≤ π / 2\nhxy : x < y\n⊢ -2 * sin ((y + x) / 2) * sin ((y - x) / 2) < 0",
"state_before": "x y : ℝ\nhx₁ : 0 ≤ x\nhy₂ : y ≤ π / 2\nhxy : x < y\n⊢ cos y < cos x",
"tactic": "rw [← sub_lt_zero, cos_sub_cos]"
},
{
"state_after": "x y : ℝ\nhx₁ : 0 ≤ x\nh... | [
561,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | mem_tangentCone_of_segment_subset | [] | [
250,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Data/Fintype/Prod.lean | Finset.univ_product_univ | [] | [
53,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/Order/Basic.lean | Filter.Eventually.exists_Ioo_subset | [] | [
1340,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1338,
1
] |
Mathlib/Topology/UrysohnsBounded.lean | exists_bounded_zero_one_of_closed | [] | [
42,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.pure_bind | [] | [
240,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nontrivial_pair | [] | [
2466,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2465,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | sq_eq_sq | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.244980\nA : Type ?u.244983\nG : Type ?u.244986\nM : Type ?u.244989\nR : Type u_1\ninst✝ : LinearOrderedSemiring R\na✝ b✝ a b : R\nha : 0 ≤ a\nhb : 0 ≤ b\n⊢ 0 < 2",
"tactic": "decide"
}
] | [
616,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.IsLimit.aleph0_le | [
{
"state_after": "α β : Type u\nc : Cardinal\nh : IsLimit c\nh' : c < ℵ₀\n⊢ False",
"state_before": "α β : Type u\nc : Cardinal\nh : IsLimit c\n⊢ ℵ₀ ≤ c",
"tactic": "by_contra' h'"
},
{
"state_after": "case intro.zero\nα β : Type u\nh : IsLimit ↑Nat.zero\nh' : ↑Nat.zero < ℵ₀\n⊢ False\n\ncase int... | [
1456,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1451,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.norm_sub_le_of_mem_a | [
{
"state_after": "F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nr x : ℝ\nhr : 0 < r\nε : ℝ\nL₁ L₂ : F\nh₁ : x ∈ A f L₁ r ε\nh₂ : x ∈ A f L₂ r ε\nH : ‖(r / 2) • (L₁ - L₂)‖ ≤ r / 2 * (4 * ε)\n⊢ ‖L₁ - L₂‖ ≤ 4 * ε\n\ncase H\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\n... | [
572,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_nhds_top | [] | [
178,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_le_tsum | [] | [
831,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
11
] |
Mathlib/Data/Vector/Mem.lean | Vector.not_mem_zero | [] | [
48,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/RingTheory/Polynomial/RationalRoot.lean | num_isRoot_scaleRoots_of_aeval_eq_zero | [
{
"state_after": "A : Type u_1\nK : Type u_2\nR : Type ?u.42738\nS : Type ?u.42741\ninst✝⁹ : CommRing A\ninst✝⁸ : Field K\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\nM : Submonoid A\ninst✝⁵ : Algebra A S\ninst✝⁴ : IsLocalization M S\ninst✝³ : Algebra A K\ninst✝² : IsFractionRing A K\ninst✝¹ : IsDomain A\ninst✝ :... | [
58,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.strictConvex | [
{
"state_after": "ι : Type ?u.151565\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nh : Set.Pairwise (s \\ interior s) fun x y... | [
277,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
11
] |
Mathlib/Topology/MetricSpace/Metrizable.lean | Inducing.pseudoMetrizableSpace | [] | [
68,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | abs_pow_eq_one | [
{
"state_after": "case h.e'_1.h.e'_2\nβ : Type ?u.248186\nA : Type ?u.248189\nG : Type ?u.248192\nM : Type ?u.248195\nR : Type u_1\ninst✝ : LinearOrderedRing R\na : R\nn : ℕ\nh : 0 < n\n⊢ abs (a ^ n) = abs a ^ n\n\ncase h.e'_1.h.e'_3\nβ : Type ?u.248186\nA : Type ?u.248189\nG : Type ?u.248192\nM : Type ?u.24819... | [
639,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.zero_apply | [] | [
673,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.of_prod_left | [] | [
918,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.smul_measure | [] | [
1735,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1733,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | inv_pow_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.100696\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝³ : Group G\ninst✝² : Group H\ninst✝¹ : AddGroup A\ninst✝ : AddGroup B\na : G\nm n : ℕ\nh : n ≤ m\n⊢ a⁻¹ ^ (m - n) = (a ^ m)⁻¹ * a ^ n",
... | [
437,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
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