file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_sSup | [] | [
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Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atTop_isLUB | [
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Mathlib/RingTheory/Ideal/LocalRing.lean | isLocalRingHom_of_comp | [] | [
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256,
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Mathlib/Analysis/SpecialFunctions/CompareExp.lean | Complex.IsExpCmpFilter.tendsto_abs | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_lt_top | [] | [
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68
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Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_bot | [] | [
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Mathlib/InformationTheory/Hamming.lean | hammingDist_comm | [
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | isBoundedLinearMap_prod_multilinear | [
{
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Mathlib/RingTheory/Localization/AtPrime.lean | Localization.AtPrime.comap_maximalIdeal | [] | [
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | fderiv_fst | [] | [
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_le_toNNReal | [] | [
666,
23
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Mathlib/Data/Matrix/Basic.lean | RingHom.map_dotProduct | [
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src/lean/Init/Data/List/Basic.lean | List.append_eq_appendTR | [
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Mathlib/CategoryTheory/Subobject/MonoOver.lean | CategoryTheory.MonoOver.lift_comm | [] | [
182,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_balanceR | [
{
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}
] | [
371,
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Mathlib/Data/Part.lean | Part.mem_coe | [] | [
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15
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Mathlib/Topology/Order/Basic.lean | Monotone.map_ciSup_of_continuousAt | [
{
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Mathlib/Algebra/Order/ToIntervalMod.lean | self_sub_toIcoMod | [
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}
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Mathlib/Data/Int/Interval.lean | Int.card_Ioo_of_lt | [
{
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}
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Mathlib/CategoryTheory/Limits/Constructions/Equalizers.lean | CategoryTheory.Limits.HasEqualizersOfHasPullbacksAndBinaryProducts.pullbackFst_eq_pullback_snd | [
{
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58,
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Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | ContinuousMonoidHom.ext | [] | [
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20
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Mathlib/MeasureTheory/Lattice.lean | AEMeasurable.const_sup | [] | [
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Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_iff_isCompact | [] | [
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35
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Mathlib/RingTheory/RootsOfUnity/Complex.lean | Complex.card_primitiveRoots | [
{
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{
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... | [
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Mathlib/NumberTheory/PythagoreanTriples.lean | pythagoreanTriple_comm | [
{
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{
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Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_mul_self | [
{
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"tactic": "rw [sym_mul_sym, ← two_mul, invOf_mul_self_assoc]"
}
] | [
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Mathlib/Data/List/Perm.lean | List.DecEq_eq | [
{
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.star_subset_adjoin | [] | [
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Mathlib/Analysis/SpecificLimits/Normed.lean | NormedField.tendsto_zero_smul_of_tendsto_zero_of_bounded | [
{
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Mathlib/LinearAlgebra/Matrix/Charpoly/Eigs.lean | Matrix.det_eq_prod_roots_charpoly | [] | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Formula.equivSentence_inf | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Sign.lean | sign_pow | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly.comp₂ | [
{
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340,
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Mathlib/Data/Complex/Basic.lean | Complex.range_abs | [
{
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] | [
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48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
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Mathlib/Data/PNat/Factors.lean | PrimeMultiset.card_ofPrime | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.map | [] | [
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32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/Algebra/GroupPower/Order.lean | Right.pow_le_one_of_le | [
{
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.tendsto_approxBounded_ae | [
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Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two | [
{
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Mathlib/Order/Disjoint.lean | IsCompl.symm | [] | [
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Mathlib/Topology/Algebra/Group/Basic.lean | tendsto_inv_nhdsWithin_Iio_inv | [
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_extend_le | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.one_mulVec | [
{
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Mathlib/Topology/Basic.lean | mem_closure_iff_comap_neBot | [
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"tactic": "simp_rw [mem_closure_iff_nhds, comap_neBot_iff, Set.inter_nonempty... | [
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Mathlib/Topology/Algebra/Group/Basic.lean | tendsto_inv_nhdsWithin_Iic_inv | [
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Mathlib/Topology/Separation.lean | t1Space_iff_specializes_imp_eq | [] | [
520,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Analysis/Convex/Integral.lean | StrictConvex.ae_eq_const_or_average_mem_interior | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.2067161\nm0 : MeasurableSpace α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nμ : MeasureTheory.Measure α\ns : Set E\nt : Set α\nf : ... | [
284,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Order/Filter/CountableInter.lean | Filter.countableGenerate_isGreatest | [
{
"state_after": "ι : Sort ?u.24738\nα : Type u_1\nβ : Type ?u.24744\nl : Filter α\ninst✝ : CountableInterFilter l\ng : Set (Set α)\n⊢ countableGenerate g ∈ upperBounds {f | CountableInterFilter f ∧ g ⊆ f.sets}",
"state_before": "ι : Sort ?u.24738\nα : Type u_1\nβ : Type ?u.24744\nl : Filter α\ninst✝ : Coun... | [
271,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
src/lean/Init/SimpLemmas.lean | dite_congr | [
{
"state_after": "no goals",
"state_before": "b c : Prop\nα : Sort u_1\nx✝ : Decidable b\ninst✝ : Decidable c\nx : b → α\nu : c → α\ny : ¬b → α\nv : ¬c → α\nh₁ : b = c\nh₂ : ∀ (h : c), x (_ : b) = u h\nh₃ : ∀ (h : ¬c), y (_ : ¬b) = v h\n⊢ dite b x y = dite c u v",
"tactic": "cases Decidable.em c with\n|... | [
74,
65
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
66,
1
] |
Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.map_integerMultiple | [] | [
140,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | newton_seq_is_cauchy | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\nε : ℝ\nhε : ε > 0\n⊢ ∃ i, ∀ (j : ℕ), j ≥ i → ‖newton_seq j - newton_seq i‖ < ε",
"state_before": "p : ℕ\n... | [
382,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
9
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.antidiagonalTuple_zero_zero | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | tsub_nonpos | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.30124\ninst✝³ : Preorder α\ninst✝² : AddCommMonoid α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\n⊢ a - b ≤ 0 ↔ a ≤ b",
"tactic": "rw [tsub_le_iff_left, add_zero]"
}
] | [
250,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/SetTheory/Lists.lean | Lists'.mem_of_subset | [] | [
450,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.sup_support_list_prod_le | [
{
"state_after": "R : Type u_3\nA : Type u_2\nT : Type ?u.27671\nB : Type u_1\nι : Type ?u.27677\ninst✝¹¹ : SemilatticeSup B\ninst✝¹⁰ : OrderBot B\ninst✝⁹ : SemilatticeInf T\ninst✝⁸ : OrderTop T\ninst✝⁷ : Semiring R\ninst✝⁶ : AddMonoid A\ninst✝⁵ : AddMonoid B\ninst✝⁴ : CovariantClass B B (fun x x_1 => x + x_1) ... | [
104,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.eta | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
9
] |
Mathlib/Algebra/SMulWithZero.lean | smul_inv₀ | [
{
"state_after": "case inl\nR : Type ?u.35696\nR' : Type ?u.35699\nM : Type ?u.35702\nM' : Type ?u.35705\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : GroupWithZero α\ninst✝³ : GroupWithZero β\ninst✝² : MulActionWithZero α β\ninst✝¹ : SMulCommClass α β β\ninst✝ : IsScalarTower α β β\nx : β\n⊢ (0 • x)⁻¹ = 0⁻¹ • x⁻¹\n\nc... | [
222,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.univ_pi_Ioc_ae_eq_Icc | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.4569072\nα : ι → Type u_1\ninst✝⁴ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ninst✝³ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝² : ∀ (i : ι), SigmaFinite (μ i)\ninst✝¹ : (i : ι) → PartialOrder (α i)\ninst✝ : ∀ (i : ι), NoAtoms (μ i)\nf g... | [
531,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_right | [] | [
251,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_subset_vsub | [] | [
1519,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1518,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_self | [
{
"state_after": "no goals",
"state_before": "⊢ descFactorial 0 0 = 0!",
"tactic": "rw [descFactorial_zero, factorial_zero]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ descFactorial (succ n) (succ n) = (succ n)!",
"tactic": "rw [succ_descFactorial_succ, descFactorial_self ... | [
393,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Order/Basic.lean | min_rec | [] | [
941,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.pred_le_iff | [
{
"state_after": "case zero\nn k l : ℕ\n⊢ zero ≤ succ n → pred zero ≤ n\n\ncase succ\nn k l n✝ : ℕ\n⊢ succ n✝ ≤ succ n → pred (succ n✝) ≤ n",
"state_before": "m n k l : ℕ\n⊢ m ≤ succ n → pred m ≤ n",
"tactic": "cases m"
},
{
"state_after": "no goals",
"state_before": "case succ\nn k l n✝ : ℕ... | [
238,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.IsFixedPt.perm_inv | [] | [
109,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
11
] |
Mathlib/Topology/Covering.lean | IsCoveringMapOn.isLocallyHomeomorphOn | [
{
"state_after": "E : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace E\ninst✝ : TopologicalSpace X\nf : E → X\ns : Set X\nhf : IsCoveringMapOn f s\nx : E\nhx : x ∈ f ⁻¹' s\n⊢ ∃ e, x ∈ e.source ∧ ∀ (y : E), y ∈ e.source → f y = ↑e y",
"state_before": "E : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace ... | [
130,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Topology/Bornology/Constructions.lean | Bornology.isBounded_induced | [] | [
136,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.succ_ne_zero | [] | [
433,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
432,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/NormalMono/Equalizers.lean | CategoryTheory.NormalMonoCategory.epi_of_zero_cokernel | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.76906\ninst✝⁴ : Category C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasFiniteProducts C\ninst✝¹ : HasKernels C\ninst✝ : NormalMonoCategory C\nX Y : C\nf : X ⟶ Y\nZ : C\n⊢ f ≫ 0 = 0",
"tactic": "simp"
},
{
"state_after": "case mk\nC : Type u... | [
168,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Topology/Algebra/UniformConvergence.lean | UniformOnFun.hasBasis_nhds_one_of_basis | [
{
"state_after": "α : Type u_1\nG : Type u_2\nι : Type u_3\ninst✝² : Group G\n𝔖✝ : Set (Set α)\ninst✝¹ : UniformSpace G\ninst✝ : UniformGroup G\n𝔖 : Set (Set α)\nh𝔖₁ : Set.Nonempty 𝔖\nh𝔖₂ : DirectedOn (fun x x_1 => x ⊆ x_1) 𝔖\np : ι → Prop\nb : ι → Set G\nh : HasBasis (𝓝 1) p b\nthis : HasBasis (comap (f... | [
190,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin_symm_of_refl | [
{
"state_after": "no goals",
"state_before": "n : ℕ\np : Fin (n + 1)\n⊢ ↑decomposeFin.symm (p, Equiv.refl (Fin n)) = swap 0 p",
"tactic": "simp [Equiv.Perm.decomposeFin, Equiv.permCongr_def]"
}
] | [
34,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.brange_const | [
{
"state_after": "α : Type u_2\nβ : Type ?u.276922\nγ : Type ?u.276925\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nho : o ≠ 0\nc : α\n⊢ range (familyOfBFamily o fun x x => c) = {c}",
"state_before": "α : Type u_2\nβ : Type ?u.276922\nγ : Type ?u.276925\nr : α → α → Prop\ns : β → β → ... | [
1217,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.union_mul_inter_subset_union | [] | [
472,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le.intro | [] | [
358,
23
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
357,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.ext | [] | [
657,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Order/CountableDenseLinearOrder.lean | Order.embedding_from_countable_to_dense | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : LinearOrder β\ninst✝² : Encodable α\ninst✝¹ : DenselyOrdered β\ninst✝ : Nontrivial β\nx y : β\nhxy : x < y\n⊢ Nonempty (α ↪o β)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : Lin... | [
219,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.IsInternal.isCompl | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : Semiring R\nι : Type v\ndec_ι : DecidableEq ι\nM : Type u_1\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nA✝ A : ι → Submodule R M\ni j : ι\nhij : i ≠ j\nh : Set.univ = {i, j}\nhi : IsInternal A\n⊢ iSup A = A i ⊔ A j",
"tactic": "rw [← ... | [
385,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_wcovby | [] | [
629,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_nndist | [] | [
1571,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairOpEquiv_counitIso_zero | [] | [
196,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/GroupTheory/GroupAction/Units.lean | IsUnit.inv_smul | [] | [
50,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.map_neg | [] | [
313,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
11
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.one_apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_self_mono | [] | [
681,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.tendsto_iff_forall_testAgainstNN_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝⁶ : MeasurableSpace Ω\nR : Type ?u.142439\ninst✝⁵ : SMul R ℝ≥0\ninst✝⁴ : SMul R ℝ≥0∞\ninst✝³ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → FiniteMeasure Ω\nμ :... | [
510,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.mapTermRel_mapTermRel | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.61221\nP : Type ?u.61224\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nγ : Type u_5\nn✝¹ : ℕ\nL'' : Language\nft : (n : ℕ) → Term L (α ⊕ Fin n) → Term L' (β ⊕ Fin n)\nfr : (n :... | [
545,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Topology/Semicontinuous.lean | IsOpen.upperSemicontinuousOn_indicator | [] | [
745,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.nullMeasurableSet_eq | [] | [
362,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.infEdist_empty | [] | [
61,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.map_id | [] | [
352,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.Lex.refl_left | [] | [
245,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Control/LawfulFix.lean | Part.fix_eq | [
{
"state_after": "α✝ : Type u_1\nβ : α✝ → Type u_2\nα : Type ?u.14701\nf : ((a : α✝) → Part (β a)) →o (a : α✝) → Part (β a)\nhc : Continuous f\n⊢ ωSup (approxChain f) = ωSup (Chain.map (approxChain f) f)",
"state_before": "α✝ : Type u_1\nβ : α✝ → Type u_2\nα : Type ?u.14701\nf : ((a : α✝) → Part (β a)) →o (... | [
189,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_toDual_comp_iff | [] | [
152,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.of_arrow_iso_right | [
{
"state_after": "C : Type u_2\ninst✝ : Category C\nA✝ B✝ B' X✝ Y✝ Y'✝ : C\ni✝ : A✝ ⟶ B✝\ni' : B✝ ⟶ B'\np✝ : X✝ ⟶ Y✝\np'✝ : Y✝ ⟶ Y'✝\nA B X Y X' Y' : C\ni : A ⟶ B\np : X ⟶ Y\np' : X' ⟶ Y'\ne : Arrow.mk p ≅ Arrow.mk p'\nhip : HasLiftingProperty i p\n⊢ HasLiftingProperty i (e.inv.left ≫ p ≫ e.hom.right)",
"st... | [
134,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.coe_lt_coe | [
{
"state_after": "no goals",
"state_before": "x y : ℕ\n⊢ ↑x < ↑y ↔ x < y",
"tactic": "rw [lt_iff_le_not_le, lt_iff_le_not_le, coe_le_coe, coe_le_coe]"
}
] | [
281,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropWithinAt_mono | [
{
"state_after": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\nX : Type ?u.49347\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : StructureGr... | [
459,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_neg | [] | [
237,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.head_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\n⊢ head nil = Computation.pure none",
"tactic": "simp [head]"
}
] | [
658,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.inf_orthogonal_eq_bot | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.37226\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace 𝕜 F\nK : Submodule 𝕜 E\n⊢ K ⊓ Kᗮ ≤ ⊥",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.37... | [
113,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_injective | [
{
"state_after": "case ofFractionRing.ofFractionRing\nK : Type u\ninst✝⁵ : CommRing K\nG₀ : Type ?u.685775\nL : Type ?u.685778\nR : Type u_2\nS : Type u_3\nF : Type u_1\ninst✝⁴ : CommGroupWithZero G₀\ninst✝³ : Field L\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : MonoidHomClass F R[X] S[X]\nφ : F\nhφ : R[X... | [
668,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.einfsep_iUnion_mem_option | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.18395\ninst✝ : EDist α\nx y : α\ns✝ t : Set α\nι : Type u_1\no : Option ι\ns : ι → Set α\n⊢ einfsep (⋃ (i : ι) (_ : i ∈ o), s i) = ⨅ (i : ι) (_ : i ∈ o), einfsep (s i)",
"tactic": "cases o <;> simp"
}
] | [
141,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
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