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/Data/List/Rdrop.lean | List.rdropWhile_eq_self_iff | [
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Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.toSignedMeasure_zero | [
{
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Mathlib/LinearAlgebra/Dimension.lean | linearIndependent_le_infinite_basis | [
{
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Mathlib/Data/Rat/Defs.lean | Rat.coe_int_num | [] | [
53,
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Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.condition | [
{
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"tactic": "rw [← app_right_eq_ι_comp_fst, ← a... | [
388,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
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Mathlib/Analysis/NormedSpace/Banach.lean | LinearMap.continuous_of_isClosed_graph | [
{
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462,
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Mathlib/Topology/MetricSpace/Basic.lean | eq_of_nndist_eq_zero | [
{
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"tactic": "simp only [← NNReal.eq_iff, ← dist_nndist, imp_self, NNReal.coe_zero, dist_eq_zero... | [
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86
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Mathlib/Logic/Equiv/Defs.lean | Equiv.self_comp_symm | [] | [
292,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Int/Lemmas.lean | Int.eq_one_of_mul_eq_self_right | [
{
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}
] | [
1323,
59
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_top_of_eq_top | [] | [
870,
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Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.ediam_image_inter_le_of_le | [] | [
180,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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Mathlib/LinearAlgebra/Alternating.lean | Equiv.Perm.ModSumCongr.swap_smul_involutive | [
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_pointReflection | [
{
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850,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Cycle.lean | Cycle.chain_iff_pairwise | [
{
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86
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion | [
{
"state_after": "case refine'_1\nι : Type u_1\nI J✝ : Box ι\nπ π₁ π₂ : TaggedPrepartition I\nx : ι → ℝ\nr r₁ r₂ : (ι → ℝ) → ↑(Ioi 0)\nh₁ : IsHenstock π₁\nh₂ : IsHenstock π₂\nh : Disjoint (iUnion π₁) (iUnion π₂)\nJ : Box ι\nhJ✝ : J ∈ TaggedPrepartition.disjUnion π₁ π₂ h\nhJ : J ∈ π₁.boxes\n⊢ tag (TaggedPreparti... | [
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392,
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.sub_apply | [] | [
455,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/Order/Hom/Lattice.lean | SupHom.const_apply | [] | [
454,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
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Std/Data/Int/Lemmas.lean | Int.neg_eq_zero | [] | [
90,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
90,
11
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Mathlib/Topology/Maps.lean | QuotientMap.continuous | [] | [
318,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
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src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.run_throw | [] | [
56,
102
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Data/Nat/Units.lean | Nat.addUnits_eq_zero | [] | [
24,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
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Mathlib/Data/Fintype/Basic.lean | Function.Injective.left_inv_of_invOfMemRange | [] | [
497,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
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Mathlib/Init/Data/Nat/Lemmas.lean | Nat.one_lt_bit1 | [
{
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},
{
"state_after": "n : ℕ\nx✝ : succ n ≠ 0\n⊢ 1 < succ (succ (bit1 n))",
"state_before": "n : ℕ\nx✝ : succ n ≠ 0\n⊢ 1 < bit1 (succ n)",
"tactic": "rw [Nat.bit1_succ_eq]"
},
{
"state... | [
166,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | OrderIso.map_csSup' | [] | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1329,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnion_congr | [
{
"state_after": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nhi : ∀ (J : Box ι), J ∈ π₁ → πi₁ J = πi₂ J\n⊢ biUnion π₁ πi₁ = biUnion π₁ πi₂",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : ... | [
335,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
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Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_singleton_add_smul_div_singleton_add_smul | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type ?u.2022767\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Nor... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup'_eq_sup | [] | [
993,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.congr' | [] | [
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63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
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Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_div_mul_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.63975\nG : Type ?u.63978\nα : Type u_1\nM : Type ?u.63984\nN : Type ?u.63987\ninst✝ : DivisionCommMonoid α\na✝ b✝ c d : α\nh : IsUnit c\na b : α\n⊢ c * a / (c * b) = a / b",
"tactic": "rw [mul_comm c, mul_comm c, h.mul_div_mul_right]"
}
] | [
484,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
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Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.LaxMonoidalFunctor.prod'_toFunctor | [] | [
405,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousOn.aestronglyMeasurable_of_isCompact | [
{
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551,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
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Mathlib/Algebra/Ring/Prod.lean | NonUnitalRingHom.coe_snd | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Topology/SubsetProperties.lean | Prod.noncompactSpace_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.103613\nπ : ι → Type ?u.103618\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\n⊢ NoncompactSpace (α × β) ↔ NoncompactSpace α ∧ Nonempty β ∨ Nonempty α ∧ NoncompactSpace β",
"tactic": "simp [← Filter.... | [
1006,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.toList_getLast? | [
{
"state_after": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.490904\ninst✝ : Monoid N\ni j : ι\nw : NeWord M i j\n⊢ { fst := j, snd := last w } ∈ List.getLast? (toList w)",
"state_before": "ι : Type u_1\nM : ι → Type u_2\ninst✝¹ : (i : ι) → Monoid (M i)\nN : Type ?u.490904\... | [
543,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
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Mathlib/Data/Prod/Basic.lean | Prod.map_bijective | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_4\nδ : Type u_3\ninst✝¹ : Nonempty α\ninst✝ : Nonempty β\nf : α → γ\ng : β → δ\nthis : Nonempty γ\n⊢ Bijective (map f g) ↔ Bijective f ∧ Bijective g",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_4\nδ : Type u_3\ninst✝¹ : Nonempty α\ninst✝ ... | [
384,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
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Mathlib/Topology/Constructions.lean | nhds_ofMul | [] | [
130,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_Icc | [] | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_congr_ae | [
{
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Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_add_mul_right_left | [
{
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}
] | [
56,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_compl_self | [
{
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"tac... | [
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81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_sum | [] | [
2054,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2052,
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_le_self | [] | [
110,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.map_mvPolynomial_eq_eval₂ | [
{
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1138,
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Mathlib/RepresentationTheory/Action.lean | Action.zero_hom | [] | [
349,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
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Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | mem_span_gramSchmidt | [
{
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145,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
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Mathlib/Topology/Algebra/Module/StrongTopology.lean | ContinuousLinearMap.strongUniformity.uniformAddGroup | [
{
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119,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.GrothendieckTopology.closed_iff_closed | [] | [
179,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_le_comap_of_inverse | [] | [
1369,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_toSubring | [] | [
231,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Std/WF.lean | Acc.ndrec_eq_ndrecC | [
{
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"state_before": "⊢ @ndrec = @Acc.ndrecC",
"tactic": "funext α r ... | [
78,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
76,
18
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Mathlib/Logic/Lemmas.lean | dite_dite_distrib_left | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q r : Prop\ninst✝¹ : Decidable p\ninst✝ : Decidable q\na✝ b✝ c✝ : α\na : p → α\nb : ¬p → q → α\nc : ¬p → ¬q → α\n⊢ (dite p a fun hp => dite q (b hp) (c hp)) = if hq : q then dite p a fun hp => b hp hq else dite p a fun hp => c hp hq",
"tactic... | [
37,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_inl_pushoutLeftPushoutInrIso_hom | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nW X Y Z : C\nf : X ⟶ Y\ng : X ⟶ Z\ng' : Z ⟶ W\ninst✝² : HasPushout f g\ninst✝¹ : HasPushout pushout.inr g'\ninst✝ : HasPushout f (g ≫ g')\n⊢ pushout.inl ≫ pushout.inl ≫ (pushoutLeftPushoutInrIso ... | [
2240,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2238,
1
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_mk | [] | [
423,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Homeomorph.measurable | [] | [
914,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
913,
11
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | Polynomial.card_roots_le_derivative | [
{
"state_after": "no goals",
"state_before": "p : ℝ[X]\n⊢ ∑ x in Multiset.toFinset (roots p), (Multiset.count x (roots p) - 1 + 1) =\n ∑ x in Multiset.toFinset (roots p), (rootMultiplicity x p - 1) + Finset.card (Multiset.toFinset (roots p))",
"tactic": "simp only [Finset.sum_add_distrib, Finset.card... | [
407,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Algebra/Ring/Units.lean | Units.divp_sub_divp_same | [
{
"state_after": "no goals",
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"tactic": "rw [sub_eq_add_neg, sub_eq_add_neg, neg_divp, divp_add_divp_same]"
}
] | [
70,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.comp_zero | [
{
"state_after": "case H\nV : Type ?u.476976\nV₁ : Type u_3\nV₂ : Type u_1\nV₃ : Type u_2\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf✝ g : NormedAddGroupHom V₁ V₂\nf : NormedAddGroupHom V₂ V₃\nx✝ : V₁\n⊢ ↑(Norme... | [
692,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.lt_ediv_of_mul_lt | [] | [
468,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
11
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto | [
{
"state_after": "E : Type u_1\nf f' : ℝ → E\ng g' : ℝ → ℝ\na b l : ℝ\nm : E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhcont : ContinuousOn f (Ici a)\nhderiv : ∀ (x : ℝ), x ∈ Ioi a → HasDerivAt f (f' x) x\nf'int : IntegrableOn f' (Ioi a)\nhf : Tendsto f atTop (𝓝 m)\n⊢ T... | [
684,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Module.End_isUnit_inv_apply_apply_of_isUnit | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nf : End R M\nh : IsUnit f\nx : M\n⊢ ↑((IsUnit.unit h).inv * f) x = x",
"tactic": "simp"
}
] | [
651,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.bind_apply | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.toMeasurable_ae_eq | [
{
"state_after": "ι : Type ?u.6547\nα : Type u_1\nβ : Type ?u.6553\nγ : Type ?u.6556\nm0 : MeasurableSpace α\nμ : Measure α\ns t : Set α\nh : NullMeasurableSet s\n⊢ Exists.choose ?hc =ᵐ[μ] s\n\ncase hc\nι : Type ?u.6547\nα : Type u_1\nβ : Type ?u.6553\nγ : Type ?u.6556\nm0 : MeasurableSpace α\nμ : Measure α\ns ... | [
241,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_congr | [] | [
1527,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.dirac_prod | [
{
"state_after": "α : Type u_1\nα' : Type ?u.4491225\nβ : Type u_2\nβ' : Type ?u.4491231\nγ : Type ?u.4491234\nE : Type ?u.4491237\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MeasurableSpace α'\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace β'\ninst✝³ : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
564,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.le_sqrt' | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ m ≤ sqrt n ↔ m ^ 2 ≤ n",
"tactic": "simpa only [pow_two] using le_sqrt"
}
] | [
92,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_mod_opow_log_lt_log_self | [
{
"state_after": "case inl\nb o : Ordinal\nhb : 1 < b\nho : o ≠ 0\nhbo : b ≤ o\nh : o % b ^ log b o = 0\n⊢ log b (o % b ^ log b o) < log b o\n\ncase inr\nb o : Ordinal\nhb : 1 < b\nho : o ≠ 0\nhbo : b ≤ o\nh : o % b ^ log b o ≠ 0\n⊢ log b (o % b ^ log b o) < log b o",
"state_before": "b o : Ordinal\nhb : 1 ... | [
394,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_le_of_limit_aux | [
{
"state_after": "α✝ : Type ?u.196573\nβ✝ : Type ?u.196576\nγ : Type ?u.196579\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u_1\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : IsWellOrder β s\nc : Ordinal\nh : IsLimit (type s)\nH : ∀ (b' : Ordinal), b' < type s ... | [
793,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
9
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.hasStrictFDerivAt | [] | [
63,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
11
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.set_index_mem | [] | [
309,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.map | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_1\np : α → Prop\nα✝ : Type u_1\nq : α✝ → Prop\nf : α → α✝\ninst✝¹ : Functor m\ninst✝ : LawfulFunctor m\nx : m α\nhx✝ : SatisfiesM p x\nhf : ∀ {a : α}, p a → q (f a)\nx' : m { a // p a }\nhx : Subtype.val <$> x' = x\n⊢ SatisfiesM q (f <$> x)",
"state_befo... | [
96,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
92,
11
] |
Mathlib/Data/List/Sort.lean | List.sorted_singleton | [] | [
110,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_mul | [] | [
656,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_mul | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ x y : ℝ≥0\n⊢ ↑sqrt (x * y) = ↑sqrt x * ↑sqrt y",
"tactic": "rw [sqrt_eq_iff_sq_eq, mul_pow, sq_sqrt, sq_sqrt]"
}
] | [
109,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.comap_subtype_self | [] | [
1642,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_of_one_lt_sumInv_aux | [
{
"state_after": "p q r : ℕ+\nhs : List.Sorted (fun x x_1 => x ≤ x_1) [p, q, r]\nx✝ : List.length [p, q, r] = 3\nH : 1 < sumInv ↑[p, q, r]\n⊢ (p ≤ q ∧ p ≤ r) ∧ q ≤ r\n\ncase intro.intro\np q r : ℕ+\nhs : List.Sorted (fun x x_1 => x ≤ x_1) [p, q, r]\nx✝ : List.length [p, q, r] = 3\nH : 1 < sumInv ↑[p, q, r]\nhqr... | [
261,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.liftNC_one | [] | [
1324,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1322,
1
] |
Mathlib/Topology/PathConnected.lean | Path.extend_extends' | [] | [
280,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/List/Basic.lean | List.foldr_join | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.232055\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β → β\na : β\nl : List α\nL : List (List α)\n⊢ foldr f a (join (l :: L)) = foldr (fun l b => foldr f b l) a (l :: L)",
"tactic": "simp only [join, foldr_append, foldr... | [
2450,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2447,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inclusion_eq_id | [] | [
2777,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2776,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.triangle | [
{
"state_after": "case H\nR : Type u\ninst✝ : CommRing R\nM N : ModuleCat R\n⊢ ∀ (x : ↑M) (y : ↑(of R R)) (z : ↑N),\n ↑((associator M (of R R) N).hom ≫ tensorHom (𝟙 M) (leftUnitor N).hom) ((x ⊗ₜ[R] y) ⊗ₜ[R] z) =\n ↑(tensorHom (rightUnitor M).hom (𝟙 N)) ((x ⊗ₜ[R] y) ⊗ₜ[R] z)",
"state_before": "R : ... | [
185,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node4L | [
{
"state_after": "case nil\nα : Type u_1\ninst✝ : Preorder α\nl : Ordnode α\nx y : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhl : Valid' o₁ l ↑x\nhr : Valid' (↑y) r o₂\nhm : Valid' (↑x) nil ↑y\nHm : 0 < size nil\nH :\n size l = 0 ∧ size nil = 1 ∧ size r ≤ 1 ∨\n 0 < size l ∧\n ratio * size r ≤ s... | [
1216,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.le_comap_mkQ | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p'✝ : Submodule R M\nR₂ : Type ?u.225550\nM₂ : Type ?u.225553\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R₂\np' : Sub... | [
385,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.coe_srangeRestrict | [] | [
878,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
877,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_eq_neg_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na b c : α\n⊢ abs a = -a ↔ a ≤ 0",
"tactic": "simp [abs_eq_max_neg]"
}
] | [
65,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basis_eq_prod_sub_inv_mul_nodal_div | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhi : i ∈ s\n⊢ Lagrange.basis s v i = ↑C (nodalWeight s v i) * (nodal s v / (X - ↑C (v i)))",
"tactic": "simp_rw [Lagrange.basis, basisDivis... | [
583,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | UpperSemicontinuous.measurable | [] | [
1049,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Data/List/Sigma.lean | List.mem_keys_of_mem_keys_kerase | [] | [
428,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.left_mem_image_Ioi | [] | [
760,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.inv_mem_inv | [] | [
507,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.carrier_eq_coe | [] | [
88,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
9
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.Polynomial.quotQuotEquivComm_symm_mk_mk | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nI : Ideal R\nf p : R[X]\n⊢ ↑(RingEquiv.symm (quotQuotEquivComm I f))\n (↑(Ideal.Quotient.mk (span {↑(Ideal.Quotient.mk (Ideal.map C I)) f})) (↑(Ideal.Quotient.mk (Ideal.map C I)) p)) =\n ↑(Ideal.Quo... | [
811,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\nr : R\n⊢ ↑toLaurent (↑Polynomial.C r * X ^ n) = ↑C r * T ↑n",
"tactic": "simp only [_root_.map_mul, Polynomial.toLaurent_C, Polynomial.toLaurent_X_pow]"
}
] | [
254,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.inv_zero | [
{
"state_after": "no goals",
"state_before": "⊢ 0⁻¹ = 0",
"tactic": "rw [← ofReal_zero, ← ofReal_inv, inv_zero]"
}
] | [
752,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
11
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_map | [] | [
816,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.bsup_lt_ord | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.41767\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nc : Ordinal\nho : card o < cof c\n⊢ Cardinal.lift (card o) < cof c",
"tactic": "rwa [o.card.lift_id]"
}
] | [
474,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Finset.hasSum_compl_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.430427\nδ : Type ?u.430430\ninst✝² : AddCommGroup α\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalAddGroup α\nf g : β → α\na a₁ a₂ : α\ns : Finset β\n⊢ HasSum f (∑ b in s, f b + a) ↔ HasSum f (a + ∑ i in s, f i)",
"... | [
874,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_x | [] | [
1857,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | StrictMonoOn.continuousAt_of_image_mem_nhds | [] | [
241,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Category/ModuleCat/Basic.lean | ModuleCat.ofHom_apply | [] | [
187,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.finsuppProdLEquiv_symm_apply | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.645884\nM✝ : Type ?u.645887\nN : Type ?u.645890\nP : Type ?u.645893\nR✝ : Type ?u.645896\nS : Type ?u.645899\ninst✝¹⁰ : Semiring R✝\ninst✝⁹ : Semiring S\ninst✝⁸ : AddCommMonoid M✝\ninst✝⁷ : Module R✝ M✝\ninst✝⁶ : AddCommMonoid N\ninst✝⁵ : Module R✝ ... | [
1026,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
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