file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.gc_map_comap | [] | [
475,
22
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474,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | ContDiffOn.arctan | [] | [
227,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiffAt_of_subsingleton | [
{
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116,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_inl_pushoutAssoc_hom | [
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Mathlib/Order/SuccPred/Basic.lean | LE.le.exists_pred_iterate | [] | [
1412,
30
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Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.sum | [
{
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818,
31
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803,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.ennnorm_integral_le_lintegral_ennnorm | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.964234\n𝕜 : Type ?u.964237\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.gMul_eq_coe_linearMap | [] | [
102,
6
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Mathlib/Algebra/Bounds.lean | BddBelow.mul | [] | [
137,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Order/Heyting/Basic.lean | hnot_le_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.173522\nα : Type u_1\nβ : Type ?u.173528\ninst✝ : CoheytingAlgebra α\na b c : α\n⊢ ￢a ≤ b ↔ ￢b ≤ a",
"tactic": "rw [hnot_le_iff_codisjoint_right, hnot_le_iff_codisjoint_left]"
}
] | [
1027,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.le_inv_smul_iff | [
{
"state_after": "no goals",
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"tactic": "simpa [hr₀, ENNReal.smul_def] using (mul_le_iff_le_inv (coe_ne_zero.mpr hr₀) coe_ne_top).symm"
}
] | [
1663,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.Prepartition.distortion_toSubordinate | [] | [
201,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_direction_eq_vsub_set | [] | [
246,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Order/Hom/Lattice.lean | SupHom.comp_id | [] | [
421,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
9
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.map_sub | [] | [
2258,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2257,
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Mathlib/Order/SymmDiff.lean | symmDiff_symmDiff_inf | [
{
"state_after": "no goals",
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"tactic": "rw [← symmDiff_sdiff_inf a, sdiff_symmDiff_eq_sup, symmDiff_sup_inf]"
}
] | [
209,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/Data/Set/Prod.lean | Set.subset_pi_eval_image | [] | [
866,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_sub | [
{
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1291,
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1289,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_def | [] | [
794,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.bot_toSubmonoid | [] | [
898,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_le_of_nonempty | [
{
"state_after": "F : Type ?u.1006929\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : SeminormedAddCommGroup β\nf✝ g : α →ᵇ β\nx : α\nC : ℝ\ninst✝ : Nonempty α\nf : α →ᵇ β\nM : ℝ\n⊢ dist f 0 ≤ M ↔ ∀ (x : α), dist (↑f x) 0 ≤ M",
"state_before": "F : Type ?u.1006929\nα : Type u\nβ :... | [
847,
32
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845,
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Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_val | [] | [
3124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3123,
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Mathlib/RingTheory/Localization/Basic.lean | Localization.mk_eq_mk'_apply | [
{
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"tactic": "rw [mk_eq_mon... | [
1029,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.reduceOption_singleton | [
{
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"tactic": "cases x <;> rfl"
}
] | [
3480,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3480,
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Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | FundamentalGroupoid.id_eq_path_refl | [] | [
336,
81
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Mathlib/Data/Set/Sigma.lean | Set.union_sigma | [] | [
136,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
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Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.pow_smul_le_pow_smul | [
{
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Mathlib/Topology/UniformSpace/Equicontinuity.lean | Set.Equicontinuous.mono | [] | [
204,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.mul_one | [
{
"state_after": "no goals",
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"tactic": "refine TensorProduct.induction_on x ?_ ?_ ?_ <;> simp (... | [
429,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Set.powerset_nonempty | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.equiv | [
{
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src/lean/Init/Data/Nat/Basic.lean | Nat.le_or_eq_of_le_succ | [] | [
338,
41
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Algebra/MonoidAlgebra/NoZeroDivisors.lean | AddMonoidAlgebra.mul_apply_add_eq_mul_of_forall_ne | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Add A\nf g : AddMonoidAlgebra R A\na0 b0 : A\nh : ∀ {a b : A}, a ∈ f.support → b ∈ g.support → a ≠ a0 ∨ b ≠ b0 → a + b ≠ a0 + b0\n⊢ (sum f fun a₁ b₁ => sum g fun a₂ b₂ => if a₁ + a₂ = a0 + b0 then b₁ * b₂ else 0) = ↑f a0 * ↑g b0",
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68,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.bddAbove_iff_small | [
{
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"state_before": "α β : Type u\ns : Set Cardinal\n⊢ Small ↑s → BddAbove s",
"tactic": "rintro ⟨ι, ⟨e⟩⟩"
},
{
"state_after": "case mk.intro.intro\nα β : Type u\ns : Set Cardinal\nι : Type ... | [
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40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
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Mathlib/Algebra/Order/Field/Basic.lean | lt_inv_of_neg | [] | [
780,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
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] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.norm_image_sub_le_of_norm_hasDerivWithin_le | [
{
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635,
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631,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_bot | [] | [
244,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/Sym/Basic.lean | Sym.map_injective | [] | [
407,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
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Mathlib/Data/Finset/Basic.lean | coe_notMemRangeEquiv_symm | [
{
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}
] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3105,
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.tFAE | [
{
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383,
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Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.map_zero | [] | [
204,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
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] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | NeZero.pos | [] | [
313,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Complex/ReImTopology.lean | Complex.isHomeomorphicTrivialFiberBundle_re | [] | [
48,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/Catalan.lean | gosper_trick | [
{
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Mathlib/Topology/MetricSpace/Basic.lean | eq_of_forall_dist_le | [] | [
2874,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2873,
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Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_le_pow_card | [
{
"state_after": "case h\nι : Type ?u.120163\nα : Type u_1\nβ : Type ?u.120169\nγ : Type ?u.120172\ninst✝ : OrderedCommMonoid α\ns t : Multiset α\na n : α\na✝ : List α\nh : ∀ (x : α), x ∈ Quotient.mk (List.isSetoid α) a✝ → x ≤ n\n⊢ prod (Quotient.mk (List.isSetoid α) a✝) ≤ n ^ ↑card (Quotient.mk (List.isSetoid ... | [
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Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.lift_fst_comp_snd_comp | [
{
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744,
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Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_ofENat | [
{
"state_after": "no goals",
"state_before": "n : ℕ∞\nx✝ : Decidable (↑n).Dom\n⊢ toWithTop ↑n = n",
"tactic": "induction n with\n| none => simp\n| some n =>\n simp only [toWithTop_natCast', ofENat_some]\n rfl"
},
{
"state_after": "no goals",
"state_before": "case none\nx✝ : Decidable (↑Opt... | [
655,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_subset_left | [] | [
267,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | cmp_mul_neg_right | [] | [
1163,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/Data/Fintype/Pi.lean | Fintype.coe_piFinset | [
{
"state_after": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nδ : α → Type u_1\nt : (a : α) → Finset (δ a)\nx : (a : α) → δ a\n⊢ x ∈ ↑(piFinset t) ↔ ∀ (i : α), x i ∈ ↑(t i)",
"state_before": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nδ : α → Type u_1\nt : (a : α) → Finset (δ a)\n... | [
53,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_bot_top | [] | [
182,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.symm_comp_self | [] | [
444,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.hasStrictFDerivAt | [] | [
266,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
11
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_comp_rpow_iff | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\np : ℝ\nhp : p ≠ 0\nS : Set ℝ := Ioi 0\n⊢ IntegrableOn (fun x => (abs p * x ^ (p - 1)) • f (x ^ p)) (Ioi 0) ↔ IntegrableOn f (Ioi 0)",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : Norme... | [
927,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
905,
1
] |
Mathlib/Data/Finsupp/ToDfinsupp.lean | Finsupp.toDfinsupp_coe | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Order/Filter/Extr.lean | isMinFilter_const | [] | [
181,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_cons | [] | [
840,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.nonempty_of_pos_dist | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\nh : 0 < dist G u v\n⊢ Set.Nonempty Set.univ",
"tactic": "simpa [Set.range_nonempty_iff_nonempty, Set.nonempty_iff_univ_nonempty] using\n Nat.nonempty_of_pos_sInf h"
}
] | [
105,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Filter.frequently_cofinite_iff_infinite | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1622\nα : Type u_1\nβ : Type ?u.1628\nl : Filter α\np : α → Prop\n⊢ (∃ᶠ (x : α) in cofinite, p x) ↔ Set.Infinite {x | p x}",
"tactic": "simp only [Filter.Frequently, Filter.Eventually, mem_cofinite, compl_setOf, not_not,\n Set.Infinite]"
}
] | [
72,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasStrictDerivAt | [
{
"state_after": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 →ᵃ[𝕜] E\na b : E\nL : Filter 𝕜\ns : Set 𝕜\nx : 𝕜\n⊢ HasStrictDerivAt (↑f.linear + fun x => ↑f 0) (↑f.linear 1) x",
"state_before": "𝕜 : Type u_1\ninst✝² : ... | [
34,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardFactors_apply_prime_pow | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.561753\np k : ℕ\nhp : Prime p\n⊢ ↑Ω (p ^ k) = k",
"tactic": "rw [cardFactors_apply, hp.factors_pow, List.length_replicate]"
}
] | [
897,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_zero | [] | [
1857,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1856,
1
] |
Mathlib/Analysis/ODE/Gronwall.lean | dist_le_of_approx_trajectories_ODE_of_mem_set | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type ?u.38955\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nv : ℝ → E → E\ns : ℝ → Set E\nK : ℝ\nhv : ∀ (t : ℝ) (x : E), x ∈ s t → ∀ (y : E), y ∈ s t → dist (v t x) (v t y) ≤ K * dist x y\nf g f' g' : ℝ → E\n... | [
174,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots_pow | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\n⊢ roots (p ^ Nat.zero) = Nat.zero • roots p\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\na b : R\nn✝ : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\nn : ℕ\ni... | [
713,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.fst_surjective | [] | [
142,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.pow_neg_one | [] | [
466,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_lt_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.19414\nι : Type ?u.19417\nα : Type u_1\nβ : Type ?u.19423\ninst✝¹ : OrderedRing α\ninst✝ : Nontrivial α\nn : ℤ\n⊢ ↑n < 0 ↔ n < 0",
"tactic": "rw [← cast_zero, cast_lt]"
}
] | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_neg_add_of_add_le | [
{
"state_after": "a b c : Int\nh✝ : a + b ≤ c\nh : -a + (a + b) ≤ -a + c\n⊢ b ≤ -a + c",
"state_before": "a b c : Int\nh : a + b ≤ c\n⊢ b ≤ -a + c",
"tactic": "have h := Int.add_le_add_left h (-a)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a + b ≤ c\nh : -a + (a + b)... | [
956,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
954,
11
] |
Mathlib/FieldTheory/Normal.lean | isSolvable_of_isScalarTower | [
{
"state_after": "F : Type u_1\nK : Type ?u.546000\ninst✝¹⁶ : Field F\ninst✝¹⁵ : Field K\ninst✝¹⁴ : Algebra F K\nK₁ : Type u_2\nK₂ : Type ?u.546093\nK₃ : Type ?u.546096\ninst✝¹³ : Field F\ninst✝¹² : Field K₁\ninst✝¹¹ : Field K₂\ninst✝¹⁰ : Field K₃\ninst✝⁹ : Algebra F K₁\ninst✝⁸ : Algebra F K₂\ninst✝⁷ : Algebra ... | [
474,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_smul | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np : P\nv : V\nr : ℝ\nhr : r ≠ 0\n⊢ (-2 * (r * inner v (p -ᵥ s.center)) / r / r / inner v v * r) • v +ᵥ p =\n (-2 * inner v (p -ᵥ s.ce... | [
111,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Algebra/Group/Conj.lean | ConjClasses.quotient_mk_eq_mk | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | smul_sphere | [
{
"state_after": "case inl\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁴ : NormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : Nontrivial E\nx : E\nr : ℝ\nhr : 0 ≤ r\n⊢ 0 • sphere x r = sphere (0 • x) (‖0‖ * r)\n\ncase inr\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁴ : Nor... | [
432,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | ContDiff.differentiable_iteratedDeriv | [] | [
285,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.compl_eq_univ_sdiff | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/AlgebraicTopology/ExtraDegeneracy.lean | SSet.Augmented.StandardSimplex.shiftFun_succ | [
{
"state_after": "n : ℕ\nX : Type u_1\ninst✝ : Zero X\nf : Fin n → X\ni : Fin n\n⊢ (if x : Fin.succ i = 0 then 0 else f (Fin.pred (Fin.succ i) x)) = f i",
"state_before": "n : ℕ\nX : Type u_1\ninst✝ : Zero X\nf : Fin n → X\ni : Fin n\n⊢ shiftFun f (Fin.succ i) = f i",
"tactic": "dsimp [shiftFun]"
},
... | [
169,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.copy_eq | [] | [
288,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | DifferentiableOn.mul_const | [] | [
434,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.eq_of_drop_last_eq | [
{
"state_after": "n : ℕ\nα : TypeVec (n + 1)\nβ : TypeVec (n + 1)\nf g : α ⟹ β\nh₀ : dropFun f = dropFun g\nh₁ : lastFun f = lastFun g\nx : Fin2 (n + 1)\n⊢ f x = g x",
"state_before": "n : ℕ\nα : TypeVec (n + 1)\nβ : TypeVec (n + 1)\nf g : α ⟹ β\nh₀ : dropFun f = dropFun g\nh₁ : lastFun f = lastFun g\n⊢ f =... | [
180,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_mul_add_lt_opow_mul_succ | [
{
"state_after": "no goals",
"state_before": "b u w v : Ordinal\nhw : w < b ^ u\n⊢ b ^ u * v + w < b ^ u * succ v",
"tactic": "rwa [mul_succ, add_lt_add_iff_left]"
}
] | [
403,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/Order/Height.lean | Set.le_chainHeight_add_nat_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9871\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\nn m : ℕ\n⊢ ↑n ≤ chainHeight s + ↑m ↔ ∃ l, l ∈ subchain s ∧ n ≤ length l + m",
"tactic": "simp_rw [← tsub_le_iff_right, ← ENat.coe_sub, (le_chainHeight_TFAE s (n - m)... | [
162,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_antitone_left | [] | [
207,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.gc_map_comap | [] | [
249,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.quotientPiLift_mk | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.ne_zero_iff_nequiv_zero | [] | [
306,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/Divisibility/Units.lean | IsUnit.dvd_mul_left | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : CommMonoid α\na b : α\nu : αˣ\n⊢ a ∣ ↑u * b ↔ a ∣ b",
"state_before": "α : Type u_1\ninst✝ : CommMonoid α\na b u : α\nhu : IsUnit u\n⊢ a ∣ u * b ↔ a ∣ b",
"tactic": "rcases hu with ⟨u, rfl⟩"
},
{
"state_after": "no goals",
"state_before": "... | [
108,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.smul_zero_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.67549\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.67558\ninst✝² : Zero α\ninst✝¹ : Zero β\ninst✝ : SMulWithZero α β\ns✝ : Set α\nt : Set β\ns : Set α\n⊢ s • 0 ⊆ 0",
"tactic": "simp [subset_def, mem_smul]"
}
] | [
795,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.casesOn | [
{
"state_after": "no goals",
"state_before": "P : PartENat → Prop\n⊢ ∀ (a : PartENat), P ⊤ → (∀ (n : ℕ), P ↑n) → P a",
"tactic": "exact PartENat.casesOn'"
}
] | [
152,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
11
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.finite_mul | [] | [
513,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.hausdorffDist_coe | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.mem_span_iff_repr_mem | [
{
"state_after": "ι : Type u_3\nι' : Type ?u.1303683\nR : Type u_2\nR₂ : Type ?u.1303689\nK : Type ?u.1303692\nM : Type u_1\nM' : Type ?u.1303698\nM'' : Type ?u.1303701\nV : Type u\nV' : Type ?u.1303706\nS : Type u_4\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring S\ninst✝⁶ : Nontrivial S\ninst✝⁵ : AddCommGroup M\ninst✝⁴ :... | [
1689,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.update_inl_apply_inl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type ?u.19213\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq (α ⊕ β)\nf : α ⊕ β → γ\ni j : α\nx : γ\n⊢ update f (inl i) x (inl j) = update (f ∘ inl) i x j",
"tactic": "rw [← update_inl_comp_in... | [
297,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.le_def | [] | [
55,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/MeasureTheory/Function/LpOrder.lean | MeasureTheory.Lp.coeFn_nonneg | [
{
"state_after": "α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\np : ℝ≥0∞\ninst✝ : NormedLatticeAddCommGroup E\nf : { x // x ∈ Lp E p }\n⊢ 0 ≤ᵐ[μ] ↑↑f ↔ ↑↑0 ≤ᵐ[μ] ↑↑f",
"state_before": "α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\np : ℝ≥0∞\ninst✝ : NormedLatticeAddCom... | [
54,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedEmbedding_of_pairwise_le_dist | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nX : Type ?u.557273\nι : Type ?u.557276\ninst✝³ : PseudoMetricSpace α✝\nγ : Type w\ninst✝² : MetricSpace γ\nx : γ\ns : Set γ\nα : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : DiscreteTopology α\nε : ℝ\nhε : 0 < ε\nf : α → γ\nhf : Pairwi... | [
2952,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2949,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.map_id | [] | [
311,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/List/Basic.lean | List.takeI_nil | [] | [
2332,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2330,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.coeFn_univ_ne_zero | [
{
"state_after": "no goals",
"state_before": "Ω : Type u_1\ninst✝ : MeasurableSpace Ω\nν : ProbabilityMeasure Ω\n⊢ (fun s => ENNReal.toNNReal (↑↑↑ν s)) univ ≠ 0",
"tactic": "simp only [coeFn_univ, Ne.def, one_ne_zero, not_false_iff]"
}
] | [
148,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.isUnit_pure | [] | [
881,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.map_toSubring | [
{
"state_after": "case a\nR : Type u\nS : Type ?u.101158\ninst✝¹ : Ring R\ninst✝ : Semiring S\nf : R →+* S\nx : S\np : R[X]\nT : Subring R\nhp : ↑(frange p) ⊆ ↑T\nn : ℕ\n⊢ coeff (map (Subring.subtype T) (toSubring p T hp)) n = coeff p n",
"state_before": "R : Type u\nS : Type ?u.101158\ninst✝¹ : Ring R\nins... | [
411,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
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