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/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_prod | [
{
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Mathlib/Analysis/LocallyConvex/Polar.lean | LinearMap.polar_antitone | [] | [
101,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Field/Basic.lean | NormedField.exists_norm_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.373469\nγ : Type ?u.373472\nι : Type ?u.373475\ninst✝ : NontriviallyNormedField α\nr : ℝ\nhr : 0 < r\nw : α\nhw : r⁻¹ < ‖w‖\n⊢ 0 < ‖w⁻¹‖ ∧ ‖w⁻¹‖ < r",
"tactic": "rwa [← Set.mem_Ioo, norm_inv, ← Set.mem_inv, Set.inv_Ioo_0_left hr]"
... | [
737,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/GroupTheory/OrderOfElement.lean | isOfFinAddOrder_ofMul_iff | [] | [
69,
10
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_of_open | [
{
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525,
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522,
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Mathlib/Order/WithBot.lean | IsMin.withTop | [
{
"state_after": "α : Type u_1\nβ : Type ?u.76189\nγ : Type ?u.76192\nδ : Type ?u.76195\na b : α\ninst✝ : LE α\nh : IsMin a\nb✝ : WithTop α\nhb : b✝ ≤ ↑a\n⊢ ↑a ≤ b✝",
"state_before": "α : Type u_1\nβ : Type ?u.76189\nγ : Type ?u.76192\nδ : Type ?u.76195\na b : α\ninst✝ : LE α\nh : IsMin a\n⊢ IsMin ↑a",
... | [
872,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | measure_Icc_lt_top | [] | [
4590,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4589,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_eq_zero_iff' | [
{
"state_after": "n : ℕ\n⊢ ↑Multiset.toFinsupp ↑(factors n) = 0 ↔ n = 0 ∨ n = 1",
"state_before": "n : ℕ\n⊢ factorization n = 0 ↔ n = 0 ∨ n = 1",
"tactic": "rw [factorization_eq_factors_multiset n]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑Multiset.toFinsupp ↑(factors n) = ... | [
214,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
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Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.exists_of | [
{
"state_after": "no goals",
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439,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
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Mathlib/RingTheory/IntegralClosure.lean | RingHom.isIntegralElem_leadingCoeff_mul | [
{
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795,
61
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778,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | vsub_set_subset_vectorSpan | [] | [
95,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.universalMulHom_commutes | [
{
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"state_before": "R : Type u_2\ninst✝² : Monoid R\nS : Submonoid R\ninst✝¹ : OreSet S\nT : Type u_1\ninst✝ : Monoid T\nf : R →* T\nfS : { x // x ∈ S } →* Tˣ\nhf : ∀ (s : { x // x ∈ S }), ↑f ↑s = ↑(↑fS s)\nr : R\n⊢ ↑(universalMulHom f fS hf) (↑numeratorHom r) = ↑f r",
"tactic"... | [
424,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.coeFn_add | [
{
"state_after": "case h\nΩ : Type u_1\ninst✝⁴ : MeasurableSpace Ω\nR : Type ?u.11466\ninst✝³ : SMul R ℝ≥0\ninst✝² : SMul R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nμ ν : FiniteMeasure Ω\nx✝ : Set Ω\n⊢ ENNReal.toNNReal (↑↑↑(μ + ν) x✝) = ((fun s => ENNReal.toNNReal (↑↑↑μ s)) + ... | [
242,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/Data/Nat/Prime.lean | Nat.prime_of_coprime | [
{
"state_after": "n : ℕ\nh1 : 1 < n\nh : ∀ (m : ℕ), m < n → m ≠ 0 → coprime n m\nm : ℕ\nmlt : m < n\nmdvd : m ∣ n\n⊢ m = 1",
"state_before": "n : ℕ\nh1 : 1 < n\nh : ∀ (m : ℕ), m < n → m ≠ 0 → coprime n m\n⊢ Prime n",
"tactic": "refine' prime_def_lt.mpr ⟨h1, fun m mlt mdvd => _⟩"
},
{
"state_afte... | [
155,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_empty | [] | [
150,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/Data/Finset/Sym.lean | Finset.diag_mem_sym2_mem_iff | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\na b : α\nm : Sym2 α\n⊢ Sym2.diag a ∈ Finset.sym2 s ↔ a ∈ s",
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"tactic": "rw [← mem_sym2_iff]"
... | [
106,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.map_obj_hom | [] | [
433,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_neg | [
{
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712,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Module/Injective.lean | Module.Baer.extensionOfMax_to_submodule_eq_top | [
{
"state_after": "R : Type u\ninst✝⁷ : Ring R\nQ : TypeMax\ninst✝⁶ : AddCommGroup Q\ninst✝⁵ : Module R Q\nM N : Type (max u v)\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\ninst✝ : Fact (Function.Injective ↑i)\nh : Baer R Q\ny : N\n⊢ y... | [
448,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Separation.lean | nhds_le_nhdsSet_iff | [
{
"state_after": "no goals",
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"tactic": "rw [← nhdsSet_singleton, nhdsSet_le_iff, singleton_subset_iff]"
}
] | [
706,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Real/CauSeq.lean | CauSeq.le_inf | [
{
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"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\n... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.exp_two_pi_mul_I | [] | [
1375,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_le_prod_of_mem | [
{
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"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nl : List (Per... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Quot.lean | forall_quotient_iff | [] | [
305,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.inseparable_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.166352\nι : Type ?u.166355\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ Inseparable x y ↔ dist x y = 0",
"tactic": "rw [EMetric.inseparable_iff, edist_nndist, dist_nndist, ENNReal.coe_eq_zero, NNReal.coe_eq_zero]"
}
] | [
1229,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Basic.lean | GT.gt.lt | [] | [
330,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Contraction.lean | rTensorHomEquivHomRTensor_apply | [
{
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299,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/ZMod/Basic.lean | ZMod.val_eq_ite_valMinAbs | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ ↑(val a) = (if val a ≤ n / 2 then ↑(val a) else ↑(val a) - ↑n) + ↑(if val a ≤ n / 2 then 0 else n)",
"state_before": "n : ℕ\ninst✝ : NeZero n\na : ZMod n\n⊢ ↑(val a) = valMinAbs a + ↑(if val a ≤ n / 2 then 0 else n)",
"tactic": "rw [valMinAbs_def_... | [
1038,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
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Mathlib/Analysis/NormedSpace/Extend.lean | ContinuousLinearMap.extendTo𝕜_apply | [] | [
167,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Finset/Basic.lean | Finset.val_injective | [] | [
158,
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158,
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Mathlib/Data/Set/Prod.lean | Set.eval_preimage' | [
{
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"state_before": "ι : Type u_1\nα : ι → Type u_2... | [
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842,
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Mathlib/Order/Lattice.lean | Prod.swap_sup | [] | [
1289,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.hasSum_repr_symm | [
{
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471,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.fderiv | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.erase | [] | [
458,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isDetector_def | [
{
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"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nG : C\n... | [
490,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
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Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_bind₁ | [
{
"state_after": "no goals",
"state_before": "σ : Type u_4\nτ : Type u_3\nR : Type u_1\nS : Type u_2\nT : Type ?u.930023\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* S\ng : τ → S\nh : σ → MvPolynomial τ R\nφ : MvPolynomial σ R\n⊢ ↑(eval₂Hom ... | [
308,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
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Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.mem_top | [] | [
314,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/Data/Multiset/Basic.lean | Multiset.recOn_0 | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_inf_subset_left | [] | [
173,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Computability/Language.lean | Language.le_mul_congr | [
{
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Mathlib/Analysis/NormedSpace/BallAction.lean | ne_neg_of_mem_sphere | [
{
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207,
76
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206,
1
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Std/Data/Int/Lemmas.lean | Int.sign_neg | [
{
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},
{
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}
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212,
44
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211,
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Mathlib/Data/Finset/Card.lean | Finset.pred_card_le_card_erase | [
{
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157,
25
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153,
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Mathlib/Order/MinMax.lean | min_eq_right_iff | [] | [
142,
15
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141,
1
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Mathlib/Data/Option/Basic.lean | Option.some_injective | [] | [
65,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
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Mathlib/Data/Nat/Cast/Basic.lean | ext_nat | [
{
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] | [
274,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/CategoryTheory/Monoidal/Types/Basic.lean | CategoryTheory.rightUnitor_hom_apply | [] | [
54,
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52,
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Mathlib/Algebra/Order/Field/Basic.lean | two_inv_lt_one | [] | [
538,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
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Mathlib/Topology/ContinuousOn.lean | Continuous.continuousOn | [
{
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908,
31
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906,
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.TransvectionStruct.toMatrix_reindexEquiv | [
{
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306,
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299,
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.finite_mul_iff | [] | [
518,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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Mathlib/Order/Disjoint.lean | IsCompl.Antitone | [] | [
555,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.abs_toReal_le_pi | [] | [
571,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
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Mathlib/Analysis/Convex/Segment.lean | Convex.mem_Ioc | [
{
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565,
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Mathlib/Data/Fintype/Basic.lean | Finset.compl_inter | [] | [
218,
12
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217,
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Mathlib/Topology/Category/Profinite/Basic.lean | Profinite.to_compHausToTopCat | [] | [
181,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
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Mathlib/Data/Multiset/FinsetOps.lean | Multiset.mem_ndinter | [
{
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] | [
244,
29
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243,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.left | [] | [
1096,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
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Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.comp_id | [] | [
632,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
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Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coe_coordChangeL | [] | [
308,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.mulRight_symm | [] | [
169,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
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Mathlib/Order/SupIndep.lean | Finset.supIndep_pair | [
{
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"tactic": "simp"
},
{
"st... | [
118,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_lt_pow_of_lt_left | [] | [
991,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
21
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Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.ext | [] | [
1245,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1244,
1
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Mathlib/Logic/Basic.lean | congr_arg_heq | [] | [
68,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardObj_map | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
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Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_ofBounded_iff | [] | [
250,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Data/List/BigOperators/Basic.lean | List.SublistForall₂.prod_le_prod' | [] | [
300,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
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Mathlib/Data/Nat/Digits.lean | Nat.digits_ne_nil_iff_ne_zero | [] | [
303,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/Data/W/Constructions.lean | WType.leftInverse_list | [
{
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"state_before": "γ : Type u\nf : Listβ γ Listα.nil → WType (Listβ γ)\n⊢ ofList γ (toList γ (mk Listα.nil f)) = mk Listα.nil f",
"tactic": "simp only [toList, ofList, mk.injEq, heq_eq_eq, true_and]"
},
{
"s... | [
173,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Data/Fin/Basic.lean | Fin.natAdd_castSucc | [] | [
1473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1472,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | derivWithin_const_sub | [
{
"state_after": "no goals",
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372,
49
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370,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_diagonal_left | [
{
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148,
61
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142,
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Mathlib/Order/SuccPred/Basic.lean | Wcovby.le_succ | [
{
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435,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.ofCone_π | [
{
"state_after": "no goals",
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}
] | [
654,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
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Mathlib/Data/Stream/Init.lean | Stream'.map_tail | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_X | [] | [
61,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.isOpen_thickening | [] | [
919,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.norm_setToFun_le_mul_norm | [
{
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1696,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1694,
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Mathlib/Algebra/Order/Archimedean.lean | exists_nat_ge | [
{
"state_after": "α : Type u_1\ninst✝² : StrictOrderedSemiring α\ninst✝¹ : Archimedean α\nx : α\ninst✝ : Nontrivial α\n⊢ ∃ n, x ≤ ↑n",
"state_before": "α : Type u_1\ninst✝¹ : StrictOrderedSemiring α\ninst✝ : Archimedean α\nx : α\n⊢ ∃ n, x ≤ ↑n",
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},
{
"state_after": "n... | [
122,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | dist_mul_mul_le | [
{
"state_after": "no goals",
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1429,
95
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1428,
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.comp_id | [] | [
349,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.incl_isIdealMorphism | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
1148,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | aemeasurable_sum_measure_iff | [] | [
117,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_finset_product_right' | [] | [
634,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.eqvGen_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.10696\nr : α → α → Prop\ns : Setoid α\nh : ∀ (x y : α), r x y → Rel s x y\n⊢ sInf {s | ∀ ⦃x y : α⦄, r x y → Rel s x y} ≤ s",
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262,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.insert_eq_insertWith | [
{
"state_after": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (match cmpLE x y with\n | Ordering.lt => balanceL (Ordnode.insert x l) y r\n | Ordering.eq => node size✝ l x r\n | Ordering.gt => balanceR l y (Ordnod... | [
1544,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1540,
1
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Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.pairwiseDisjoint | [] | [
282,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_pow_eq_top | [
{
"state_after": "α : Type u\nβ : Type v\na b : α\ninst✝ : CommSemiring α\nI : Ideal α\ns : Set α\nhs : span s = ⊤\nn : ℕ\n⊢ 1 ∈ span ((fun x => x ^ n) '' s)",
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642,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
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Mathlib/Data/List/Intervals.lean | List.Ico.filter_lt_of_le_bot | [
{
"state_after": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈ Ico n m\n⊢ l ≤ k",
"state_before": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈ Ico n m\n⊢ ¬decide (k < l) = true",
"tactic": "simp only [decide_eq_true_eq, not_lt]"
},
{
"state_after": "n m l : ℕ\nhln : l ≤ n\nk : ℕ\nhk : k ∈ Ico n m\n⊢ n ≤ ... | [
168,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | cauchySeq_finset_iff_vanishing_norm | [
{
"state_after": "ι : Type u_2\nα : Type ?u.23\nE : Type u_1\nF : Type ?u.29\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : SeminormedAddCommGroup F\nf : ι → E\n⊢ (∀ (i : ℝ), 0 < i → ∃ s, ∀ (t : Finset ι), Disjoint t s → ∑ b in t, f b ∈ ball 0 i) ↔\n ∀ (ε : ℝ), ε > 0 → ∃ s, ∀ (t : Finset ι), Disjoint t s → ‖∑ i... | [
49,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.lift_ι | [
{
"state_after": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nW : A\ne : W ⟶ cokernel f\nhe : e ≫ cokernel.desc f g w = 0\n⊢ (kernel.lift (cokernel.desc f g w) e he ≫ (homologyIsoKernelDesc f g w).inv) ≫\n (homologyIsoKernelDesc f g w).hom ≫ kernel.ι ... | [
150,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.cg_iff_countable | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\ninst✝¹ : Structure L M\ninst✝ : Countable ((l : ℕ) × Functions L l)\n⊢ CG L M ↔ Countable M",
"tactic": "rw [cg_def, Substructure.cg_iff_countable, topEquiv.toEquiv.countable_iff]"
}
] | [
251,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/MonoidAlgebra/NoZeroDivisors.lean | AddMonoidAlgebra.NoZeroDivisors.of_right_ordered | [
{
"state_after": "R : Type u_1\nA : Type u_2\ninst✝⁴ : Semiring R\ninst✝³ : NoZeroDivisors R\ninst✝² : AddLeftCancelSemigroup A\ninst✝¹ : LinearOrder A\ninst✝ : CovariantClass A A (Function.swap fun x x_1 => x + x_1) fun x x_1 => x < x_1\nf g : AddMonoidAlgebra R A\nfg : f ≠ 0 ∧ g ≠ 0\n⊢ f * g ≠ 0",
"state_... | [
162,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.div_card_le | [] | [
571,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.coe_normUnit | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizationMonoid R\np : R[X]\n⊢ ↑(normUnit p) = ↑C ↑(normUnit (leadingCoeff p))",
"tactic": "simp [normUnit]"
}
] | [
97,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Icc a b = Icc ↑a ↑b",
"tactic": "rw [← preimage_coe_Icc, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left\n (Subset.trans Icc_subset_Ici_self <| Ici_subset_Ioi.2 <| bot_lt_c... | [
219,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.mem_image₂_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.11378\nβ : Type u_2\nβ' : Type ?u.11384\nγ : Type u_3\nγ' : Type ?u.11390\nδ : Type ?u.11393\nδ' : Type ?u.11396\nε : Type ?u.11399\nε' : Type ?u.11402\nζ : Type ?u.11405\nζ' : Type ?u.11408\nν : Type ?u.11411\ninst✝⁷ : DecidableEq α'\... | [
78,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_coe_angle_eq_iff | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ ↑(arg x) = ↑(arg y) ↔ arg x = arg y",
"tactic": "simp_rw [← Real.Angle.toReal_inj, arg_coe_angle_toReal_eq_arg]"
}
] | [
504,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
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