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/SetTheory/Game/PGame.lean | PGame.neg_add_le | [] | [
1626,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1625,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_apply | [] | [
408,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.gc_map_comap | [] | [
2152,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2151,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.cycleRange_zero' | [
{
"state_after": "case zero\nh : 0 < Nat.zero\n⊢ cycleRange { val := 0, isLt := h } = 1\n\ncase succ\nn : ℕ\nh : 0 < Nat.succ n\n⊢ cycleRange { val := 0, isLt := h } = 1",
"state_before": "n : ℕ\nh : 0 < n\n⊢ cycleRange { val := 0, isLt := h } = 1",
"tactic": "cases' n with n"
},
{
"state_after"... | [
245,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.map_valEmbedding_Ioi | [
{
"state_after": "case a\nn : ℕ\na b : Fin n\nx : ℕ\n⊢ x ∈ map valEmbedding (Ioi a) ↔ x ∈ Ioc (↑a) (n - 1)",
"state_before": "n : ℕ\na b : Fin n\n⊢ map valEmbedding (Ioi a) = Ioc (↑a) (n - 1)",
"tactic": "ext x"
},
{
"state_after": "case a\nn : ℕ\na b : Fin n\nx : ℕ\n⊢ (∃ a_1, a < a_1 ∧ ↑valEmbe... | [
161,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Topology/Separation.lean | SeparatedNhds.symm | [] | [
123,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_differentiableAt_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_2\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
109,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Std/Logic.lean | or_left_comm | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ a ∨ b ∨ c ↔ b ∨ a ∨ c",
"tactic": "rw [← or_assoc, ← or_assoc, @or_comm a b]"
}
] | [
276,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
276,
1
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Mathlib/Order/UpperLower/Basic.lean | isLowerSet_iInter₂ | [] | [
170,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Irreducible.coprime_iff_not_dvd | [
{
"state_after": "case mp\nR : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : GCDMonoid R\np n : R\npp : Irreducible p\n⊢ IsCoprime p n → ¬p ∣ n\n\ncase mpr\nR : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\... | [
440,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/CategoryTheory/Subterminal.lean | CategoryTheory.subterminals_to_monoOver_terminal_comp_forget | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.flip_a | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_triple_of_mem_affineSpan_pair | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.333927\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np₁ p₂ p₃ p₄ p₅ : P\nh₁ : p₁ ∈ affineSpan k {p₄, p₅}\nh₂ : p₂ ∈ affineSpan k {p₄, p₅}\nh₃ : p₃ ∈ affineSpan k {p₄, p₅}\n⊢ {p₁, p₂, p₃} ⊆ ... | [
598,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_apply_infinite | [
{
"state_after": "α : Type u_1\nβ : Type ?u.374309\nγ : Type ?u.374312\nδ : Type ?u.374315\nι : Type ?u.374318\nR : Type ?u.374321\nR' : Type ?u.374324\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝ : MeasurableSpace α\nh... | [
2237,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2230,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_prod | [] | [
1654,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1654,
1
] |
Mathlib/Control/LawfulFix.lean | Part.Fix.approx_mono | [
{
"state_after": "case zero\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\ni j : ℕ\nhij✝ : i ≤ j\nhij : i ≤ Nat.zero\n⊢ approx (↑f) i ≤ approx (↑f) Nat.zero\n\ncase succ\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\ni j✝ : ℕ\nhij✝ : i ... | [
71,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.mul_le_sin | [
{
"state_after": "x : ℝ\nhx : 0 ≤ x\nhx' : x ≤ π / 2\n⊢ (π / 2)⁻¹ * x ≤ sin x",
"state_before": "x : ℝ\nhx : 0 ≤ x\nhx' : x ≤ π / 2\n⊢ 2 / π * x ≤ sin x",
"tactic": "rw [← inv_div]"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 ≤ x\nhx' : x ≤ π / 2\n⊢ (π / 2)⁻¹ * x ≤ sin x",... | [
253,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.inv_inv_symm_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : DivisionMonoid G\na x y : G\n⊢ (a⁻¹ * x⁻¹)⁻¹ = (y⁻¹ * a⁻¹)⁻¹ ↔ SemiconjBy a y x",
"tactic": "rw [mul_inv_rev, mul_inv_rev, inv_inv, inv_inv, inv_inv, eq_comm, SemiconjBy]"
}
] | [
188,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_radical_of_surjective | [
{
"state_after": "R : Type u_1\nS : Type u_2\nF : Type ?u.1989731\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : R →+* S\nhf : Function.Surjective ↑f\nI : Ideal R\nh : RingHom.ker f ≤ I\n⊢ map f (sInf {J | I ≤ J ∧ IsPrime J}) = sInf {J | map f I ≤ J ∧ IsPrime J}",
"state_before": "R : Type u_1\nS : Type u_2\... | [
2182,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2170,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.card_le_card_of_le | [] | [
826,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.all_one_of_le_one_le_of_prod_eq_one | [] | [
521,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | padic_polynomial_dist | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\nx y z : ℤ_[p]\nhz : Polynomial.eval x F - Polynomial.eval y F = z * (x - y)\n⊢ ‖Polynomial.eval x F - Polynomial.eval y F‖ = ‖z‖ * ‖x - y‖",
"tactic": "simp [hz]"
},
{
"state_after": "case h\np... | [
51,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_mul_left' | [] | [
1011,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
21
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup'_apply | [] | [
1045,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
11
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.inner_le_Lp_mul_Lq | [
{
"state_after": "case pos\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\np q : ℝ\nhpq : Real.IsConjugateExponent p q\nhF_zero : ∑ i in s, f i ^ p = 0\n⊢ ∑ i in s, f i * g i ≤ (∑ i in s, f i ^ p) ^ (1 / p) * (∑ i in s, g i ^ q) ^ (1 / q)\n\ncase neg\nι : Type u\ns : Finset ι\nf g : ι → ℝ≥0\np q : ℝ\nhpq : Real.IsCon... | [
377,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.ennrealRatEmbed_encode | [
{
"state_after": "α : Type ?u.833800\nβ : Type ?u.833803\nγ : Type ?u.833806\nδ : Type ?u.833809\ninst✝ : MeasurableSpace α\nK : Type ?u.833815\nq : ℚ\n⊢ ENNReal.ofReal ↑(Option.getD (Option.some q) 0) = ↑(Real.toNNReal ↑q)",
"state_before": "α : Type ?u.833800\nβ : Type ?u.833803\nγ : Type ?u.833806\nδ : T... | [
885,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.sumCongr_apply | [] | [
308,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.range_algebraMap | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nA✝ : Type v\nB : Type w\ninst✝⁷ : CommSemiring R✝\ninst✝⁶ : Semiring A✝\ninst✝⁵ : Algebra R✝ A✝\ninst✝⁴ : Semiring B\ninst✝³ : Algebra R✝ B\nS✝ : Subalgebra R✝ A✝\nα : Type ?u.1952524\nβ : Type ?u.1952527\nR : Type u_1\nA : Type u_2\ninst✝² : CommRi... | [
1323,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1320,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.ge_iff | [] | [
456,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Std/Data/List/Lemmas.lean | List.mem_of_mem_eraseP | [] | [
998,
87
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
998,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.tsum_mul_le_mul_norm' | [] | [
553,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
11
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.init_update_castSucc | [
{
"state_after": "case h\nm n : ℕ\nα : Fin (n + 1) → Type u\nx : α (last n)\nq : (i : Fin (n + 1)) → α i\np : (i : Fin n) → α (↑castSucc i)\ni : Fin n\ny : α (↑castSucc i)\nz : α (last n)\nj : Fin n\n⊢ init (update q (↑castSucc i) y) j = update (init q) i y j",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Ty... | [
569,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.Subgroup.val_conj_smul | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.blocks_length | [] | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.map_comp_C | [
{
"state_after": "case a\nσ : Type u_3\nτ : Type ?u.756968\nR : Type u_1\nS : Type u_2\nT : Type ?u.756977\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* S\nx✝ : R\n⊢ ↑(RingHom.comp (map f) C) x✝ = ↑(RingHom.comp C f) x✝",
"state_before": "σ :... | [
283,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_le_neg_iff | [] | [
1322,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.map_comp | [
{
"state_after": "case h\nC : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\nf : X ⟶ Y\ng : Y ⟶ Z\ninst✝¹ : Mono f\ninst✝ : Mono g\nt : MonoOver X\n⊢ (map (f ≫ g)).obj (Quotient.mk'' t) = (map g).obj ((map f).obj (Quotient.mk'' t))",
"state_before": "C : Type u₁\ninst✝³ : Categor... | [
592,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.IsPartition.iUnion_subset | [] | [
742,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.cancel_iso_hom_right | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX✝ Y✝ Z✝ X Y Z : C\nf f' : X ⟶ Y\ng : Y ≅ Z\n⊢ f ≫ g.hom = f' ≫ g.hom ↔ f = f'",
"tactic": "simp only [cancel_mono]"
}
] | [
550,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_self | [
{
"state_after": "n : Nat\nH : 0 < n\nt : (0 + n) / n = succ (0 / n) := add_div_right 0 H\n⊢ n / n = 1",
"state_before": "n : Nat\nH : 0 < n\n⊢ n / n = 1",
"tactic": "let t := add_div_right 0 H"
},
{
"state_after": "no goals",
"state_before": "n : Nat\nH : 0 < n\nt : (0 + n) / n = succ (0 / ... | [
578,
40
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
576,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_sUnion | [
{
"state_after": "no goals",
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180,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_le_index | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nK : Compacts G\nhU : Set.Nonempty (interior U)\n⊢ ↑(index (↑K) U) / ↑(index (↑K₀) U) ≤ ↑(index ↑K ↑K₀)",
"state_before": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : To... | [
307,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_positive | [
{
"state_after": "α : Type u_1\nβ : Type ?u.63811\ninst✝² : MeasurableSpace α\ns : SignedMeasure α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nu v w : Set α\nhu : MeasurableSet u\nhv : MeasurableSet v\nhw : MeasurableSet w\nhsu : VectorMeasure.restrict 0 u ≤ VectorMeasure.restrict s... | [
345,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mul_mem_sup | [] | [
827,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.trans | [] | [
1662,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1661,
1
] |
Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.toOrdinal_eq_one | [] | [
120,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_map_snoc_le | [
{
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1317,
23
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1310,
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Mathlib/Order/SuccPred/Basic.lean | Order.covby_succ | [] | [
362,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.nat_cast_mul | [] | [
929,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
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Mathlib/Data/List/Basic.lean | List.getD_nil | [] | [
4376,
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4375,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_mul_of_not_infinitesimal_pos_infinitePos | [] | [
826,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Basic.lean | min_def' | [
{
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_mul | [] | [
326,
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Mathlib/Order/Lattice.lean | Prod.mk_inf_mk | [] | [
1264,
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1262,
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Mathlib/Algebra/Order/Field/Basic.lean | min_div_div_right_of_nonpos | [] | [
993,
71
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992,
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Std/Data/Nat/Gcd.lean | Nat.gcd_dvd_gcd_mul_left | [] | [
132,
51
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131,
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Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_restrict_of_forall_set_integral_eq | [
{
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408,
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.injective | [] | [
126,
28
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_X | [
{
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880,
26
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879,
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Mathlib/Data/ZMod/Basic.lean | ZMod.natAbs_min_of_le_div_two | [
{
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{
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1103,
44
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1090,
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Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsBigO.trans_isTheta | [] | [
92,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/Data/Fin/Basic.lean | Fin.ext_iff | [] | [
185,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.coequalizer.hom_ext | [] | [
1006,
51
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1004,
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Mathlib/Data/Finset/Basic.lean | Finset.union_idempotent | [] | [
1409,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
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Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_E8 | [] | [
159,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.eq_factorization_iff | [
{
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321,
49
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Mathlib/Analysis/Convex/Gauge.lean | gauge_lt_eq' | [
{
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179,
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173,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.restrict_map | [] | [
4318,
41
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Mathlib/Logic/Basic.lean | Eq.congr | [
{
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{
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578,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_comap_pow | [
{
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1835,
67
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.coeFn_negPart_eq_max | [
{
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1125,
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1122,
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Mathlib/Algebra/Group/Defs.lean | inv_one | [] | [
993,
22
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992,
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Mathlib/Topology/Algebra/Monoid.lean | exists_nhds_one_split | [] | [
489,
33
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486,
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Mathlib/Analysis/Calculus/MeanValue.lean | StrictAnti.strictConcaveOn_univ_of_deriv | [] | [
1163,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
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Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.isSymmetric_iff_inner_map_self_real | [
{
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163,
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149,
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Mathlib/Data/Nat/Cast/Basic.lean | Nat.coe_castAddMonoidHom | [] | [
49,
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48,
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Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_ge_of_bot | [] | [
247,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.characteristic_iff_le_comap | [] | [
2017,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2014,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | ClosedEmbedding.set_integral_map | [] | [
500,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
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Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.integral_prod_mul | [
{
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_mul_X | [
{
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"tactic": "induction p using Polynomial.induction_on' with\n| h_add p q ph qh =>\n simp only [add_mul, eval_add, ph,... | [
459,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_eq_pow | [] | [
44,
56
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.centralizer_le | [] | [
2312,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2311,
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_eq_zero | [
{
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"tactic": "rw [← NNReal.coe_zero, NNReal.coe_eq]"
}
] | [
216,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.nhds_right' | [] | [
60,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.tendsto_nhds | [] | [
1075,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1073,
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Mathlib/Data/Part.lean | Part.eq_none_iff' | [] | [
185,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.mapRingHom_comp | [] | [
903,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
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Mathlib/Algebra/Lie/Solvable.lean | LieIdeal.derivedSeries_map_eq | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nM : Type w\nL' : Type w₁\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nI J : LieIdeal R L\nf : L' →ₗ⁅R⁆ L\nh : Function.Surjective ↑f\n⊢ map f (derivedSeries R L' Nat.zero) = derivedSeries R L... | [
197,
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Mathlib/Data/Set/Sigma.lean | Set.univ_sigma_univ | [] | [
103,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.mul_div_mul_comm_of_dvd_dvd | [
{
"state_after": "case inl\nR : Type u\ninst✝ : EuclideanDomain R\na b d : R\nhbd : d ∣ b\nhac : 0 ∣ a\n⊢ a * b / (0 * d) = a / 0 * (b / d)\n\ncase inr\nR : Type u\ninst✝ : EuclideanDomain R\na b c d : R\nhac : c ∣ a\nhbd : d ∣ b\nhc0 : c ≠ 0\n⊢ a * b / (c * d) = a / c * (b / d)",
"state_before": "R : Type ... | [
357,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/Sub.lean | MeasureTheory.Measure.sub_apply | [
{
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99,
40
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_congr_measure_of_integrable | [
{
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.Tendsto.pow | [] | [
476,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
11
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Mathlib/LinearAlgebra/Matrix/Dual.lean | LinearMap.toMatrix_transpose | [
{
"state_after": "case a.h\nK : Type u_1\nV₁ : Type u_2\nV₂ : Type u_3\nι₁ : Type u_4\nι₂ : Type u_5\ninst✝⁸ : Field K\ninst✝⁷ : AddCommGroup V₁\ninst✝⁶ : Module K V₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module K V₂\ninst✝³ : Fintype ι₁\ninst✝² : Fintype ι₂\ninst✝¹ : DecidableEq ι₁\ninst✝ : DecidableEq ι₂\nB₁ : ... | [
40,
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35,
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Mathlib/Algebra/NeZero.lean | eq_zero_or_neZero | [] | [
48,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.const_contLinear | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
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Mathlib/Data/List/Forall2.lean | List.forall₂_same | [
{
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : T... | [
61,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_mapTermRel_add_castLe | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type ?u.78808\nP : Type ?u.78811\ninst✝³ : Structure L M\ninst✝² : Structure L N\ninst✝¹ : Structure L P\nα : Type u'\nβ : Type v'\nn✝¹ l : ℕ\nφ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝¹ : Fin l → M... | [
398,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/FieldTheory/Normal.lean | AlgEquiv.restrictNormal_commutes | [] | [
362,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
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