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/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_pi_div_two_sub | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ sin (↑π / 2 - x) = cos x",
"tactic": "simp [sub_eq_add_neg, sin_add]"
}
] | [
1285,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Mathlib/Topology/Constructions.lean | continuous_swap | [] | [
489,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.associator_naturality_right | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng : b ⟶ c\nh h' : c ⟶ d\nη : h ⟶ h'\n⊢ (f ≫ g) ◁ η ≫ (α_ f g h').hom = (α_ f g h).hom ≫ f ◁ g ◁ η",
"tactic": "simp"
}
] | [
375,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/CategoryTheory/Sums/Associator.lean | CategoryTheory.sum.associator_obj_inl_inr | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.ext_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.309500\nδ : Type ?u.309503\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf g : α →ₘ[μ] β\nh : f = g\n⊢ ↑f =ᵐ[μ] ↑g",
"tactic": "rw [... | [
180,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel_map_comp_cokernelComparison | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁸ : Category C\ninst✝⁷ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\nD : Type u₂\ninst✝⁶ : Category D\ninst✝⁵ : HasZeroMorphisms D\nG : C ⥤ D\ninst✝⁴ : Functor.PreservesZeroMorphisms G\nX' Y' : C\ninst✝³ : HasCokernel f\ninst✝² : HasCokernel (G.map ... | [
1159,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.normSq_exp | [
{
"state_after": "no goals",
"state_before": "q : ℍ\n⊢ ↑normSq (exp ℝ q) = ↑normSq (exp ℝ q.re • (↑(Real.cos ‖im q‖) + (Real.sin ‖im q‖ / ‖im q‖) • im q))",
"tactic": "rw [exp_eq]"
},
{
"state_after": "no goals",
"state_before": "q : ℍ\n⊢ ↑normSq (exp ℝ q.re • (↑(Real.cos ‖im q‖) + (Real.sin... | [
133,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_neg_index | [] | [
298,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_neg_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.130316\nE : Type u_2\nF : Type ?u.130322\nG : Type ?u.130325\nE' : Type ?u.130328\nF' : Type u_3\nG' : Type ?u.130334\nE'' : Type ?u.130337\nF'' : Type ?u.130340\nG'' : Type ?u.130343\nR : Type ?u.130346\nR' : Type ?u.130349\n𝕜 : Type ... | [
864,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.836623\nβ : Type ?u.836626\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na b : ℝ≥0∞\n⊢ ENNReal.toNNReal (a / b) = ENNReal.toNNReal a / ENNReal.toNNReal b",
"tactic": "rw [div_eq_mul_inv, toNNReal_mul, toNNReal_inv, div_eq_mul_inv]"
}
] | [
2318,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2317,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.seq_post | [] | [
136,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
11
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.IsFundamentalSequence.ord_cof | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.68576\nr : α → α → Prop\na o : Ordinal\nf : (b : Ordinal) → b < o → Ordinal\nhf : IsFundamentalSequence a o f\ni : Ordinal\nhi : i < ord (cof a)\n⊢ ord (cof a) ≤ o",
"tactic": "rw [hf.cof_eq]"
},
{
"state_after": "α : Type ?u.68576\nr : α... | [
575,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_dvd_gcd_mul_left_right | [] | [
492,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.ae_eq | [] | [
2427,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2426,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.ext_aux | [
{
"state_after": "case zero\nF : PFunctor\nX : Type ?u.30265\nf : X → Obj F X\ninst✝¹ : Inhabited (M F)\ninst✝ : DecidableEq F.A\nn : ℕ\nx✝ y✝ z✝ : M F\nhx✝ : Agree' n z✝ x✝\nhy✝ : Agree' n z✝ y✝\nhrec✝ : ∀ (ps : Path F), n = length ps → iselect ps x✝ = iselect ps y✝\nx y z : M F\nhx : Agree' zero z x\nhy : Agr... | [
623,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_sub | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.5157046\ninst✝ : IsROrC K\nz w : K\n⊢ ↑normSq (z - w) = ↑normSq z + ↑normSq w - 2 * ↑re (z * ↑(starRingEnd K) w)",
"tactic": "simp only [normSq_add, sub_eq_add_neg, map_neg, mul_neg, normSq_neg, map_neg]"
}
] | [
532,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_iff_vanishing | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.690029\nδ : Type ?u.690032\ninst✝³ : AddCommGroup α\ninst✝² : UniformSpace α\ninst✝¹ : UniformAddGroup α\nf g : β → α\na a₁ a₂ : α\ninst✝ : CompleteSpace α\n⊢ Summable f ↔ ∀ (e : Set α), e ∈ 𝓝 0 → ∃ s, ∀ (t : Finset β), D... | [
1152,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
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Mathlib/Data/Finset/Pointwise.lean | Finset.coeMonoidHom_apply | [] | [
842,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.isStrongLimit_aleph0 | [
{
"state_after": "case intro\nα : Type ?u.113582\nr : α → α → Prop\nn : ℕ\nhx : ↑n < ℵ₀\n⊢ 2 ^ ↑n < ℵ₀",
"state_before": "α : Type ?u.113582\nr : α → α → Prop\nx : Cardinal\nhx : x < ℵ₀\n⊢ 2 ^ x < ℵ₀",
"tactic": "rcases lt_aleph0.1 hx with ⟨n, rfl⟩"
},
{
"state_after": "no goals",
"state_bef... | [
874,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_symm | [] | [
61,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measurePreserving_prod_div | [] | [
399,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.neg_re | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticOn.mono | [] | [
591,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.stdBasis_apply | [] | [
56,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.surjective_comp | [] | [
375,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_diff_right_self | [] | [
2070,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2069,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.copy_eq | [] | [
875,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.erase_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\na : R\n⊢ (erase n (↑(monomial n) a)).toFinsupp = 0.toFinsupp",
"tactic": "simp"
}
] | [
1063,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/Order/WithBot.lean | IsMax.withBot | [] | [
247,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.cosh | [] | [
1082,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1081,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Set.prod_self_eq_iUnion_perm | [
{
"state_after": "case h.mk\nι : Type ?u.3084179\nα : Type u_1\nβ : Type ?u.3084185\ninst✝ : DecidableEq α\nf : Perm α\ns : Set α\nhf : IsCycleOn f s\na b : α\n⊢ (a, b) ∈ s ×ˢ s ↔ (a, b) ∈ ⋃ (n : ℤ), (fun a => (a, ↑(f ^ n) a)) '' s",
"state_before": "ι : Type ?u.3084179\nα : Type u_1\nβ : Type ?u.3084185\ni... | [
1917,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1909,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.update_eq_erase_add_single | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ✝ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β✝ i)\ns : Finset ι\nx : (i : ↑↑s) → β✝ ↑i\ni✝ : ι\nf✝ : Π₀ (i : ι), β✝ i\nb✝ : β✝ i✝\nj✝ : ι\nβ : ι → Type u_1\ninst✝ : (i : ι) → AddZeroClass (β i)\nf : Π₀ (i : ... | [
862,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_neg | [] | [
1550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1549,
1
] |
Mathlib/Order/Monotone/Odd.lean | strictMono_of_odd_strictMonoOn_nonneg | [
{
"state_after": "G : Type u_2\nH : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : OrderedAddCommGroup H\nf : G → H\nh₁ : ∀ (x : G), f (-x) = -f x\nh₂ : StrictMonoOn f (Ici 0)\nx : G\nhx : x ∈ Iic 0\ny : G\nhy : y ∈ Iic 0\nhxy : x < y\n⊢ -f y < -f x",
"state_before": "G : Type u_2\nH : Type u_1\nin... | [
33,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.comp_assoc | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.Icc_pred_right | [
{
"state_after": "case a\na b✝ c b : ℕ\nh : 0 < b\nx : ℕ\n⊢ x ∈ Icc a (b - 1) ↔ x ∈ Ico a b",
"state_before": "a b✝ c b : ℕ\nh : 0 < b\n⊢ Icc a (b - 1) = Ico a b",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case a\na b✝ c b : ℕ\nh : 0 < b\nx : ℕ\n⊢ x ∈ Icc a (b - 1) ↔... | [
177,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | dist_mul_right | [] | [
374,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineEquiv.sOppSide_map_iff | [] | [
141,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/FieldTheory/MvPolynomial.lean | MvPolynomial.rank_mvPolynomial | [
{
"state_after": "no goals",
"state_before": "σ K : Type u\ninst✝ : Field K\n⊢ Module.rank K (MvPolynomial σ K) = Cardinal.mk (σ →₀ ℕ)",
"tactic": "rw [← Cardinal.lift_inj, ← (basisMonomials σ K).mk_eq_rank]"
}
] | [
62,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_neg' | [] | [
403,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
11
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Ioi | [] | [
94,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_of_le_one_left' | [] | [
364,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Order/PartialSups.lean | ciSup_partialSups_eq | [
{
"state_after": "case refine'_1\nα : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nf : ℕ → α\nh : BddAbove (Set.range f)\nn : ℕ\n⊢ ↑(partialSups f) n ≤ ⨆ (n : ℕ), f n\n\ncase refine'_2\nα : Type u_1\ninst✝ : ConditionallyCompleteLattice α\nf : ℕ → α\nh : BddAbove (Set.range f)\n⊢ BddAbove (Set.range fun n ... | [
167,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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] |
Mathlib/Combinatorics/Composition.lean | Composition.ones_length | [] | [
499,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_lt_of_le_left | [] | [
317,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_Iio | [] | [
181,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Topology/Separation.lean | disjoint_nhds_nhdsSet | [] | [
1528,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1527,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_distrib_iInter_left | [] | [
1398,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/Data/List/Cycle.lean | List.isRotated_prev_eq | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ : α\nl l' : List α\nh : l ~r l'\nhn : Nodup l\nx : α\nhx : x ∈ l\n⊢ next (reverse l) x (_ : x ∈ reverse l) = next (reverse l') x (_ : x ∈ reverse l')",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ : α\nl l' : Lis... | [
440,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | le_nhds_of_limsSup_eq_limsInf | [] | [
157,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Algebra/GroupWithZero/Divisibility.lean | mul_dvd_mul_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\na b c : α\nhc : c ≠ 0\nd : α\n⊢ b * c = a * c * d ↔ b = a * d",
"tactic": "rw [mul_right_comm, mul_left_inj' hc]"
}
] | [
60,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.add_top | [] | [
1083,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.gc_map_comap | [] | [
842,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
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Mathlib/Data/Rat/Lemmas.lean | Rat.coe_nat_div | [
{
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{
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255,
22
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252,
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Mathlib/Data/Nat/Parity.lean | Nat.even_pow | [
{
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}
] | [
175,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
17
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Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.qRight_zero_left | [
{
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] | [
193,
83
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192,
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.m_le_pos | [] | [
245,
14
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244,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | factorization_one | [
{
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}
] | [
2020,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2020,
1
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Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.recOn_one | [] | [
170,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.tprod_eq_tprodCoeff_one | [] | [
323,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Ioi_of_neg | [
{
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}
] | [
649,
64
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647,
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.isUnit_toStalk | [
{
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473,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
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src/lean/Init/Core.lean | Iff.subst | [] | [
1176,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1175,
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Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.sheafify_isSheaf | [
{
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257,
18
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218,
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Mathlib/Analysis/Convex/Slope.lean | ConvexOn.slope_mono_adjacent | [
{
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52,
14
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.tensor_dite | [
{
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218,
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216,
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Mathlib/Data/Set/Basic.lean | Set.forall_in_swap | [
{
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}
] | [
252,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousLinearMap.toLinear_compLeftContinuousCompact | [
{
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424,
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421,
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Mathlib/Analysis/Complex/CauchyIntegral.lean | DiffContOnCl.hasFPowerSeriesOnBall | [] | [
581,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.IsZero.of_epi | [
{
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244,
31
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241,
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Mathlib/GroupTheory/Congruence.lean | Con.toSetoid_inj | [] | [
203,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Order/CompleteLattice.lean | sInf_eq_iInf' | [] | [
695,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
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Mathlib/RingTheory/Ideal/MinimalPrime.lean | Ideal.exists_comap_eq_of_mem_minimalPrimes | [
{
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"state_before": "R : Type u_2\nS : Type u_1\ninst✝¹ : CommRi... | [
156,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
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Mathlib/Data/Complex/Basic.lean | Complex.abs_im_le_abs | [
{
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"state_before": "z : ℂ\n⊢ z.im ^ 2 ≤ ↑normSq z",
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},
{
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1039,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.card_rootsOfUnity | [
{
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816,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.sSup_add | [
{
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"tactic": "rw [sSup_eq_iSup, biSup_add hs]"
}
] | [
590,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.add_zero' | [
{
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197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_nonempty | [
{
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267,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
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Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_range_succ_div_top | [] | [
240,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Submodule.exists_finset_of_mem_iSup | [
{
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1163,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
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Mathlib/Algebra/Free.lean | Magma.AssocQuotient.quot_mk_assoc | [] | [
355,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Mathlib/NumberTheory/Multiplicity.lean | Int.two_pow_sub_pow' | [
{
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330,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.Orthogonal.indefiniteDiagonal_assoc | [
{
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375,
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362,
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Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Down.card_compression | [
{
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216,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/Data/Sum/Order.lean | WithBot.orderIsoPUnitSumLex_toLex | [] | [
755,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.direction_eq_vectorSpan | [] | [
207,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.zpowers_ne_bot | [] | [
219,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/Parity.lean | even_iff_exists_bit0 | [] | [
236,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_one_left_iff | [
{
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"tactic": "simp [coprime]"
}
] | [
209,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Embedding.map_mem_edgeSet_iff | [] | [
1782,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1781,
1
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mem_graph_snd_inj | [
{
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815,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_ofNat | [
{
"state_after": "no goals",
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"tactic": "rw [Polynomial.map_nat_cast]"
}
] | [
767,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
11
] |
Mathlib/Order/CompleteLattice.lean | ofDual_iSup | [] | [
455,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Data/Subtype.lean | Subtype.ext_val | [] | [
90,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/GameAdd.lean | Sym2.GameAdd.snd_fst | [
{
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197,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | tendsto_zero_of_norm_tendsto_zero | [
{
"state_after": "no goals",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nncs : CauSeq ℤ_[p] norm\nF : Polynomial ℤ_[p]\nhnorm : Tendsto (fun i => ‖Polynomial.eval (↑ncs i) F‖) atTop (𝓝 0)\n⊢ Tendsto (fun e => ‖Polynomial.eval (↑ncs e) F - 0‖) atTop (𝓝 0)",
"tactic": "simpa using hnorm"
}
] | [
87,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
9
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_inv_reverse | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.112709\nα : Type ?u.112712\nM : Type ?u.112715\nN : Type ?u.112718\nP : Type ?u.112721\nM₀ : Type ?u.112724\nG : Type u_1\nR : Type ?u.112730\ninst✝ : Group G\n⊢ (prod [])⁻¹ = prod (reverse (map (fun x => x⁻¹) []))",
"tactic": "simp"
},
{
... | [
417,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.setOf_pow_dvd_eq_Icc_factorization | [
{
"state_after": "case h\nn p : ℕ\npp : Prime p\nhn : n ≠ 0\nx✝ : ℕ\n⊢ x✝ ∈ {i | i ≠ 0 ∧ p ^ i ∣ n} ↔ x✝ ∈ Set.Icc 1 (↑(factorization n) p)",
"state_before": "n p : ℕ\npp : Prime p\nhn : n ≠ 0\n⊢ {i | i ≠ 0 ∧ p ^ i ∣ n} = Set.Icc 1 (↑(factorization n) p)",
"tactic": "ext"
},
{
"state_after": "no... | [
719,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_eq_of_sum_1 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nE : Type u_3\nF : Type ?u.30257\nι : Type u_2\nι' : Type ?u.30263\nα : Type ?u.30266\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ni... | [
77,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_six | [
{
"state_after": "x : ℝ\n⊢ sqrt 3 = cos (π / 6) * 2",
"state_before": "x : ℝ\n⊢ cos (π / 6) = sqrt 3 / 2",
"tactic": "suffices sqrt 3 = cos (π / 6) * 2 by\n field_simp [(by norm_num : 0 ≠ 2)]\n exact this.symm"
},
{
"state_after": "x : ℝ\n⊢ (cos (π / 6) * 2) ^ 2 = 3\n\ncase hx\nx : ℝ\n⊢ 0 ≤ 3\... | [
885,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
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