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/EulerSineProd.lean | EulerSine.integral_cos_mul_cos_pow_aux | [
{
"state_after": "z : ℂ\nn : ℕ\nhn : 2 ≤ n\nhz : z ≠ 0\nder1 : ∀ (x : ℝ), x ∈ uIcc 0 (π / 2) → HasDerivAt (fun y => ↑(cos y) ^ n) (-↑n * ↑(sin x) * ↑(cos x) ^ (n - 1)) x\n⊢ (∫ (x : ℝ) in 0 ..π / 2, Complex.cos (2 * z * ↑x) * ↑(cos x) ^ n) =\n ↑n / (2 * z) * ∫ (x : ℝ) in 0 ..π / 2, Complex.sin (2 * z * ↑x) * ... | [
92,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/Data/Finset/Basic.lean | Finset.not_mem_range_self | [] | [
3013,
30
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3012,
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Mathlib/Logic/Unique.lean | unique_subtype_iff_exists_unique | [
{
"state_after": "case e_val\nα : Sort u_1\np : α → Prop\nx✝¹ : ∃! a, p a\na : α\nha : (fun a => p a) a\nhe : ∀ (y : α), (fun a => p a) y → y = a\nx✝ : Subtype p\nb : α\nhb : p b\n⊢ b = a",
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78,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
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Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.one_def | [] | [
552,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_ite_eq | [] | [
537,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.sum_boole | [
{
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"tactic": "simp only [a... | [
1767,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1764,
1
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Mathlib/Topology/Algebra/FilterBasis.lean | ContinuousSMul.of_basis_zero | [
{
"state_after": "case hmul\nR : Type u_2\nM : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : TopologicalSpace R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\nB : ModuleFilterBasis R M\nι : Type u_1\ninst✝² : TopologicalRing R\ninst✝¹ : TopologicalSpace M\ninst✝ : TopologicalAddGroup M\np : ι → Prop\nb : ι → Set M\nh... | [
433,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_coe_angle_toReal_eq_arg | [
{
"state_after": "z : ℂ\n⊢ arg z ∈ Set.Ioc (-π) π",
"state_before": "z : ℂ\n⊢ Angle.toReal ↑(arg z) = arg z",
"tactic": "rw [Real.Angle.toReal_coe_eq_self_iff_mem_Ioc]"
},
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ arg z ∈ Set.Ioc (-π) π",
"tactic": "exact arg_mem_Ioc _"
}
... | [
494,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_restrict_of_ae_eq_of_ae_restrict | [
{
"state_after": "no goals",
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2927,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2926,
1
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Mathlib/Topology/Algebra/Ring/Basic.lean | TopologicalRing.of_nhds_zero | [] | [
219,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_one | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.openEmbedding_of_pullback_open_embeddings | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\ng : Y ⟶ S\nH₁ : OpenEmbedding ((forget TopCat).map f)\nH₂ : OpenEmbedding ((forget TopCat).map g)\ne_2✝ : (forget TopCat).obj ((cospan f g).obj WalkingCospan.one) = (forget TopCat).obj S\n⊢ (forget... | [
341,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_cos_pow_three | [
{
"state_after": "a b : ℝ\nn : ℕ\nthis : (∫ (x : ℝ) in a..b, sin x ^ 0 * cos x ^ (2 * 1 + 1)) = ∫ (u : ℝ) in sin a..sin b, u ^ 0 * (1 - u ^ 2) ^ 1\n⊢ (∫ (x : ℝ) in a..b, cos x ^ 3) = sin b - sin a - (sin b ^ 3 - sin a ^ 3) / 3",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, cos x ^ 3) = sin b - sin... | [
783,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.zero | [] | [
361,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inl_desc | [] | [
1377,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1375,
1
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Mathlib/Data/Rat/Defs.lean | Rat.coe_int_eq_divInt | [] | [
112,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_restrict | [] | [
1639,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.ext' | [] | [
62,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardObj_obj | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_comm | [] | [
310,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Set/Function.lean | Set.RightInvOn.mono | [] | [
1143,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Left.mul_lt_one_of_lt_of_le | [] | [
626,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Data/Part.lean | Part.div_def | [] | [
702,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.bot_mul | [
{
"state_after": "α : Type ?u.250853\nG : Type ?u.250856\nM : Type ?u.250859\nR : Type u_1\nA : Type ?u.250865\ninst✝² : Monoid M\ninst✝¹ : AddMonoid A\ninst✝ : NonUnitalNonAssocSemiring R\nS : AddSubmonoid R\nm : R\nhm : m = 0\nn : R\nhn : n ∈ S\n⊢ m * n = 0",
"state_before": "α : Type ?u.250853\nG : Type ... | [
582,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | IsEquivalent.summable_iff | [] | [
712,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_diff_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.210763\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioc a b \\ Iic c = Ioc (max a c) b",
"tactic": "rw [diff_eq, compl_Iic, Ioc_inter_Ioi, sup_eq_max]"
}
] | [
1837,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1836,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotientInfEquivSupQuotient_symm_apply_left | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\nM₂ : Type ?u.100895\nM₃ : Type ?u.100898\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M₂\ninst✝³ : AddCommGroup M₃\ninst✝² : Module R M\ninst✝¹ : Module R M₂\ninst✝ : Module R M₃\nf : M →ₗ[R] M₂\np p' : Submodule R... | [
133,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.support_C_mul_T | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\na : R\nn : ℤ\n⊢ (Finsupp.single n a).support ⊆ {n}",
"state_before": "R : Type u_1\ninst✝ : Semiring R\na : R\nn : ℤ\n⊢ (↑C a * T n).support ⊆ {n}",
"tactic": "rw [← single_eq_C_mul_T]"
},
{
"state_after": "no goals",
"state_before": "R : T... | [
438,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.uncurrySum_apply | [] | [
1805,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
1
] |
Mathlib/Analysis/NormedSpace/Star/Basic.lean | CstarRing.nnnorm_star_mul_self | [] | [
134,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeRing.coe_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u\nx y : FreeRing α\n⊢ ↑(x - y) = ↑x - ↑y",
"tactic": "rw [castFreeCommRing, map_sub]"
}
] | [
355,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
11
] |
Mathlib/Order/RelClasses.lean | transitive_gt | [] | [
913,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.unit_mul_pow_congr_pow | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\np q : R\nhp : Irreducible p\nhq : Irreducible q\nu v : Rˣ\nm n : ℕ\nh : ↑u * p ^ m = ↑v * q ^ n\nkey : Associated (Multiset.prod (Multiset.replicate m p)) (Multiset.prod (Multiset.replicate n q))\n⊢ m = n"... | [
382,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_neg_right | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1737773\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ↑(starRingEnd 𝕜) (-inner y x) = -inner x y",
"state_before"... | [
641,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_mk_le | [] | [
494,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_proj_le | [] | [
389,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Data/Nat/Cast/Defs.lean | two_add_one_eq_three | [
{
"state_after": "α : Type u_1\ninst✝ : AddMonoidWithOne α\n⊢ ↑(1 + 1 + 1) = 3",
"state_before": "α : Type u_1\ninst✝ : AddMonoidWithOne α\n⊢ 2 + 1 = 3",
"tactic": "rw [←one_add_one_eq_two, ←Nat.cast_one, ←Nat.cast_add, ←Nat.cast_add]"
},
{
"state_after": "case h\nα : Type u_1\ninst✝ : AddMonoid... | [
236,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | isometry_id | [] | [
99,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Finsupp/BigOperators.lean | Finset.mem_sup_support_iff | [] | [
80,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Nat/Size.lean | Nat.size_eq_bits_len | [
{
"state_after": "case z\n\n⊢ List.length (bits 0) = size 0\n\ncase f\nb : Bool\nn : ℕ\nh : n = 0 → b = true\nih : List.length (bits n) = size n\n⊢ List.length (bits (bit b n)) = size (bit b n)",
"state_before": "n : ℕ\n⊢ List.length (bits n) = size n",
"tactic": "induction' n using Nat.binaryRec' with ... | [
182,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.StructuredArrow.ext | [] | [
143,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.any_functor_const_on_obj | [
{
"state_after": "case as\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : IsPreconnected J\nα : Type u₁\nF : J ⥤ Discrete α\nj j' : J\n⊢ (F.obj j).as = (F.obj j').as",
"state_before": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : IsPreconnected J\n... | [
103,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.add | [
{
"state_after": "no goals",
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522,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
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] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_hasBasis | [] | [
86,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
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] |
Mathlib/Topology/ContinuousOn.lean | continuous_piecewise | [] | [
1205,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1202,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.disjoint_sup_right | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.140859\nα : Type u_1\nβ : Type ?u.140865\nγ : Type ?u.140868\nι : Type u_2\nκ : Type ?u.140874\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\ns : Finset ι\nt : Finset κ\nf : ι → α\ng : κ → α\na : α\n⊢ _root_.Disjoint a (sup s f) ↔ ∀ ⦃i : ι⦄, i ∈ s →... | [
528,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
11
] |
Mathlib/Order/Basic.lean | lt_of_le_of_ne' | [] | [
100,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.isSymmetric_iff_sesqForm | [] | [
73,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_splits_gcd_left | [] | [
261,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | dist_midpoint_midpoint_le' | [
{
"state_after": "α : Type ?u.73606\nV : Type u_3\nP : Type u_1\nW : Type ?u.73615\nQ : Type ?u.73618\ninst✝⁹ : SeminormedAddCommGroup V\ninst✝⁸ : PseudoMetricSpace P\ninst✝⁷ : NormedAddTorsor V P\ninst✝⁶ : NormedAddCommGroup W\ninst✝⁵ : MetricSpace Q\ninst✝⁴ : NormedAddTorsor W Q\n𝕜 : Type u_2\ninst✝³ : Norme... | [
220,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | subobject_ofLE_as_imageToKernel | [] | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lsub_pos | [] | [
1669,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1668,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.div_eq_mul_inv | [
{
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587,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
11
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Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.transAssocReparamAux_mem_I | [
{
"state_after": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\nt : ↑I\n⊢ (if ↑t ≤ 1 / 4 then 2 * ↑t else if ↑t ≤ 1 / 2 then ↑t + 1 / 4 else 1 / 2 * (↑t + 1)) ∈ I",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\... | [
215,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
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Std/Data/List/Lemmas.lean | List.erase_subset | [] | [
1077,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1077,
1
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Mathlib/Topology/UniformSpace/Basic.lean | mem_nhds_right | [] | [
801,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Topology/Basic.lean | interior_eq_univ | [] | [
339,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Order/Antisymmetrization.lean | toAntisymmetrization_le_toAntisymmetrization_iff | [] | [
185,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.of_discrete | [] | [
71,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_sub | [] | [
219,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_iSup_decode₂ | [
{
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720,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | dist_vsub_cancel_right | [] | [
164,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.range_le | [] | [
145,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
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Mathlib/Analysis/NormedSpace/Pointwise.lean | ball_sub_ball | [
{
"state_after": "no goals",
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355,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
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Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.toMonoidHom_coe | [] | [
639,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.toPlus_mk | [
{
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193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
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Mathlib/Data/Multiset/Sum.lean | Multiset.disjSum_zero | [] | [
43,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernelIsoOfEq_refl | [
{
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"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms ... | [
352,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_ncard_insert | [
{
"state_after": "no goals",
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"tactic": "classical\nrefine'\n s.finite_or_infinite.elim (fun h ↦ _) (fun h ↦ by (rw [h.ncard]; exact Nat.zero_le _))\nrw [ncard_inse... | [
177,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Algebra/Order/Interval.lean | Interval.length_pure | [] | [
696,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
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Mathlib/Algebra/DirectLimit.lean | Field.DirectLimit.inv_mul_cancel | [
{
"state_after": "no goals",
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736,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
11
] |
Mathlib/Analysis/Calculus/Deriv/Star.lean | HasDerivAtFilter.star | [
{
"state_after": "no goals",
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40,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
18
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | Basis.exists_op_nnnorm_le | [
{
"state_after": "case intro\n𝕜 : Type u\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type v\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type w\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nF' : Type x\ninst✝⁶ : AddCommGroup F'\ninst✝⁵ : Module 𝕜 F'\ninst✝⁴ : TopologicalSpace F'... | [
306,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_self_symm | [] | [
996,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.mem_map_rangeS | [
{
"state_after": "case mp\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\np : S[X]\n⊢ p ∈ RingHom.rangeS (mapRingHom f) → ∀ (n : ℕ), coeff p n ∈ RingHom.rangeS f\n\ncase mpr\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na... | [
926,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
915,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_inv | [] | [
733,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.mul_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\ninst✝¹ : LinearOrderedAddCommMonoidWithTop R✝\nR : Type u_1\ninst✝ : LinearOrderedAddCommMonoid R\na b : Tropical (WithTop R)\n⊢ a * b = 0 ↔ a = 0 ∨ b = 0",
"tactic": "simp [← untrop_inj_iff, WithTop.add_eq_top]"
}
] | [
580,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.uniformEquiv_mk_coe_symm | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Trivialization.Prod.continuous_to_fun | [
{
"state_after": "B : Type u_3\ninst✝⁴ : TopologicalSpace B\nF₁ : Type u_5\ninst✝³ : TopologicalSpace F₁\nE₁ : B → Type u_2\ninst✝² : TopologicalSpace (TotalSpace E₁)\nF₂ : Type u_4\ninst✝¹ : TopologicalSpace F₂\nE₂ : B → Type u_1\ninst✝ : TopologicalSpace (TotalSpace E₂)\ne₁ : Trivialization F₁ TotalSpace.proj... | [
186,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_mem_nhds | [] | [
701,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/LinearAlgebra/Matrix/Trace.lean | Matrix.trace_transpose | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.zero_apply | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.finset_iUnion_left_iff | [] | [
126,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.fract_mem | [] | [
63,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.uniformContinuous_neg | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nε : ℝ\nε0 : ε > 0\na✝ b✝ : ℝ\nh : dist b✝ a✝ < ε\n⊢ dist (-a✝) (-b✝) < ε",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nε : ℝ\nε0 : ε > 0\na✝ b✝ : ℝ\nh : dist a✝ b✝ < ε\n⊢ dist (-a✝) (-b✝) < ε",
"tactic": "rw [dist_comm] at h"
},
{
"s... | [
49,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | Submodule.eq_top_of_nonempty_interior' | [
{
"state_after": "case intro\nR : Type u_1\nM : Type u_2\ninst✝⁷ : Ring R\ninst✝⁶ : TopologicalSpace R\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : AddCommGroup M\ninst✝³ : ContinuousAdd M\ninst✝² : Module R M\ninst✝¹ : ContinuousSMul R M\ninst✝ : NeBot (𝓝[{x | IsUnit x}] 0)\ns : Submodule R M\ny : M\nhy : y ∈ inter... | [
74,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.is_rat | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ_[p]\nh : q = 0\n⊢ ‖q‖ = ↑0",
"tactic": "simp [h]"
}
] | [
883,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
11
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.even_card_iff_char_two | [
{
"state_after": "case intro.intro\nK : Type ?u.1097070\nR : Type ?u.1097073\nF : Type u_1\ninst✝¹ : Field F\ninst✝ : Fintype F\nn : ℕ+\nhp : Nat.Prime (ringChar F)\nh : Fintype.card F = ringChar F ^ ↑n\n⊢ ringChar F = 2 ↔ Fintype.card F % 2 = 0",
"state_before": "K : Type ?u.1097070\nR : Type ?u.1097073\nF... | [
513,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_le_re_and_im_le | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\n⊢ frontier {z | a ≤ z.re ∧ z.im ≤ b} = {z | a ≤ z.re ∧ z.im = b ∨ z.re = a ∧ z.im ≤ b}",
"tactic": "simpa only [closure_Ici, closure_Iic, frontier_Ici, frontier_Iic] using\n frontier_reProdIm (Ici a) (Iic b)"
}
] | [
199,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_comp | [] | [
123,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.unit_mul_pow_congr_unit | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\nϖ : R\nhirr : Irreducible ϖ\nu v : Rˣ\nm : ℕ\nh : ↑u * ϖ ^ m = ↑v * ϖ ^ m\n⊢ u = v",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : DiscreteValuationRing R\nϖ : R\nhir... | [
393,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.invertible_iff_generator_nonzero | [
{
"state_after": "case mp\nR : Type ?u.77862\nA : Type ?u.77865\nK : Type u_2\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : IsDomain A\nR₁ : Type u_1\ninst✝⁷ : CommRing R₁\ninst✝⁶ : IsDomain R₁\ninst✝⁵ : Algebra R₁ K\ninst✝⁴ : IsFractionRing R₁ K\nI✝ J : FractionalIdeal R₁⁰ K\nK' : Typ... | [
227,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mul_single_zero_apply | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.2056792\ninst✝¹ : Semiring k\ninst✝ : AddZeroClass G\nf : AddMonoidAlgebra k G\nr : k\nx a : G\n⊢ a + 0 = x ↔ a = x",
"tactic": "rw [add_zero]"
}
] | [
1632,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1630,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.pullback_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nX Y Z : C\nf✝ : Y ⟶ X\nS✝ R : Sieve X\nf : Y ⟶ X\ng : Z ⟶ Y\nS : Sieve X\n⊢ pullback (g ≫ f) S = pullback g (pullback f S)",
"tactic": "simp [Sieve.ext_iff]"
}
] | [
473,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | Differentiable.prod | [] | [
116,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.coe_equivMapOfInjective_apply | [] | [
781,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_eq_of_bounds | [] | [
290,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Std/Data/List/Init/Lemmas.lean | List.head?_cons | [] | [
25,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
25,
9
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.FamilyOfElements.compPresheafMap_comp | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/List/Destutter.lean | List.destutter'_sublist | [
{
"state_after": "case nil\nα : Type u_1\nl : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝¹ b a✝ a : α\n⊢ destutter' R a [] <+ [a]\n\ncase cons\nα : Type u_1\nl✝ : List α\nR : α → α → Prop\ninst✝ : DecidableRel R\na✝¹ b✝ a✝ b : α\nl : List α\nhl : ∀ (a : α), destutter' R a l <+ a :: l\na : α\n⊢ destutte... | [
73,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
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