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/Data/Fin/Tuple/Basic.lean | Fin.preimage_insertNth_Icc_of_mem | [
{
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824,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
821,
1
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Mathlib/Analysis/Convex/Topology.lean | Convex.subset_interior_image_homothety_of_one_lt | [] | [
338,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
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Mathlib/LinearAlgebra/Contraction.lean | dualTensorHomEquivOfBasis_symm_cancel_left | [
{
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197,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.algebraMap_apply | [
{
"state_after": "σ : Type u_1\nR : Type u_3\nA : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nr : R\n⊢ ↑(RingHom.comp (map σ (algebraMap R A)) (C σ R)) r = ↑(C σ A) (↑(algebraMap R A) r)",
"state_before": "σ : Type u_1\nR : Type u_3\nA : Type u_2\ninst✝² : CommSemiring R\nin... | [
653,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
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Mathlib/Data/List/Nodup.lean | List.Nodup.filter | [
{
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"tactic": "simpa using Pairwise.filter (fun a ↦ p a)"
}
] | [
295,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Order/Max.lean | not_isMax_of_lt | [] | [
324,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left | [] | [
375,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
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Mathlib/Data/Nat/Order/Basic.lean | Nat.div_le_of_le_mul' | [
{
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"state_before": "m n k l : ℕ\nh : m ≤ k * n\nk0 : k = 0\n⊢ m / k ≤ n",
"tactic": "rw [k0, Nat.div_zero]"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nh : m ≤ k * n\nk0 : k = 0\n⊢ 0 ≤ n",
"tactic": "apply... | [
386,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
11
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\n⊢ (X ^ n).toFinsupp = Finsupp.single n 1",
"tactic": "rw [X_pow_eq_monomial, toFinsupp_monomial]"
}
] | [
895,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.map_erase | [
{
"state_after": "case empty\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.127295\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nhf : Injective f\nx : α\n⊢ map f (erase 0 x) = erase (map f 0) (f x)\n\ncase cons\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.127295\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β... | [
1338,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_zero_pos | [
{
"state_after": "no goals",
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}
] | [
103,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
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Mathlib/Analysis/Convex/Strict.lean | strictConvex_iff_div | [
{
"state_after": "𝕜 : Type u_1\n𝕝 : Type ?u.221625\nE : Type u_2\nF : Type ?u.221631\nβ : Type ?u.221634\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : AddCommGroup F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\ns : Set E\nx✝ : E\nh : StrictConvex 𝕜 s\nx : E\nh... | [
415,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
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Mathlib/Data/Subtype.lean | Subtype.exists' | [] | [
64,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
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Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.closure_inv | [
{
"state_after": "case a\nα : Type ?u.59382\nG : Type u_1\nM : Type ?u.59388\nR : Type ?u.59391\nA : Type ?u.59394\ninst✝² : Monoid M\ninst✝¹ : AddMonoid A\ns✝ t u : Set M\ninst✝ : Group G\ns : Set G\n⊢ closure s⁻¹ ≤ (closure s)⁻¹\n\ncase a\nα : Type ?u.59382\nG : Type u_1\nM : Type ?u.59388\nR : Type ?u.59391\... | [
174,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | Monotone.vecCons | [] | [
81,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_Prop | [
{
"state_after": "α : Type ?u.126304\nβ : Type ?u.126307\nγ : Type ?u.126310\n⊢ univ.val = True ::ₘ {False}",
"state_before": "α : Type ?u.126304\nβ : Type ?u.126307\nγ : Type ?u.126310\n⊢ univ.val = {True, False}.val",
"tactic": "simp"
},
{
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"state_before": "α : Ty... | [
996,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Data/Option/Basic.lean | Option.pmap_some | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.mul_bot_of_neg | [] | [
969,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
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Mathlib/Data/Option/Basic.lean | Option.map_injective | [
{
"state_after": "no goals",
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"tactic": "rw [Hf (Option.some.inj H)]"
}
] | [
71,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Order.le_cof | [
{
"state_after": "α : Type u_1\nr✝ r : α → α → Prop\ninst✝ : IsRefl α r\nc : Cardinal\n⊢ (∀ (b : Cardinal), b ∈ {c | ∃ S, (∀ (a : α), ∃ b, b ∈ S ∧ r a b) ∧ (#↑S) = c} → c ≤ b) ↔\n ∀ {S : Set α}, (∀ (a : α), ∃ b, b ∈ S ∧ r a b) → c ≤ (#↑S)",
"state_before": "α : Type u_1\nr✝ r : α → α → Prop\ninst✝ : IsRe... | [
87,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
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Mathlib/CategoryTheory/Subobject/Comma.lean | CategoryTheory.StructuredArrow.projectSubobject_factors | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nS : D\nT : C ⥤ D\ninst✝¹ : HasLimits C\ninst✝ : PreservesLimits T\nA P : StructuredArrow S T\nf : P ⟶ A\nhf : Mono f\n⊢ (P.hom ≫ T.map (Subobject.underlyingIso f.right).inv) ≫ T.map (Subobject.arrow (Subobject.mk f.right)) = A... | [
71,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Order/InitialSeg.lean | InitialSeg.acc | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.24005\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : r ≼i s\na✝ : α\nh : Acc r a✝\na : α\nx✝ : ∀ (y : α), r y a → Acc r y\nha : ∀ (y : α), r y a → Acc s (↑f y)\nb : β\nhb : s b (↑f a)\n⊢ Acc s b",
"state_before": "α : Type u_1\nβ : Type u... | [
219,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
11
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.preimage_sphere | [] | [
1039,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
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Mathlib/GroupTheory/Abelianization.lean | Abelianization.map_comp | [] | [
193,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.idealRange_eq_map | [
{
"state_after": "case h\nR : 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... | [
913,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.preimage | [] | [
892,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Monoid.fg_def | [] | [
103,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.prod_right | [] | [
930,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
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] |
Std/Data/Int/Lemmas.lean | Int.le_add_of_neg_add_le_left | [
{
"state_after": "a b c : Int\nh : a + -b ≤ c\n⊢ a ≤ b + c",
"state_before": "a b c : Int\nh : -b + a ≤ c\n⊢ a ≤ b + c",
"tactic": "rw [Int.add_comm] at h"
},
{
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"state_before": "a b c : Int\nh : a + -b ≤ c\n⊢ a ≤ b + c",
"tactic": "exact Int.le_add_of_sub_left_... | [
1000,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
998,
11
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Mathlib/Data/Complex/Exponential.lean | Complex.exp_sum | [] | [
537,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
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Mathlib/Algebra/Ring/BooleanRing.lean | mul_add_mul | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.4614\nγ : Type ?u.4617\ninst✝ : BooleanRing α\na b : α\n⊢ a * b + b * a = 0",
"tactic": "have : a +... | [
103,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.modEq_comm | [] | [
78,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivWithinAt.sub_const | [] | [
539,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.MemBaseSet.mono' | [] | [
365,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.le_nfpBFamily | [] | [
274,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_δ'' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 3)\nj : Fin (n + 2)\nH : i ≤ ↑Fin.castSucc j\n⊢ X.map (SimplexCategory.δ (Fin.succ j)).op ≫ X.map (SimplexCategory.δ (Fin.castLT i (_ : ↑i < n + 2))).op =\n X.map (SimplexCategory.δ i).op ≫ X.map (SimplexCategory.δ ... | [
129,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
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Mathlib/Analysis/Normed/Field/Basic.lean | one_le_nnnorm_one | [] | [
210,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_add | [] | [
780,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
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Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.tMin_le_tMax | [] | [
98,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.of_horiz_isIso | [
{
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324,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
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Mathlib/Order/Filter/Archimedean.lean | atTop_hasAntitoneBasis_of_archimedean | [] | [
107,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Part.lean | Part.ext | [] | [
120,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/Topology/UniformSpace/Basic.lean | mem_nhds_uniformity_iff_left | [
{
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709,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.intervalIntegral_pos_of_pos | [] | [
1320,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
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Mathlib/Order/WithBot.lean | WithTop.ofDual_lt_iff | [] | [
901,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_eq_nnreal | [
{
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_zero | [
{
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Mathlib/Data/Finset/Lattice.lean | Finset.inf_id_set_eq_sInter | [] | [
750,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.two_mul_odd_div_two | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nhn : n % 2 = 1\n⊢ 2 * (n / 2) = n - 1",
"tactic": "conv =>\n rhs\n rw [← Nat.mod_add_div n 2, hn, @add_tsub_cancel_left]"
}
] | [
456,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_lt_of_injective_not_surjective | [] | [
482,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.not_mem_bot | [] | [
728,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Data/Set/Basic.lean | Set.compl_def | [] | [
1624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1623,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieModule.map_lowerCentralSeries_le | [
{
"state_after": "case zero\nR : Type u\nL : Type v\nM : Type w\ninst✝¹⁰ : CommRing R\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\nk : ℕ\nN : LieSubmodule R L M\nM₂ : Type w₁\ninst✝³ : AddCommGroup M₂\ninst✝² : ... | [
168,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_eq_of_degree_eq | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝¹ : Semiring R\np q✝ r : R[X]\ninst✝ : Semiring S\nq : S[X]\nh : degree p = degree q\n⊢ WithBot.unbot' 0 (degree p) = WithBot.unbot' 0 (degree q)",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝¹ : Semiring R\np q✝ r ... | [
166,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_sigma' | [] | [
811,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
11
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.comp_assoc | [] | [
470,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.const_sub | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\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.531341\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
605,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.mkContinuous₂_norm_le | [] | [
768,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.tsum_coe_indicator_ne_top | [] | [
83,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.nonempty_coe | [] | [
108,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_image2_eq_csInf_csSup | [] | [
1400,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.coe_fn_injective | [] | [
113,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/CategoryTheory/Monoidal/CoherenceLemmas.lean | CategoryTheory.MonoidalCategory.unitors_inv_equal | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\n⊢ (λ_ (𝟙_ C)).inv = (ρ_ (𝟙_ C)).inv",
"tactic": "coherence"
}
] | [
76,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.comap_neg_atTop | [] | [
844,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | mem_vectorSpan_pair | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_1\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.372847\np₁ p₂ : P\nv : V\n⊢ v ∈ vectorSpan k {p₁, p₂} ↔ ∃ r, r • (p₁ -ᵥ p₂) = v",
"tactic": "rw [vectorSpan_pair, Su... | [
1282,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Algebra/Parity.lean | Even.isSquare_zpow | [
{
"state_after": "case intro\nF : Type ?u.50615\nα : Type u_1\nβ : Type ?u.50621\nR : Type ?u.50624\ninst✝ : Group α\nn : ℤ\na : α\n⊢ IsSquare (a ^ (n + n))",
"state_before": "F : Type ?u.50615\nα : Type u_1\nβ : Type ?u.50621\nR : Type ?u.50624\ninst✝ : Group α\nn : ℤ\n⊢ Even n → ∀ (a : α), IsSquare (a ^ n... | [
218,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.multiset_prod_mem | [] | [
175,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_le_mul_iff | [
{
"state_after": "α β : Type u\na b : Cardinal\nh : ¬a * b < ℵ₀ ↔ ¬(a = 0 ∨ b = 0 ∨ a < ℵ₀ ∧ b < ℵ₀) := Iff.not mul_lt_aleph0_iff\n⊢ ℵ₀ ≤ a * b ↔ a ≠ 0 ∧ b ≠ 0 ∧ (ℵ₀ ≤ a ∨ ℵ₀ ≤ b)",
"state_before": "α β : Type u\na b : Cardinal\n⊢ ℵ₀ ≤ a * b ↔ a ≠ 0 ∧ b ≠ 0 ∧ (ℵ₀ ≤ a ∨ ℵ₀ ≤ b)",
"tactic": "let h := (@mu... | [
1579,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1577,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.ringEquiv_apply | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Init/Logic.lean | cast_proof_irrel | [] | [
50,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.pow_ne_one_of_pos_of_lt | [] | [
373,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | NNReal.tsum_le_of_sum_range_le | [] | [
1156,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.preimage_image_sigmaMk_of_ne | [
{
"state_after": "case h\nι : Type u_1\nι' : Type ?u.678\nα : ι → Type u_2\nβ : ι → Type ?u.688\ns✝ s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx✝ : (i : ι) × α i\ni j : ι\na : α i\nh : i ≠ j\ns : Set (α j)\nx : α i\n⊢ x ∈ Sigma.mk i ⁻¹' (Sigma.mk j '' s) ↔ x ∈ ∅",
"state_before":... | [
36,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.update_eq_erase_add_single | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.300562\nγ : Type ?u.300565\nι : Type ?u.300568\nM : Type u_2\nM' : Type ?u.300574\nN : Type ?u.300577\nP : Type ?u.300580\nG : Type ?u.300583\nH : Type ?u.300586\nR : Type ?u.300589\nS : Type ?u.300592\ninst✝ : AddZeroClass M\nf : α →₀ M\na : α\nb : M\nj : α\n... | [
1056,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean | Complex.cpow_neg_one | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ x ^ (-1) = x⁻¹",
"tactic": "simpa using cpow_neg x 1"
}
] | [
114,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.dvd | [
{
"state_after": "case pos\nA : Type u_1\nB : Type u_2\ninst✝² : Field A\ninst✝¹ : Ring B\ninst✝ : Algebra A B\nx : B\np : A[X]\nhp : ↑(Polynomial.aeval x) p = 0\nhp0 : p = 0\n⊢ minpoly A x ∣ p\n\ncase neg\nA : Type u_1\nB : Type u_2\ninst✝² : Field A\ninst✝¹ : Ring B\ninst✝ : Algebra A B\nx : B\np : A[X]\nhp :... | [
83,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_of_nonpos_of_nonpos | [] | [
385,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.drop_drop | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\nn m : ℕ\ns : Stream' α\nn✝ : ℕ\n⊢ nth (drop n (drop m s)) n✝ = nth (drop (n + m) s) n✝",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nn m : ℕ\ns : Stream' α\n⊢ drop n (drop m s) = drop (n + m) s",
"tactic": "ext"
},
{
"state_a... | [
68,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/Maps.lean | OpenEmbedding.map_nhds_eq | [] | [
558,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.pointed_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.98911\nG : Type ?u.98914\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\n⊢ Pointed 0",
"tactic": "rw [Pointed, mem_zero]"
}
] | [
460,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_add_nat_mul_two_pi | [] | [
1177,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.exists_le_of_le | [
{
"state_after": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\na b : α\nP Q : Finpartition a\nh : P ≤ Q\nhb : b ∈ Q.parts\nH : ¬∃ c, c ∈ P.parts ∧ c ≤ b\n⊢ False",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderBot α\na b : α\nP Q : Finpartition a\nh : P ≤ Q\nhb : b ∈... | [
340,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/List/Basic.lean | List.Sublist.map | [] | [
3412,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3411,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.toDual_min' | [
{
"state_after": "F : Type ?u.354773\nα : Type u_1\nβ : Type ?u.354779\nγ : Type ?u.354782\nι : Type ?u.354785\nκ : Type ?u.354788\ninst✝ : LinearOrder α\ns✝ : Finset α\nH : Finset.Nonempty s✝\nx : α\ns : Finset α\nhs : Finset.Nonempty s\n⊢ ↑(↑toDual (min' s hs)) = ↑(max' (image (↑toDual) s) (_ : Finset.Nonempt... | [
1452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.sin_eq_zero_iff_angle_eq_zero_or_angle_eq_pi | [] | [
501,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
8
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_le_iff_le_toReal | [
{
"state_after": "case intro\nα : Type ?u.809256\nβ : Type ?u.809259\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ\nb : ℝ≥0\n⊢ ENNReal.ofReal a ≤ ↑b ↔ a ≤ ENNReal.toReal ↑b",
"state_before": "α : Type ?u.809256\nβ : Type ?u.809259\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ\nb : ℝ≥0∞\nhb : b ≠ ⊤\n⊢ ENNReal.ofReal a ≤ b ↔... | [
2140,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2137,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.apply_lineMap | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV1 : Type u_2\nP1 : Type u_3\nV2 : Type u_4\nP2 : Type u_5\nV3 : Type ?u.494433\nP3 : Type ?u.494436\nV4 : Type ?u.494439\nP4 : Type ?u.494442\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ :... | [
603,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsInf_principal | [] | [
567,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.has_compl_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nd : DynkinSystem α\na : Set α\nh : Has d (aᶜ)\n⊢ Has d a",
"tactic": "simpa using d.has_compl h"
}
] | [
569,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.le_toMeasure_apply | [] | [
676,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_zero | [] | [
422,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.order_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\n𝕜' : Type u'\nE : Type v\nF : Type w\nG : Type x\ninst✝¹⁰ : CommRing 𝕜\nn : ℕ\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module 𝕜 E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : TopologicalAddGroup E\ninst✝⁵ : ContinuousConstSMul 𝕜 E\ninst✝⁴ : AddCommGroup F\n... | [
244,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.of_equivalence | [] | [
746,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.pow_totient | [
{
"state_after": "case zero\nK : Type ?u.893582\nR : Type ?u.893585\nx : (ZMod Nat.zero)ˣ\n⊢ x ^ φ Nat.zero = 1\n\ncase succ\nK : Type ?u.893582\nR : Type ?u.893585\nn✝ : ℕ\nx : (ZMod (Nat.succ n✝))ˣ\n⊢ x ^ φ (Nat.succ n✝) = 1",
"state_before": "K : Type ?u.893582\nR : Type ?u.893585\nn : ℕ\nx : (ZMod n)ˣ\n... | [
371,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_neg_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ -Ioo a b = Ioo (-b) (-a)",
"tactic": "simp [← Ioi_inter_Iio, inter_comm]"
}
] | [
167,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Set/Basic.lean | Set.le_eq_subset | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LieSubmodule.toEndomorphism_restrict_eq_toEndomorphism | [
{
"state_after": "case h.a\nR : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN : LieSubmodule R L M\nx : L\nh :\n optParam\n (∀ (m : M) (hm : m ∈ ↑N),\n ... | [
282,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.isOpenMap | [
{
"state_after": "𝕜 : Type u_3\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nf : E →L[𝕜] F\ninst✝¹ : CompleteSpace F\ninst✝ : CompleteSpace E\nsurj : Surjective ↑f\ns : Set E... | [
262,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
11
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.Ioi_top | [] | [
1123,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
8
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.distortion_disjUnion | [] | [
694,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
] |
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