file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/SymmDiff.lean | bihimp_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.36681\nα : Type u_1\nβ : Type ?u.36687\nπ : ι → Type ?u.36692\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ a ⇔ a = ⊤",
"tactic": "rw [bihimp, inf_idem, himp_self]"
}
] | [
246,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Basic.lean | OrderEmbedding.strictMono | [] | [
669,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.support_toSubring | [
{
"state_after": "case a\nR : Type u\nS : Type ?u.88744\ninst✝¹ : Ring R\ninst✝ : Semiring S\nf : R →+* S\nx : S\np : R[X]\nT : Subring R\nhp : ↑(frange p) ⊆ ↑T\ni : ℕ\n⊢ i ∈ support (toSubring p T hp) ↔ i ∈ support p",
"state_before": "R : Type u\nS : Type ?u.88744\ninst✝¹ : Ring R\ninst✝ : Semiring S\nf :... | [
375,
86
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371,
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Mathlib/Logic/Equiv/Defs.lean | Equiv.arrowCongr_symm | [] | [
538,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Data/List/Perm.lean | List.Perm.product_right | [] | [
1108,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
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Mathlib/FieldTheory/PerfectClosure.lean | PerfectClosure.frobenius_mk | [
{
"state_after": "K : Type u\ninst✝² : CommRing K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nx : ℕ × K\n⊢ mk K p x ^ p = mk K p (x.fst, x.snd ^ p)",
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463,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.sum_mem | [] | [
247,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.mem_map_of_surjective | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
1042,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.iUnion | [] | [
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53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1703,
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Mathlib/Topology/Order.lean | isClosed_iSup_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nι : Sort v\nt : ι → TopologicalSpace α\ns : Set α\n⊢ IsClosed s ↔ ∀ (i : ι), IsClosed s",
"tactic": "simp [← @isOpen_compl_iff _ (⨆ i, t i), ← @isOpen_compl_iff _ (t _), isOpen_iSup_iff]"
}
] | [
1002,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
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Mathlib/Order/LocallyFinite.lean | Finset.coe_uIcc | [] | [
509,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
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Mathlib/Data/Set/Image.lean | Set.preimage_singleton_eq_empty | [] | [
1033,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.measurableSet_fiber | [] | [
85,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/Init/Algebra/Classes.lean | total_of | [] | [
312,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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Mathlib/RingTheory/Coprime/Basic.lean | isCoprime_one_right | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommSemiring R\nx y z : R\n⊢ 0 * x + 1 * 1 = 1",
"tactic": "rw [one_mul, zero_mul, zero_add]"
}
] | [
87,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.vector_cons | [
{
"state_after": "α : Type u_1\nβ : Type ?u.361685\nγ : Type ?u.361688\nσ : Type ?u.361691\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nn : ℕ\n⊢ Primrec fun a => a.fst :: Vector.toList a.snd",
"state_before": "α : Type u_1\nβ : Type ?u.361685\nγ : Type ?u.3... | [
1293,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
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Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.toContinuousLinearMap₁_apply | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioi_subset_Ioi_iff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.72368\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioi b ⊆ Ioi a ↔ a ≤ b",
"tactic": "refine' ⟨fun h => _, fun h => Ioi_subset_... | [
1173,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
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Mathlib/GroupTheory/GroupAction/Prod.lean | Prod.pow_swap | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Combinatorics/Composition.lean | CompositionAsSet.toComposition_blocks | [] | [
1043,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
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Mathlib/Logic/Equiv/Fin.lean | coe_finRotate_of_ne_last | [
{
"state_after": "m n : ℕ\ni : Fin (Nat.succ n)\nh : i ≠ Fin.last n\n⊢ ↑(i + 1) = ↑i + 1",
"state_before": "m n : ℕ\ni : Fin (Nat.succ n)\nh : i ≠ Fin.last n\n⊢ ↑(↑(finRotate (n + 1)) i) = ↑i + 1",
"tactic": "rw [finRotate_succ_apply]"
},
{
"state_after": "m n : ℕ\ni : Fin (Nat.succ n)\nh : i ≠ ... | [
454,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
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Mathlib/Order/Cover.lean | Set.OrdConnected.apply_covby_apply_iff | [] | [
355,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
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Mathlib/Topology/ContinuousOn.lean | continuousOn_to_generateFrom_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.347950\nδ : Type ?u.347953\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ns : Set α\nT : Set (Set β)\nf : α → β\nx : α\nx✝ : x ∈ s\n⊢ Tendsto f (𝓝[s] x) (𝓝 (f x)) ↔ ∀ (t : Set β), t ∈... | [
1049,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/AList.lean | AList.not_mem_empty | [] | [
117,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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] |
Mathlib/Data/Quot.lean | Quotient.choice_eq | [] | [
428,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rdropWhile_prefix | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ dropWhile p (reverse l) <:+ reverse l",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\n⊢ rdropWhile p l <+: l",
"tactic": "rw [← reverse_suffix, rdropWhile, reverse_reverse]"
},
{
"state_after": "no goals",
"... | [
135,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.neg | [] | [
680,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.coe_toMonoidWithZeroHom | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.comp_continuous_iff | [] | [
364,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
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] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.inner_def | [] | [
157,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/BooleanAlgebra.lean | compl_injective | [] | [
658,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenspace_le_generalizedEigenspace | [] | [
345,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.next_toList_eq_apply | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np✝ : Perm α\nx✝ : α\np : Perm α\nx y : α\nhy✝ : y ∈ toList p x\nhy : SameCycle p x y ∧ x ∈ support p\n⊢ next (toList p x) y hy✝ = ↑p y",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np✝ : Perm α\nx✝ : α\np... | [
314,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.shortExact | [] | [
328,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
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] |
Mathlib/Algebra/Parity.lean | Even.pow_pos | [
{
"state_after": "case intro\nF : Type ?u.107024\nα : Type ?u.107027\nβ : Type ?u.107030\nR : Type u_1\ninst✝ : LinearOrderedRing R\na : R\nn : ℕ\nha : a ≠ 0\nk : ℕ\nhk : n = k + k\n⊢ 0 < a ^ n",
"state_before": "F : Type ?u.107024\nα : Type ?u.107027\nβ : Type ?u.107030\nR : Type u_1\ninst✝ : LinearOrdered... | [
475,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Algebra/CharP/Basic.lean | frobenius_one | [] | [
364,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Isometry.lean | QuadraticForm.Equivalent.trans | [] | [
119,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.toNat_mul | [
{
"state_after": "case inl\nα β : Type u\ny : Cardinal\n⊢ ↑toNat (0 * y) = ↑toNat 0 * ↑toNat y\n\ncase inr\nα β : Type u\nx y : Cardinal\nhx1 : x ≠ 0\n⊢ ↑toNat (x * y) = ↑toNat x * ↑toNat y",
"state_before": "α β : Type u\nx y : Cardinal\n⊢ ↑toNat (x * y) = ↑toNat x * ↑toNat y",
"tactic": "rcases eq_or_... | [
1805,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1792,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | DirectSum.coe_of_mul_apply_add | [] | [
214,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictAnti.mul' | [] | [
1458,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1455,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.max | [] | [
617,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Dynamics/FixedPoints/Basic.lean | Function.IsFixedPt.left_of_comp | [] | [
75,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.mersenne_coe_X | [
{
"state_after": "case h₁\np : ℕ\n⊢ minFac (2 ^ p - 1) ∣ 2 ^ p - 1",
"state_before": "p : ℕ\n⊢ ↑(mersenne p) = 0",
"tactic": "ext <;> simp [mersenne, q, ZMod.nat_cast_zmod_eq_zero_iff_dvd, -pow_pos]"
},
{
"state_after": "no goals",
"state_before": "case h₁\np : ℕ\n⊢ minFac (2 ^ p - 1) ∣ 2 ^ ... | [
438,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.singleton_vsub_singleton | [] | [
660,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_nonZeroDivisors_le | [] | [
839,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.inv_le_self | [] | [
268,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/RingTheory/Polynomial/Quotient.lean | Ideal.quotient_map_C_eq_zero | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\na : R\nha : a ∈ I\n⊢ ↑(RingHom.comp (Quotient.mk (map C I)) C) a = 0",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (a : R), a ∈ I → ↑(RingHom.comp (Quotient.mk (map C I)) C) a = 0",
"tactic": "intro a ha"
},
{
... | [
83,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.not_frequently | [
{
"state_after": "no goals",
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"tactic": "simp only [Filter.Frequently, not_not]"
}
] | [
1322,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1321,
1
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isCoseparator_unop_iff | [
{
"state_after": "no goals",
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"tactic": "rw [IsSeparator, IsCoseparator, ← isCoseparating_unop_iff, Set.singleton_unop]"
}
] | [
415,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_sup_left | [
{
"state_after": "M : Type u_1\nA : Type ?u.43722\nB : Type ?u.43725\ninst✝ : MulOneClass M\nS T : Submonoid M\n⊢ S ≤ S ⊔ T",
"state_before": "M : Type u_1\nA : Type ?u.43722\nB : Type ?u.43725\ninst✝ : MulOneClass M\nS T : Submonoid M\n⊢ ∀ {x : M}, x ∈ S → x ∈ S ⊔ T",
"tactic": "rw [←SetLike.le_def]"
... | [
239,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pure_mul_pure | [] | [
366,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Filter.Tendsto.congr_dist | [] | [
1471,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_eq_cons | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ support p = u :: List.tail (support p)",
"tactic": "cases p <;> simp"
}
] | [
571,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.Polynomial.exists_of | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁴ : Ring R\nι : Type v\ndec_ι : DecidableEq ι\ninst✝³ : Preorder ι\nG : ι → Type w\ninst✝² : (i : ι) → CommRing (G i)\nf : (i j : ι) → i ≤ j → G i → G j\nf' : (i j : ι) → i ≤ j → G i →+* G j\ninst✝¹ : Nonempty ι\ninst✝ : IsDirected ι fun x x_1 =... | [
464,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
8
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.traceAux_eq | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝⁶ : CommSemiring R\nM : Type v\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nι : Type w\ninst✝³ : DecidableEq ι\ninst✝² : Fintype ι\nκ : Type u_1\ninst✝¹ : DecidableEq κ\ninst✝ : Fintype κ\nb : Basis ι R M\nc : Basis κ R M\nf : M →ₗ[R] M\n⊢ tr... | [
82,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.iSup_range_stdBasis | [
{
"state_after": "case intro\nR : Type u_3\nι : Type u_1\ninst✝⁴ : Semiring R\nφ : ι → Type u_2\ninst✝³ : (i : ι) → AddCommMonoid (φ i)\ninst✝² : (i : ι) → Module R (φ i)\ninst✝¹ : DecidableEq ι\ninst✝ : Finite ι\nval✝ : Fintype ι\n⊢ (⨆ (i : ι), range (stdBasis R φ i)) = ⊤",
"state_before": "R : Type u_3\nι... | [
142,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.uniformCauchySeqOn | [] | [
437,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.mem_centralizer_iff | [] | [
312,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_single | [] | [
124,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Abelian/RightDerived.lean | CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural | [
{
"state_after": "C : Type u\ninst✝⁵ : Category C\nD : Type u\ninst✝⁴ : Category D\nF : C ⥤ D\nX✝ Y✝ Z : C\nf✝ : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z\ninst✝³ : Abelian C\ninst✝² : Abelian D\ninst✝¹ : Functor.Additive F\ninst✝ : EnoughInjectives C\nX Y : C\nf : X ⟶ Y\nP : InjectiveResolution X\nQ : InjectiveResolution Y\n⊢ F.map... | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Topology/Bases.lean | isTopologicalBasis_singletons | [] | [
493,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.mod_zero | [
{
"state_after": "case zero\n\n⊢ mod zero 0 = zero\n\ncase pos\na✝ : PosNum\n⊢ mod (pos a✝) 0 = pos a✝",
"state_before": "n : Num\n⊢ mod n 0 = n",
"tactic": "cases n"
},
{
"state_after": "no goals",
"state_before": "case zero\n\n⊢ mod zero 0 = zero",
"tactic": "rfl"
},
{
"state_a... | [
1663,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1659,
11
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_union | [] | [
448,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.csin | [] | [
196,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1120\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ Icc a b = ∅ ↔ ¬a ≤ b",
"tactic": "rw [← coe_eq_empty, coe_Icc, Set.Icc_eq_empty_iff]"
}
] | [
70,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | derivWithin_id | [] | [
667,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullback.lift_snd | [] | [
1180,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.sum_inner_mul_inner | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.827323\n𝕜 : Type u_2\ninst✝⁹ : IsROrC 𝕜\nE : Type u_3\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.827352\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : Type ?u.827370\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ :... | [
454,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
11
] |
Mathlib/GroupTheory/Nilpotent.lean | nilpotencyClass_zero_iff_subsingleton | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝² : Group G\nH : Subgroup G\ninst✝¹ : Normal H\ninst✝ : Group.IsNilpotent G\n⊢ nilpotencyClass G = 0 ↔ Subsingleton G",
"tactic": "rw [Group.nilpotencyClass, @Nat.find_eq_zero _ (Classical.decPred _), upperCentralSeries_zero,\n subsinglet... | [
618,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
1
] |
Mathlib/Data/List/Sigma.lean | List.Perm.kreplace | [
{
"state_after": "α : Type u\nβ : α → Type v\nl l₁✝ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nb : β a\nl₁ l₂ : List (Sigma β)\nnd : NodupKeys l₁\n⊢ ∀ {a_1 b_1 : Sigma β},\n a_1.fst ≠ b_1.fst →\n ∀ (c : Sigma β),\n (c ∈ if a = a_1.fst then some { fst := a, snd := b } else none) →\n ... | [
387,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Std/Data/List/Lemmas.lean | List.Sublist.append_right | [] | [
371,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
368,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.monotone | [] | [
351,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
11
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.closedComplemented_of_closed_compl | [] | [
130,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhdsWithin_Ioi_one_neBot | [] | [
220,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_div | [] | [
131,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearEquiv.toSpanNonzeroSingleton_one | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.381021\nK : Type ?u.381024\nM : Type u_1\nM₂ : Type ?u.381030\nV : Type ?u.381033\nS : Type ?u.381036\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : NoZeroSMulDivisors R M\nx : M\nh : x ≠ 0\n⊢ ↑(↑(toSpanNonzeroSingleton R M x h) 1) = ↑{ val :... | [
1031,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumAssoc_symm_apply_inr_inr | [] | [
599,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.modOf_apply_of_not_exists_add | [] | [
138,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_le_inv_mul_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LE α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a * b⁻¹ ≤ d⁻¹ * c ↔ d * a ≤ c * b",
"tactic": "r... | [
358,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Fin/Tuple/Sort.lean | Tuple.eq_sort_iff' | [
{
"state_after": "case mp\nn : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\nh : σ = sort f\n⊢ StrictMono ↑(σ.trans (graphEquiv₁ f))\n\ncase mpr\nn : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nσ : Equiv.Perm (Fin n)\nh : StrictMono ↑(σ.trans (graphEquiv₁ f))\n⊢ σ = s... | [
139,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.Dart.edge_fiber | [
{
"state_after": "no goals",
"state_before": "V : Type u\nG : SimpleGraph V\ninst✝³ : Fintype V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype (Sym2 V)\ninst✝ : DecidableEq V\nd d' : Dart G\n⊢ d' ∈ filter (fun d' => edge d' = edge d) univ ↔ d' ∈ {d, symm d}",
"tactic": "simpa using dart_edge_eq_iff d' d... | [
88,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Iio_self | [] | [
737,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.apply_symm_apply | [] | [
165,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.neg_apply | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Multiset/Functor.lean | Multiset.id_traverse | [
{
"state_after": "F : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommApplicative F\nα' β' : Type u\nf : α' → F β'\nα : Type u_1\nx : Multiset α\n⊢ ∀ (a : List α), traverse pure (Quotient.mk (isSetoid α) a) = Quotient.mk (isSetoid α) a",
"state_before": "F : Type u → Type u\ninst✝¹ : Applicative F\nins... | [
106,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.dvd_lcm_left | [] | [
91,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.epsilon_ne_zero | [] | [
190,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | HasDerivWithinAt.arctan | [] | [
146,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.orderEmbOfFin_boundaries | [
{
"state_after": "n : ℕ\nc : Composition n\n⊢ ∀ (x : Fin (length c + 1)), ↑(boundary c) x ∈ boundaries c",
"state_before": "n : ℕ\nc : Composition n\n⊢ Finset.orderEmbOfFin (boundaries c) (_ : Finset.card (boundaries c) = length c + 1) = boundary c",
"tactic": "refine' (Finset.orderEmbOfFin_unique' _ _)... | [
302,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mk_mem_graph_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.366\nγ : Type ?u.369\nι : Type ?u.372\nM : Type u_2\nM' : Type ?u.378\nN : Type ?u.381\nP : Type ?u.384\nG : Type ?u.387\nH : Type ?u.390\nR : Type ?u.393\nS : Type ?u.396\ninst✝ : Zero M\na : α\nm : M\nf : α →₀ M\n⊢ (∃ a_1,\n ↑f a_1 ≠ 0 ∧\n ↑{ toFun := fu... | [
77,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Set/Function.lean | Set.range_restrictPreimage | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.25203\nι : Sort ?u.25206\nπ : α → Type ?u.25211\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\n⊢ range (MapsTo.restrict f (f ⁻¹' t) t (_ : MapsTo f (f ⁻¹' t) t)) = Subtype.... | [
562,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_sub_pi | [] | [
1015,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.monotone_smallSets | [] | [
94,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isGLB_ciInf_set | [] | [
509,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.one_apply | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.surjective_comp | [] | [
188,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.edgeDensity_comm | [] | [
430,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.mkPiField_eq_iff | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
915,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | hasDerivAt_of_tendstoUniformlyOnFilter | [
{
"state_after": "ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝³ : IsROrC 𝕜\nG : Type u_3\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\ninst✝ : NeBot l\nhf' : TendstoUniformlyOnFilter f' g' l (𝓝 x)\nhf : ∀ᶠ (n : ι × 𝕜) in l ×ˢ ... | [
530,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_erase | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.92014\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝ : Finset α\nt : Finset β\na✝ : α\nb✝ c : β\ninst✝ : DecidableEq α\nf : α → β\nhf : Injective f\ns : Finset α\na : α\nb : β\n⊢ b ∈ image f (erase s a) → b ∈ erase (image f s) (f a)",
"state_before": "α :... | [
522,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
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