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/NormedSpace/Exponential.lean | expSeries_sum_eq_div | [] | [
181,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.compl_not_mem_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.7081\nf g : Ultrafilter α\ns t : Set α\np q : α → Prop\nhsc : ¬sᶜ ∈ f\nh : ↑f ⊓ 𝓟 s = ⊥\n⊢ ↑f ⊓ 𝓟 (sᶜᶜ) = ⊥",
"tactic": "rwa [compl_compl]"
}
] | [
126,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Relations.realize_symmetric | [] | [
1010,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
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Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.multinomial_pos | [] | [
53,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_one | [] | [
438,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Algebra/GroupPower/Basic.lean | pow_right_comm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.22873\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\nm n : ℕ\n⊢ (a ^ m) ^ n = (a ^ n) ^ m",
"tactic": "rw [← pow_mul, Nat.mul_comm, pow_mul]"
}
] | [
160,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_subset_Ico_iff | [] | [
565,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
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Mathlib/Data/Fintype/List.lean | Multiset.mem_lists_iff | [
{
"state_after": "case h\nα : Type u_1\ninst✝ : DecidableEq α\nl a✝ : List α\n⊢ l ∈ lists (Quotient.mk (isSetoid α) a✝) ↔ Quotient.mk (isSetoid α) a✝ = Quotient.mk (isSetoid α) l",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns : Multiset α\nl : List α\n⊢ l ∈ lists s ↔ s = Quotient.mk (isSetoid α) ... | [
56,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
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Mathlib/Data/Int/Order/Basic.lean | Int.lt_mul_of_ediv_lt | [] | [
455,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
11
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.add_modEq_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\n⊢ a + b ≡ b [PMOD p] ↔ a ≡ 0 [PMOD p]",
"tactic": "simp [← modEq_sub_iff_add_modEq]"
}
] | [
289,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
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Std/Data/RBMap/WF.lean | Std.RBNode.balance1_eq | [
{
"state_after": "α : Type u_1\nc : RBColor\nn : Nat\nl : RBNode α\nv : α\nr : RBNode α\nhl : Balanced l c n\n⊢ (match l, v, r with\n | node red (node red a x b) y c, z, d => node red (node black a x b) y (node black c z d)\n | node red a x (node red b y c), z, d => node red (node black a x b) y (node bla... | [
180,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
178,
1
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_eq_rat_iff | [
{
"state_after": "f g : CircleDeg1Lift\nhf : Continuous ↑f\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ τ (f ^ n) = ↑m ↔ ∃ x, ↑(f ^ n) x = x + ↑m",
"state_before": "f g : CircleDeg1Lift\nhf : Continuous ↑f\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ τ f = ↑m / ↑n ↔ ∃ x, ↑(f ^ n) x = x + ↑m",
"tactic": "rw [eq_div_iff, mul_comm, ← tra... | [
959,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | memℓp_zero | [] | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
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Mathlib/Data/Sum/Basic.lean | Sum.LiftRel.mono | [
{
"state_after": "case inl\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type u_2\nr r₁ r₂ : α → γ → Prop\ns s₁ s₂ : β → δ → Prop\na : α\nb : β\nc : γ\nd : δ\nhr : ∀ (a : α) (b : γ), r₁ a b → r₂ a b\nhs : ∀ (a : β) (b : δ), s₁ a b → s₂ a b\na✝¹ : α\nc✝ : γ\na✝ : r₁ a✝¹ c✝\n⊢ LiftRel r₂ s₂... | [
431,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
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Mathlib/Combinatorics/Quiver/Cast.lean | Quiver.Path.cast_eq_cast | [
{
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"tactic": "rw [hu, hv]"
},
{
"state_after": "U : Type u_1\ninst✝ : Quiver U\nu' v' : U\np : Path u' v'\n⊢ cast (_ : u' = u') (_ : v' ... | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Algebra/GroupPower/Ring.lean | pow_ne_zero_iff | [] | [
77,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Algebra/Regular/Basic.lean | isLeftRegular_of_mul_eq_one | [
{
"state_after": "R : Type u_1\ninst✝ : Monoid R\na b : R\nh : b * a = 1\n⊢ IsLeftRegular 1",
"state_before": "R : Type u_1\ninst✝ : Monoid R\na b : R\nh : b * a = 1\n⊢ IsLeftRegular (?m.13569 h * a)",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : ... | [
309,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_eq_empty | [] | [
378,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.of_append_right | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\nq : Walk G v w\nh : IsPath (Walk.reverse (append p q))\n⊢ IsPath (Walk.reverse q)",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG'... | [
1002,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_node4L | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ dual (node4L l x m y r) = node4R (dual r) y (dual m) x (dual l)",
"tactic": "cases m <;> simp [node4L, node4R, node3R, dual_node3L, dual_node', add_comm]"
}
] | [
327,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.image_inf_product | [] | [
370,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.eq_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5214\nγ : Type ?u.5217\nx y z w : α\n⊢ Quotient.mk (Rel.setoid α) (x, y) = Quotient.mk (Rel.setoid α) (z, w) ↔ x = z ∧ y = w ∨ x = w ∧ y = z",
"tactic": "simp"
}
] | [
169,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_list_sum | [] | [
310,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | LocallyConstant.ext | [] | [
292,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.ne_iff | [
{
"state_after": "no goals",
"state_before": "V : Type ?u.4284\nP : Type u_1\ninst✝ : MetricSpace P\ns₁ s₂ : Sphere P\n⊢ s₁ ≠ s₂ ↔ s₁.center ≠ s₂.center ∨ s₁.radius ≠ s₂.radius",
"tactic": "rw [← not_and_or, ← Sphere.ext_iff]"
}
] | [
122,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.next_apply | [] | [
281,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_extend_bot | [
{
"state_after": "α : Type u_3\nβ : Type u_2\nβ₂ : Type ?u.142989\nγ : Type ?u.142992\nι : Sort u_1\nι' : Sort ?u.142998\nκ : ι → Sort ?u.143003\nκ' : ι' → Sort ?u.143008\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\ne : ι → β\nhe : Injective e\nf : ι → α\n⊢ ((⨆ (i : β) (_ : ∃ i_1, e i_1 = i), extend e... | [
1485,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1482,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_inter_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.204029\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Ioc a b ∩ Ioi c = Ioc (a ⊔ c) b",
"tactic": "rw [← Ioi_inter_Iic, inter_assoc, inter_comm, inter_assoc, Ioi_inter_Ioi, inter_comm,\n Ioi_i... | [
1827,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1825,
1
] |
Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.lift_of | [] | [
679,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/Topology/Basic.lean | interior_maximal | [] | [
298,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean | AffineSubspace.vadd_mem_pointwise_vadd_iff | [] | [
64,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_one | [] | [
661,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.support_mul_subset_add_support | [
{
"state_after": "Γ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y : HahnSeries Γ R\n⊢ Set.IsPwo (support x)\n\nΓ : Type u_2\nR : Type u_1\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\nx y : HahnSeries Γ R\n⊢ Set.IsPwo (su... | [
771,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.comp_tendsto | [] | [
417,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.piRing_apply | [] | [
426,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.decreasingInduction_trans | [
{
"state_after": "case refl\nm✝ n✝ k✝ : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → P (n + 1) → P n\nm n k : ℕ\nmn : m ≤ n\nhP✝ : P k\nhP : P n\n⊢ decreasingInduction h (_ : m ≤ n) hP = decreasingInduction h mn (decreasingInduction h (_ : Nat.le n n) hP)\n\ncase step\nm✝ n✝ k✝¹ : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → P (n ... | [
528,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.ker_toLin'_eq_bot_iff | [] | [
417,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.unbounded_of_unbounded_iUnion | [
{
"state_after": "α✝ : Type ?u.108841\nr✝ : α✝ → α✝ → Prop\nα β : Type u\nr : α → α → Prop\nwo : IsWellOrder α r\ns : β → Set α\nh₁ : Unbounded r (⋃₀ range fun x => s x)\nh₂ : (#β) < StrictOrder.cof r\n⊢ ∃ x, Unbounded r (s x)",
"state_before": "α✝ : Type ?u.108841\nr✝ : α✝ → α✝ → Prop\nα β : Type u\nr : α ... | [
800,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Data/Set/Prod.lean | Set.range_dcomp | [
{
"state_after": "case refine_1\nι : Type u_1\nα : ι → Type u_3\nβ : ι → Type u_2\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\nf : (i : ι) → α i → β i\n⊢ (range fun g i => f i (g i)) ⊆ pi univ fun i => range (f i)\n\ncase refine_2\nι : Type u_1\nα : ι → Type u_3\nβ : ι → Type u_2\ns s₁ s₂ : Set ι\nt ... | [
720,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Logic/Nonempty.lean | Function.Surjective.nonempty | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_const | [] | [
135,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.support_nonempty | [] | [
102,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Fintype/CardEmbedding.lean | Fintype.card_embedding_eq_of_unique | [] | [
34,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.abs_cast | [] | [
184,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.componentComplMk_mem | [] | [
73,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Equiv.trans_toEmbedding | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.mul_cancel | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\nr : R\ns t : { x // x ∈ S }\n⊢ r /ₒ s * (↑s /ₒ t) = r /ₒ t",
"tactic": "simp [oreDiv_mul_char r s s t 1 1 (by simp)]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_... | [
340,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
11
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.analyticSet_range_of_polishSpace | [
{
"state_after": "case inl\nα : Type u_2\ninst✝² : TopologicalSpace α\nι : Type ?u.684\nβ : Type u_1\ninst✝¹ : TopologicalSpace β\ninst✝ : PolishSpace β\nf : β → α\nf_cont : Continuous f\nh✝ : IsEmpty β\n⊢ AnalyticSet (range f)\n\ncase inr\nα : Type u_2\ninst✝² : TopologicalSpace α\nι : Type ?u.684\nβ : Type u_... | [
98,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.componentComplMk_mem_hom | [] | [
189,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | lt_tsub_comm | [] | [
429,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Sign.lean | SignType.coe_neg_one | [] | [
270,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_eq_max | [] | [
1365,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1363,
1
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Mathlib/Data/Set/Intervals/Group.lean | Set.sub_mem_Ioo_iff_left | [] | [
116,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Data/Finset/Card.lean | Finset.card_singleton | [] | [
89,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.lipschitz | [] | [
1316,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
11
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_mem_smul | [] | [
109,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.dist_of_mem_subset_mk_sphere | [] | [
117,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_finset_sum | [
{
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872,
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.closure_closure_coe_preimage | [
{
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630,
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625,
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Mathlib/Topology/ContinuousOn.lean | tendsto_nhdsWithin_range | [] | [
469,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.denseInducing_pureCauchy | [] | [
206,
65
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205,
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Mathlib/Topology/Algebra/ContinuousMonoidHom.lean | PontryaginDual.map_comp | [] | [
467,
34
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465,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_eq_sqrt_iff_real_inner_eq_zero | [
{
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1470,
98
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1467,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.sum_nat_of_sum_int | [
{
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1079,
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1036,
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src/lean/Init/SimpLemmas.lean | implies_dep_congr_ctx | [] | [
36,
57
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Mathlib/Data/Prod/Basic.lean | Prod.map_injective | [
{
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361,
31
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351,
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Mathlib/Topology/LocalExtr.lean | Filter.EventuallyEq.isLocalExtr_iff | [] | [
630,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
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Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_card_zpowers | [] | [
893,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
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Mathlib/Geometry/Manifold/ChartedSpace.lean | ChartedSpace.secondCountable_of_sigma_compact | [
{
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598,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
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Mathlib/Analysis/PSeries.lean | Real.summable_nat_pow_inv | [
{
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}
] | [
212,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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src/lean/Init/Core.lean | nonempty_of_exists | [] | [
855,
18
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854,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_mk_le' | [] | [
314,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/CategoryTheory/Sites/Pretopology.lean | CategoryTheory.Pretopology.le_def | [] | [
87,
10
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86,
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_iSup_directed_of_measurable | [
{
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1134,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
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Mathlib/Algebra/Order/Chebyshev.lean | MonovaryOn.sum_smul_sum_le_card_smul_sum | [
{
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67,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.exists_eq_cons_of_ne | [] | [
171,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
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Mathlib/Data/Finset/Basic.lean | Finset.update_piecewise | [
{
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"state_bef... | [
2540,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2537,
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Mathlib/Data/Rat/Lemmas.lean | Rat.inv_coe_int_den_of_pos | [
{
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"state_before": "a : ℤ\nha0 : 0 < a\n⊢ ↑(↑a)⁻¹.den = a",
"tactic": "rw [← ofInt_eq_cast, ofInt, mk_eq_divInt, Rat.inv_def', divInt_eq_div, Nat.cast_one]"
},
{
"state_after": "a : ℤ\nha0 : 0 < a\n⊢ Nat.coprime (Int.natAbs 1) (Int.natAbs... | [
273,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Topology/Bases.lean | Dense.exists_countable_dense_subset_bot_top | [
{
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527,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
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Mathlib/Analysis/Calculus/Conformal/InnerProduct.lean | conformalFactorAt_inner_eq_mul_inner | [] | [
64,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/Algebra/Module/Zlattice.lean | Zspan.fract_eq_self | [
{
"state_after": "no goals",
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"tactic": "cl... | [
150,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_mul | [] | [
354,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_transpose | [] | [
822,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
820,
1
] |
Mathlib/Algebra/Group/Units.lean | eq_one_of_mul_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝¹ : CommMonoid α\ninst✝ : Subsingleton αˣ\na b : α\nh : a * b = 1\n⊢ b * a = 1",
"tactic": "rwa [mul_comm]"
}
] | [
562,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.nthLe_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\np : Perm α\nx : α\nn : ℕ\nhn : n < length (toList p x)\n⊢ nthLe (toList p x) n hn = ↑(p ^ n) x",
"tactic": "simp [toList]"
}
] | [
250,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
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Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.tail_mk | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/Algebra/CharP/Algebra.lean | Algebra.ringChar_eq | [
{
"state_after": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : CommSemiring L\ninst✝¹ : Nontrivial L\ninst✝ : Algebra K L\n⊢ CharP L (ringChar L)",
"state_before": "K : Type u_1\nL : Type u_2\ninst✝³ : Field K\ninst✝² : CommSemiring L\ninst✝¹ : Nontrivial L\ninst✝ : Algebra K L\n⊢ ringChar K = rin... | [
110,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isCompl_span_singleton_orthogonal | [] | [
402,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_prod_iff | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.303912\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.303921\ninst✝² : AddGroup A\nH✝ K✝ : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.303948\ninst✝ : Group P\nH : Subgroup G\nK : Subgroup N\nJ : Subgroup (G ×... | [
1766,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1764,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.inter_replicate | [
{
"state_after": "no goals",
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"tactic": "rw [inter_comm, replicate_inter, min_comm]"
}
] | [
2594,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2592,
1
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Mathlib/Order/Hom/Lattice.lean | SupHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.55900\nι : Type ?u.55903\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.55915\ninst✝³ : Sup α\ninst✝² : Sup β\ninst✝¹ : Sup γ\ninst✝ : Sup δ\ng : SupHom β γ\nf₁ f₂ : SupHom α β\nhg : Injective ↑g\nh : comp g f₁ = comp g f₂\na : α\n⊢ ↑g (↑f₁ a... | [
435,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_inter_open | [] | [
955,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
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Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_inf | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.basicOpen_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\n⊢ ↑(basicOpen 𝒜 0) = ↑⊥",
"tactic": "simp"
}
] | [
419,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/Instances/Real.lean | Int.tendsto_coe_cofinite | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\n⊢ Tendsto (fun y => dist (↑y) 0) cofinite atTop",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\n⊢ Tendsto Int.cast cofinite (cocompact ℝ)",
"tactic": "refine' tendsto_cocompact_of_tendsto_dist_comp_atTop (0 : ℝ) _"
},
{
"state_after": ... | [
237,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_ceil_of_ne_zero | [] | [
374,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.sumCongrHom_injective | [
{
"state_after": "case mk.mk\nα✝ : Type u\nβ✝ : Type v\nα : Type u_1\nβ : Type u_2\nfst✝¹ : Perm α\nsnd✝¹ : Perm β\nfst✝ : Perm α\nsnd✝ : Perm β\nh : ↑(sumCongrHom α β) (fst✝¹, snd✝¹) = ↑(sumCongrHom α β) (fst✝, snd✝)\n⊢ (fst✝¹, snd✝¹) = (fst✝, snd✝)",
"state_before": "α✝ : Type u\nβ✝ : Type v\nα : Type u_1... | [
222,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.mk0_inj | [
{
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217,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Ico_zsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\na : α\n⊢ (⋃ (n : ℤ), Ico (n • p) ((n + 1) • p)) = univ",
"tactic": "simpa only [zero_add] using iUnion_Ico_add_zsmul hp 0"
}
] | [
1079,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.cons_nil_append | [] | [
252,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
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