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/Algebra/Order/ToIntervalMod.lean | AddCommGroup.modEq_iff_toIcoMod_eq_left | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na c : α\nn✝ n : ℤ\n⊢ toIcoMod hp a (a + n • p) = a",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ (∃ z, b ... | [
597,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_dvd | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b✝ b : R\n⊢ b ∣ 0 ∧ b ∣ b",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b✝ b : R\n⊢ gcd 0 b ∣ 0 ∧ gcd 0 b ∣ b",
"tactic": "rw [gcd_zero_left]"
},
{
"state_after": "no goals",
... | [
156,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀ | [] | [
412,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.nat_cast_apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.one_val | [] | [
407,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Real/Pointwise.lean | Real.iSup_mul_of_nonpos | [
{
"state_after": "no goals",
"state_before": "ι : Sort u_1\nα : Type ?u.17270\ninst✝ : LinearOrderedField α\nr : ℝ\nha : r ≤ 0\nf : ι → ℝ\n⊢ (⨆ (i : ι), f i) * r = ⨅ (i : ι), f i * r",
"tactic": "simp only [Real.mul_iSup_of_nonpos ha, mul_comm]"
}
] | [
147,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bit0_val | [] | [
124,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Sym/Card.lean | Sym.card_sym_eq_choose | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.55973\nβ : Type ?u.55976\nn : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\nk : ℕ\ninst✝ : Fintype (Sym α k)\n⊢ Fintype.card (Sym α k) = Nat.choose (Fintype.card α + k - 1) k",
"tactic": "rw [card_sym_eq_multichoose, Nat.multichoose_eq]"
}
] | [
123,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Order.cof_nonempty | [] | [
75,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_eq_foldr | [
{
"state_after": "case nil\nn : ℕ\nα : Type u_1\ninst✝ : Semiring α\nb : α\n⊢ ofDigits b [] = List.foldr (fun x y => ↑x + b * y) 0 []\n\ncase cons\nn : ℕ\nα : Type u_1\ninst✝ : Semiring α\nb : α\nd : ℕ\nL : List ℕ\nih : ofDigits b L = List.foldr (fun x y => ↑x + b * y) 0 L\n⊢ ofDigits b (d :: L) = List.foldr (f... | [
167,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_subset_iff | [] | [
1377,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.sub_apply | [] | [
958,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.param_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\nz : ℕ\ns : Set β\nhs : IsOpen s\nhs0 : 0 ∈ s\nx : α\nhx : x ∈ (fun a => k a ^ (z + 1) * f a) ⁻¹' s\n⊢ x ∈ (fun a => ... | [
111,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasStrictFDerivAt.add_const | [] | [
179,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_top | [] | [
723,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Init/Algebra/Classes.lean | incomp_trans_of | [] | [
321,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.union | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\n⊢ IsClosed s₁ → IsClosed s₂ → IsClosed (s₁ ∪ s₂)",
"tactic": "simpa only [← isOpen_compl_iff, compl_union] using IsOpen.inter"
}
] | [
215,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.measure_iUnion₀ | [
{
"state_after": "case intro.intro.intro.intro\nι : Type u_1\nα : Type u_2\nβ : Type ?u.11366\nγ : Type ?u.11369\nm0 : MeasurableSpace α\nμ : Measure α\ns t✝ : Set α\ninst✝ : Countable ι\nf : ι → Set α\nhd : Pairwise (AEDisjoint μ on f)\nh : ∀ (i : ι), NullMeasurableSet (f i)\nt : ι → Set α\n_ht_sub : ∀ (i : ι)... | [
291,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.leftInverse_surjInv | [] | [
499,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isSheafFor_iff_generate | [
{
"state_after": "C : Type u₁\ninst✝ : Category C\nP Q U : Cᵒᵖ ⥤ Type w\nX Y : C\nS : Sieve X\nR✝ : Presieve X\nJ J₂ : GrothendieckTopology C\nR : Presieve X\n⊢ (IsSeparatedFor P R ∧\n ∀ (x : FamilyOfElements P R), FamilyOfElements.Compatible x → ∃ t, FamilyOfElements.IsAmalgamation x t) ↔\n IsSheafFor ... | [
641,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_finset_sum_measure | [
{
"state_after": "α : Type u_2\nβ : Type ?u.921513\nγ : Type ?u.921516\nδ : Type ?u.921519\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nι : Type u_1\nm : MeasurableSpace α\ns : Finset ι\nf : α → ℝ≥0∞\nμ : ι → Measure α\n⊢ (∑' (i : { x // x ∈ s }), ∫⁻ (a : α), f a ∂μ ↑i) = ∑' (x : ↑↑s), ∫⁻ (a : α), f a ∂μ ↑x",
... | [
640,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_smul_of_tower | [] | [
423,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | one_lt_mul_of_le_of_lt | [] | [
318,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.sUnion_inter_sUnion | [] | [
1356,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_top | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\n⊢ ¬IsField R → ∃ I, ⊥ < I ∧ I < ⊤\n\ncase mpr\nα : Type u\nβ : Type v\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\n⊢ (∃ I, ⊥ < I ∧ I < ⊤) → ¬IsField R",
"state_before": "α : Type ... | [
765,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.yn_succ_succ | [] | [
536,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.mul_left_index_le | [
{
"state_after": "case intro.intro\nG : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK : Set G\nhK : IsCompact K\nV : Set G\nhV : Set.Nonempty (interior V)\ng : G\ns : Finset G\nh1s : K ⊆ ⋃ (g : G) (_ : g ∈ s), (fun h => g * h) ⁻¹' V\nh2s : Finset.card s = index K V\n⊢ in... | [
284,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Fintype/Card.lean | Function.Embedding.equiv_of_fintype_self_embedding_to_embedding | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.48925\nγ : Type ?u.48928\ninst✝ : Finite α\ne : α ↪ α\nx✝ : α\n⊢ ↑(Equiv.toEmbedding (equivOfFintypeSelfEmbedding e)) x✝ = ↑e x✝",
"state_before": "α : Type u_1\nβ : Type ?u.48925\nγ : Type ?u.48928\ninst✝ : Finite α\ne : α ↪ α\n⊢ Equiv.toEmbedding (equivO... | [
774,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/List/Perm.lean | List.perm_cons_append_cons | [] | [
191,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_hom_rel | [
{
"state_after": "ι : Type ?u.327698\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g✝ : α → β\ninst✝¹ : CommMonoid β\ninst✝ : CommMonoid γ\nr : β → γ → Prop\nf : α → β\ng : α → γ\ns : Finset α\nh₁ : r 1 1\nh₂ : ∀ (a : α) (b : β) (c : γ), r b c → r (f a * b) (g a * c)\n⊢ r (Multiset.prod (M... | [
726,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Algebra/Module/Basic.lean | add_smul | [] | [
95,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Std/Data/Option/Lemmas.lean | Option.bind_map_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nx : Option (Option α)\nf : α → β\n⊢ Option.bind x (Option.map f) = Option.bind (Option.map (Option.map f) x) id",
"tactic": "cases x <;> simp"
}
] | [
157,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
156,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGLB.mono | [] | [
254,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Order/Disjoint.lean | codisjoint_top_left | [] | [
245,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.coe_ofBijective | [] | [
964,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_max_of_eq | [] | [
1219,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_strong_rec | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.320238\nγ : Type ?u.320241\nσ : Type u_1\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → ℕ → σ\ng : α → List σ → Option σ\nhg : Primrec₂ g\nH : ∀ (a : α) (n : ℕ), g a (List.map (f ... | [
1157,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit_le_bit1 | [] | [
707,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_smulg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\nc n : ℤ\nx a : α\nn' : ℤ\na' : α\nh₁ : c * n = n'\nh₂ : smulg c a = a'\n⊢ smulg c (termg n x a) = termg n' x a'",
"tactic": "simp [h₂.symm, h₁.symm, termg, smulg, zsmul_add, mul_zsmul]"
}
] | [
222,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_inf | [] | [
137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_lt_div_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LT 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 a : α\n⊢ a / b < a / c ↔ c < b",
"tactic": "rw [div_eq_m... | [
942,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.rename_comp_bind₁ | [
{
"state_after": "case hf\nσ : Type u_4\nτ : Type u_2\nR : Type u_3\nS : Type ?u.503174\nT : Type ?u.503177\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nυ : Type u_1\nf : σ → MvPolynomial τ R\ng : τ → υ\ni : σ\n⊢ ↑(AlgHom.comp (rename g) (bind₁ f)) (X i) ... | [
250,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.true_eq_false_eq_False | [
{
"state_after": "no goals",
"state_before": "⊢ ¬true = false",
"tactic": "decide"
}
] | [
66,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.isClosed_range | [] | [
194,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/MvPolynomial/Counit.lean | MvPolynomial.ACounit_surjective | [] | [
64,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.ker_evalₗ | [
{
"state_after": "case intro\nσ K : Type u\ninst✝² : Fintype K\ninst✝¹ : Field K\ninst✝ : Finite σ\nval✝ : Fintype σ\n⊢ ker (evalᵢ σ K) = ⊥",
"state_before": "σ K : Type u\ninst✝² : Fintype K\ninst✝¹ : Field K\ninst✝ : Finite σ\n⊢ ker (evalᵢ σ K) = ⊥",
"tactic": "cases nonempty_fintype σ"
},
{
"... | [
251,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | derivWithin_csinh | [] | [
282,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.smul_mul | [
{
"state_after": "case a.h\nl : Type u_4\nm : Type u_3\nn : Type u_1\no : Type ?u.251620\nm' : o → Type ?u.251625\nn' : o → Type ?u.251630\nR : Type u_2\nS : Type ?u.251636\nα : Type v\nβ : Type w\nγ : Type ?u.251643\ninst✝⁵ : AddCommMonoid α\ninst✝⁴ : Mul α\ninst✝³ : Fintype n\ninst✝² : Monoid R\ninst✝¹ : Dist... | [
972,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Data/Real/Irrational.lean | Int.not_irrational | [] | [
188,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | lcm_eq_normalize | [] | [
778,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.ZeroAtFilter.neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝² : TopologicalSpace β\ninst✝¹ : AddGroup β\ninst✝ : ContinuousNeg β\nl : Filter α\nf : α → β\nhf : ZeroAtFilter l f\n⊢ ZeroAtFilter l (-f)",
"tactic": "simpa using hf.neg"
}
] | [
50,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
8
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpTo_succ_iff_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\... | [
1306,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1299,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | tangentConeAt.lim_zero | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.21028\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.21118\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nx y : E\ns t : Set... | [
125,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
src/lean/Init/Control/Lawful.lean | Id.map_eq | [] | [
91,
69
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
91,
9
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_empty | [] | [
61,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Hom.injective_of_top_hom | [
{
"state_after": "ι : Sort ?u.409745\n𝕜 : Type ?u.409748\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\nf✝ : G →g G'\nf : ⊤ →g G'\nv w : V\nh : ↑f v = ↑f w\n⊢ v = w",
"state_before": "ι : Sort ?u.409745\n𝕜 : Type ?u.409748\nV : Type u\nW : Type v... | [
1738,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1735,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_neg' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp (-a) b = -(toIocDiv hp a (-b) + 1)",
"tactic": "simpa only [neg_neg] using toIcoDiv_neg hp (-a) (-b)"
}
] | [
393,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Analysis/Calculus/Series.lean | summable_of_summable_hasFDerivAt | [
{
"state_after": "α : Type u_1\nβ : Type ?u.39280\n𝕜 : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\nu : α → ℝ\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nf' : α → E → E →L[𝕜] F\nv : ℕ ... | [
149,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.comap_top | [] | [
1087,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1086,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_three_mul | [
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ cosh (3 * x) = 4 * cosh x ^ 3 - 3 * cosh x",
"state_before": "x y : ℂ\n⊢ cosh (3 * x) = 4 * cosh x ^ 3 - 3 * cosh x",
"tactic": "have h1 : x + 2 * x = 3 * x := by ring"
},
{
"state_after": "x y : ℂ\nh1 : x + 2 * x = 3 * x\n⊢ cosh x * cosh (2 *... | [
783,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Std/Data/List/Lemmas.lean | List.filter_eq_nil | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\np : α✝ → Bool\nl : List α✝\n⊢ filter p l = [] ↔ ∀ (a : α✝), a ∈ l → ¬p a = true",
"tactic": "simp only [eq_nil_iff_forall_not_mem, mem_filter, not_and]"
}
] | [
1240,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1239,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.IsCoreflexivePair.swap | [] | [
123,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2.stmts₁_self | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ninst✝ : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nq : Stmt₂\n⊢ q ∈ stmts₁ q",
"tactic": "cases q <;> simp only [Finset.mem_insert_self, Finset.mem_singleton_self, stmts₁]"
}
] | [
2192,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2191,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.pullback_comp | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nX Y Z : C\nD : Type u₂\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nf : X ⟶ Y\ng : Y ⟶ Z\nt : MonoOver Z\n⊢ (pullback (f ≫ g)).obj (Quotient.mk'' t) = (pullback f).obj ((pullback g).obj (Quotient.mk'' t))",
"state_before": "C : Type u₁\ninst✝² : C... | [
568,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Group.conj_mem_conjugatesOfSet | [
{
"state_after": "case intro.intro\nG : Type u_1\nG' : Type ?u.436568\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.436577\ninst✝ : AddGroup A\ns : Set G\nx c : G\nH : x ∈ conjugatesOfSet s\na : G\nh₁ : a ∈ s\nh₂ : IsConj a x\n⊢ c * x * c⁻¹ ∈ conjugatesOfSet s",
"state_before": "G : Type u_1\nG' : Type ... | [
2442,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2439,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_ratCast | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : DivisionRing R\nn✝ : ℤ\n⊢ ↑↑n✝ = ↑n✝",
"tactic": "simp"
}
] | [
110,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.coe_le_coe | [] | [
92,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.not_nhds_le_map | [] | [
184,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iUnion_Ioo_coe_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.134675\nβ : Type ?u.134678\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ (⋃ (n : ℕ), Ioo a ↑n) = Ioi a \\ {⊤}",
"tactic": "simp only [← Ioi_inter_Iio, ← inter_iUnion, iUnion_Iio_coe_nat, diff_eq]"
}
] | [
879,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.Perm.ext | [] | [
134,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
8
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.nonneg' | [] | [
161,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_one | [] | [
92,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.transReflReparamAux_zero | [
{
"state_after": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ 2 < 0 → False",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ transReflReparamAux 0 = 0",
"tactic": "simp [transReflReparamAux]... | [
155,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciInf_mem | [] | [
987,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Topology/LocalExtr.lean | IsMinOn.localize | [] | [
133,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.twoBlockTriangular_det | [
{
"state_after": "α : Type ?u.59918\nβ : Type ?u.59921\nm : Type u_1\nn : Type ?u.59927\no : Type ?u.59930\nm' : α → Type ?u.59935\nn' : α → Type ?u.59940\nR : Type v\ninst✝⁵ : CommRing R\nM✝ N : Matrix m m R\nb : m → α\ninst✝⁴ : DecidableEq m\ninst✝³ : Fintype m\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nM :... | [
187,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_induction | [] | [
91,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.coe_sInf' | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.2948\nγ : Type ?u.2951\nι : Sort ?u.2954\ninst✝ : InfSet α\ns : Set α\nx : α\nhx : x ∈ s\n⊢ ↑(sInf s) = sInf ((fun a => ↑a) '' s)",
"state_before": "α : Type u_1\nβ : Type ?u.2948\nγ : Type ?u.2951\nι : Sort ?u.2954\ninst✝ : InfSet α\ns : Set α\nhs : S... | [
101,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Topology/Semicontinuous.lean | lowerSemicontinuous_biSup | [] | [
625,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.of.zero_exact_aux | [
{
"state_after": "case refine'_1\nR : Type u\ninst✝⁵ : Ring R\nι : Type v\ndec_ι : DecidableEq ι\ninst✝⁴ : Preorder ι\nG : ι → Type w\ninst✝³ : (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✝² : DirectedSystem G fun i j h => ↑(f' i j h)\ninst✝¹ : Nonempty... | [
612,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.revAt_invol | [] | [
76,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_restrictScalars | [
{
"state_after": "no goals",
"state_before": "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✝²⁰ : Fintype ι\ninst✝¹⁹ : Fintype ι'\ninst✝¹⁸ : NontriviallyNormedField 𝕜\ninst✝¹⁷ : (i : ι)... | [
593,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.lift_univ | [] | [
1495,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1494,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_coe | [] | [
282,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_def | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.sigma | [] | [
1199,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1197,
1
] |
Mathlib/Combinatorics/Quiver/Basic.lean | Quiver.empty_arrow | [] | [
178,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.concaveOn | [] | [
377,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.map_field_closure | [] | [
905,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | CommGroupCat.ofHom_apply | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/FiniteLimits.lean | CategoryTheory.Limits.hasFiniteWidePushouts_of_has_finite_limits | [] | [
268,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_ord_le | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.21275\nr : α → α → Prop\nc : Cardinal\n⊢ cof (ord c) ≤ c",
"tactic": "simpa using cof_le_card c.ord"
}
] | [
293,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Data/Finset/Sigma.lean | Finset.pairwiseDisjoint_map_sigmaMk | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\nβ : Type ?u.7974\ns s₁ s₂ : Finset ι\nt t₁ t₂ : (i : ι) → Finset (α i)\ni : ι\na✝¹ : i ∈ ↑s\nj : ι\na✝ : j ∈ ↑s\nhij : i ≠ j\n⊢ (_root_.Disjoint on fun i => map (Embedding.sigmaMk i) (t i)) i j",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : Type ?u.7... | [
84,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_injective | [
{
"state_after": "α : Type u\nn : ℕ\nf g : Fin n → α\nh : { fst := n, snd := f } = { fst := n, snd := g }\n⊢ HEq f g",
"state_before": "α : Type u\nn : ℕ\nf g : Fin n → α\nh : ofFn f = ofFn g\n⊢ HEq f g",
"tactic": "rw [ofFn_inj'] at h"
},
{
"state_after": "case refl\nα : Type u\nn : ℕ\nf : Fin ... | [
285,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.efixedPoint_isFixedPt' | [] | [
207,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.diam_cthickening_le | [
{
"state_after": "case intro\nι : Sort ?u.123224\nα✝ : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α✝\nδ : ℝ\ns✝ t : Set α✝\nx : α✝\nα : Type u_1\ninst✝ : PseudoMetricSpace α\ns : Set α\nε : ℝ≥0\n⊢ diam (cthickening (↑ε) s) ≤ diam s + 2 * ↑ε",
"state_before": "ι : Sort ?u.123224\nα✝ : Type u\nβ : Type v... | [
1220,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1214,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.one_re | [] | [
868,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
9
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.monotone_lintegral | [] | [
162,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | disjoint_sSup_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort ?u.11330\ninst✝ : Frame α\ns✝ t : Set α\na b : α\ns : Set α\n⊢ Disjoint a (sSup s) ↔ ∀ (b : α), b ∈ s → Disjoint a b",
"tactic": "simpa only [disjoint_comm] using @sSup_disjoint_iff"
}
] | [
155,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.exists_monotone_subseq | [
{
"state_after": "case intro.inl\nι : Type ?u.83266\nα : Type u_1\nβ : Type ?u.83272\nr : α → α → Prop\nr' : β → β → Prop\nf✝ : α → β\ns t : Set α\na : α\ninst✝¹ : IsRefl α r\ninst✝ : IsTrans α r\nh : PartiallyWellOrderedOn s r\nf : ℕ → α\nhf : ∀ (n : ℕ), f n ∈ s\ng : ℕ ↪o ℕ\nh1 : ∀ (m n : ℕ), m < n → r (f (↑g ... | [
356,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.