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/LinearAlgebra/AffineSpace/Midpoint.lean | midpoint_sub_left | [] | [
142,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.findMax'_dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt : Ordnode α\nx : α\n⊢ findMax' x (dual t) = findMin' t x",
"tactic": "rw [← findMin'_dual, dual_dual]"
}
] | [
586,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.invFun_eq_symm | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_eq_zero' | [
{
"state_after": "α✝ : Type ?u.142517\nβ✝ : Type ?u.142520\nγ : Type ?u.142523\nr : α✝ → α✝ → Prop\ns : β✝ → β✝ → Prop\nt : γ → γ → Prop\na b : Ordinal\nα : Type u_1\nx✝³ : α → α → Prop\nx✝² : IsWellOrder α x✝³\nβ : Type u_1\nx✝¹ : β → β → Prop\nx✝ : IsWellOrder β x✝¹\n⊢ IsEmpty (β × α) ↔ IsEmpty α ∨ IsEmpty β"... | [
684,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
679,
9
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ioo_add_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedRing α\na : α\n⊢ Pairwise (Disjoint on fun n => Ioo (a + ↑n) (a + ↑n + 1))",
"tactic": "simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using\n pairwise_disjoint_Ioo_add_zsmul a (1 : α)"
}
] | [
252,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Topology/Order/Basic.lean | Ioc_mem_nhds | [] | [
349,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.FactorSet.coe_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CancelCommMonoidWithZero α\na b : Multiset { a // Irreducible a }\n⊢ ↑(a + b) = ↑a + ↑b",
"tactic": "norm_cast"
}
] | [
1217,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Mathlib/Analysis/Convex/Integral.lean | Convex.set_average_mem_closure | [] | [
113,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Combinatorics/SetFamily/HarrisKleitman.lean | IsUpperSet.le_card_inter_finset | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\ninst✝ : Fintype α\nh𝒜✝ : IsLowerSet (↑𝒜ᶜ)\nh𝒜 : IsLowerSet ↑(𝒜ᶜ)\nhℬ : IsUpperSet ↑ℬ\n⊢ card 𝒜 * card ℬ ≤ 2 ^ Fintype.card α * card (𝒜 ∩ ℬ)",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\n𝒜... | [
135,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Topology/Order/Basic.lean | eventually_lt_nhds | [] | [
1194,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | edist_le_of_edist_le_geometric_two_of_tendsto₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.444903\nι : Type ?u.444906\ninst✝ : PseudoEMetricSpace α\nC : ℝ≥0∞\nhC : C ≠ ⊤\nf : ℕ → α\nhu : ∀ (n : ℕ), edist (f n) (f (n + 1)) ≤ C / 2 ^ n\na : α\nha : Tendsto f atTop (𝓝 a)\n⊢ edist (f 0) a ≤ 2 * C",
"tactic": "simpa only [_ro... | [
362,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Std/Data/Option/Lemmas.lean | Option.mem_iff | [] | [
13,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
13,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_equiv_neg_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ (-x ≈ -y) ↔ (x ≈ y)",
"tactic": "rw [Equiv, Equiv, neg_le_neg_iff, neg_le_neg_iff, and_comm]"
}
] | [
1337,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_inr_union_range_inl | [] | [
909,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.ofSubtype_apply_of_not_mem | [] | [
459,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Data/MvPolynomial/Derivation.lean | MvPolynomial.leibniz_iff_X | [
{
"state_after": "σ : Type u_2\nR : Type u_1\nA : Type u_3\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid A\ninst✝² : Module R A\ninst✝¹ : Module (MvPolynomial σ R) A\ninst✝ : IsScalarTower R (MvPolynomial σ R) A\nD : MvPolynomial σ R →ₗ[R] A\nh₁ : ↑D 1 = 0\nH : ∀ (s : σ →₀ ℕ) (i : σ), ↑D (↑(monomial s) 1 * X... | [
125,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Real.measurable_cos | [] | [
49,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | add_pow | [] | [
87,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | Monotone.mul_antitone | [] | [
448,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Bounded.weak_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Preorder α\no₁ : WithBot α\no₂ : WithTop α\nh : Bounded nil o₁ o₂\n⊢ Bounded nil ⊥ o₂",
"tactic": "cases o₂ <;> trivial"
}
] | [
918,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_double | [] | [
855,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.mass_toFiniteMeasure | [] | [
204,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.one_mul | [
{
"state_after": "case a.h\nl : Type ?u.315980\nm : Type u_1\nn : Type u_2\no : Type ?u.315989\nm' : o → Type ?u.315994\nn' : o → Type ?u.315999\nR : Type ?u.316002\nS : Type ?u.316005\nα : Type v\nβ : Type w\nγ : Type ?u.316012\ninst✝² : NonAssocSemiring α\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\nM : Matrix... | [
1108,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
11
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.eval_prec_zero | [
{
"state_after": "cf cg : Code\na : ℕ\n⊢ Nat.rec (eval cf (a, 0).fst)\n (fun y IH => do\n let i ← IH\n eval cg (Nat.pair (a, 0).fst (Nat.pair y i)))\n (a, 0).snd =\n eval cf a",
"state_before": "cf cg : Code\na : ℕ\n⊢ eval (prec cf cg) (Nat.pair a 0) = eval cf a",
"tactic": "r... | [
645,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | sInfHom.continuous | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝⁵ : CompleteLattice α\ninst✝⁴ : CompleteLattice β\ninst✝³ : TopologicalSpace α\ninst✝² : LowerTopology α\ninst✝¹ : TopologicalSpace β\ninst✝ : LowerTopology β\nf : sInfHom α β\nb : β\n⊢ IsClosed (↑f ⁻¹' Ici b)",
"state_before": "α : Type u_1\nβ : Type u_2\n... | [
281,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
11
] |
Mathlib/RingTheory/Prime.lean | mul_eq_mul_prime_prod | [
{
"state_after": "case empty\nR : Type u_2\ninst✝¹ : CancelCommMonoidWithZero R\nα : Type u_1\ninst✝ : DecidableEq α\nx✝ y✝ a✝ : R\ns : Finset α\np : α → R\nhp✝ : ∀ (i : α), i ∈ s → Prime (p i)\nhx✝ : x✝ * y✝ = a✝ * ∏ i in s, p i\nx y a : R\nhp : ∀ (i : α), i ∈ ∅ → Prime (p i)\nhx : x * y = a * ∏ i in ∅, p i\n⊢... | [
50,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_le_iff_le_map | [] | [
1746,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1744,
1
] |
Mathlib/Algebra/Group/Defs.lean | mul_one | [] | [
464,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Data/List/Permutation.lean | List.mem_permutationsAux2 | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.8950\nt : α\nts l✝ l' l : List α\n⊢ l' ∈ (permutationsAux2 t ts [] [] fun x => l ++ x).snd ↔\n ∃ l₁ l₂, l₂ ≠ [] ∧ [] = l₁ ++ l₂ ∧ l' = l ++ l₁ ++ t :: l₂ ++ ts\n\ncase cons\nα : Type u_1\nβ : Type ?u.8950\nt : α\nts l✝ l' : List α\ny : α\nys : List α\nih ... | [
161,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_sub_left_of_add_lt | [
{
"state_after": "a b c : Int\nh✝ : a + b < c\nh : a + b + -a < c + -a\n⊢ b < c - a",
"state_before": "a b c : Int\nh : a + b < c\n⊢ b < c - a",
"tactic": "have h := Int.add_lt_add_right h (-a)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : a + b < c\nh : a + b + -a < c ... | [
1053,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1051,
11
] |
Mathlib/RingTheory/Nilpotent.lean | IsNilpotent.map | [
{
"state_after": "R S : Type u\nx y : R\ninst✝² : MonoidWithZero R\ninst✝¹ : MonoidWithZero S\nr : R\nF : Type u_1\ninst✝ : MonoidWithZeroHomClass F R S\nhr : IsNilpotent r\nf : F\n⊢ ↑f r ^ Exists.choose hr = 0",
"state_before": "R S : Type u\nx y : R\ninst✝² : MonoidWithZero R\ninst✝¹ : MonoidWithZero S\nr... | [
64,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.symm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3489\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ns t u v : Set α\nh : AEDisjoint μ s t\n⊢ AEDisjoint μ t s",
"tactic": "rwa [AEDisjoint, inter_comm]"
}
] | [
58,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_eq_zero_of_not_summable | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.19688\nδ : Type ?u.19691\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g : β → α\na b : α\ns : Finset β\nh : ¬Summable f\n⊢ (∑' (b : β), f b) = 0",
"tactic": "simp [tsum_def, h]"
}
] | [
103,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.modByMonic_add_div | [] | [
253,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.constantCoeff_wittNeg | [
{
"state_after": "p : ℕ\nR : Type ?u.144931\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (-X 0) = 0",
"state_before": "p : ℕ\nR : Type ?u.144931\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\n⊢ ↑constantCoeff (wittNeg p n) = 0",
"tactic": "apply constantCoeff_wittStructure... | [
314,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Std/Logic.lean | exists_eq_right_right | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ (∃ a, p a ∧ b ∧ a = a') ↔ p a' ∧ b",
"tactic": "simp [← and_assoc]"
}
] | [
477,
21
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
476,
9
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_succ | [
{
"state_after": "m : ℕ\nb : Bool\nn : ℕ\n⊢ testBit (↑(Nat.bit b n)) (Nat.succ m) = testBit (↑n) m",
"state_before": "m : ℕ\nb : Bool\nn : ℕ\n⊢ testBit (bit b ↑n) (Nat.succ m) = testBit (↑n) m",
"tactic": "rw [bit_coe_nat]"
},
{
"state_after": "no goals",
"state_before": "m : ℕ\nb : Bool\nn ... | [
213,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.basisOf_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.48727\nk : Type u_3\nV : Type u_2\nP : Type u_4\ninst✝³ : AddCommGroup V\ninst✝² : AffineSpace V P\ninst✝¹ : Ring k\ninst✝ : Module k V\nb : AffineBasis ι k P\ns : Finset ι\ni✝ j✝ : ι\ne : ι ≃ ι'\ni : ι\nj : { j // j ≠ i }\n⊢ ↑(basisOf... | [
138,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.mem_rangeSingleton_apply_iff | [] | [
56,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.not_irreducible_C | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nx : R\nH : x = 0\n⊢ ¬Irreducible 0",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nx : R\nH : x = 0\n⊢ ¬Irreducible (↑C x)",
"tac... | [
491,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.exists_nat_mul_gt | [] | [
1829,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.compTendsto'_coe | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasDerivAt | [] | [
85,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_add_pi | [] | [
1303,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1302,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | measurableSet_region_between_oc | [
{
"state_after": "α : Type u_1\ninst✝ : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\nhg : Measurable g\nhs : MeasurableSet s\n⊢ MeasurableSet ({a | a.fst ∈ s} ∩ {a | a.snd ∈ {a_1 | f a.fst < a_1} ∩ {a_1 | a_1 ≤ g a.fst}})",
"state_before": "α : Type u_1\ninst✝ :... | [
500,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.eventually_left_inverse' | [] | [
243,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ ‖x‖ ^ 2 + 2 * inner x y + ‖y‖ ^ 2 = ‖x‖ ^ 2 - 2 * inner x y + ‖y‖ ^ 2 ↔ inner x y = 0",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢... | [
342,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Topology/Order.lean | tendsto_nhds_Prop | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : TopologicalSpace α\nl : Filter α\np : α → Prop\nq : Prop\n⊢ Tendsto p l (𝓝 q) ↔ q → ∀ᶠ (x : α) in l, p x",
"tactic": "by_cases q <;> simp [*]"
}
] | [
920,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagram_fstFrom | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius | [
{
"state_after": "case pos\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np₁ p₂ : P\nhp₁ : p₁ ∈ s\nhp₂ : dist p₂ s.center ≤ s.radius\nh : p₁ = p₂\n⊢ 0 < inner (p₁ -ᵥ p₂) (p₁ -ᵥ s.center) ∨ p₁ = p₂\n\n... | [
357,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.map_zero | [] | [
247,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
11
] |
Mathlib/Analysis/Normed/Ring/Seminorm.lean | MulRingNorm.ext | [] | [
317,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.op_map_comp_obj | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.range_cons_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.21635\nn' : Type ?u.21638\no' : Type ?u.21641\nx : α\nu : Fin 0 → α\n⊢ Set.range (vecCons x u) = {x}",
"tactic": "rw [range_cons, range_empty, Set.union_empty]"
}
] | [
180,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
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Mathlib/LinearAlgebra/Dual.lean | Submodule.le_dualCoannihilator_dualAnnihilator | [] | [
888,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Order/Basic.lean | Prod.mk_le_mk_iff_left | [] | [
1221,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_le_of_ae_nnnorm_bound | [] | [
423,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_restrict | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.807482\nδ : Type ?u.807485\ninst✝¹ : MeasurableSpace α\nK : Type ?u.807491\ninst✝ : Zero β\nf : α →ₛ β\ns : Set α\nhs : MeasurableSet s\n⊢ ↑(piecewise s hs f 0) = indicator s ↑f",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.807482\nδ : T... | [
755,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_sub | [] | [
791,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.not_mem_of_not_mem_closure | [] | [
573,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.deriv_integral_of_tendsto_ae_right | [] | [
769,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | gold_add_goldConj | [
{
"state_after": "⊢ (1 + sqrt 5) / 2 + (1 - sqrt 5) / 2 = 1",
"state_before": "⊢ φ + ψ = 1",
"tactic": "rw [goldenRatio, goldenConj]"
},
{
"state_after": "no goals",
"state_before": "⊢ (1 + sqrt 5) / 2 + (1 - sqrt 5) / 2 = 1",
"tactic": "ring"
}
] | [
78,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_copy | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.moveRight_neg' | [
{
"state_after": "case mk\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\ni : RightMoves (-mk α✝ β✝ a✝¹ a✝)\n⊢ moveRight (-mk α✝ β✝ a✝¹ a✝) i = -moveLeft (mk α✝ β✝ a✝¹ a✝) (↑toRightMovesNeg.symm i)",
"state_before": "x : PGame\ni : RightMoves (-x)\n⊢ moveRight (-x) i = -moveLeft x (↑toRightMovesNeg.sy... | [
1285,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/RingTheory/Polynomial/ScaleRoots.lean | Polynomial.coeff_scaleRoots_natDegree | [
{
"state_after": "no goals",
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43,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
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Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.algebraMap₀_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nn : ℕ\nr : R\na : (⨂[R]^n) M\n⊢ ↑(cast R M (_ : 0 + n = n)) (GradedMonoid.GMul.mul (↑algebraMap₀ r) a) = r • a",
"tactic": "rw [gMul_eq_coe_linearMap, algebraM... | [
247,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid.merge | [] | [
1502,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_assoc₁ | [] | [
195,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | abs_le_of_sq_le_sq' | [] | [
722,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Std/Data/List/Lemmas.lean | List.sublist_append_of_sublist_right | [] | [
356,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
355,
1
] |
Mathlib/Order/Bounds/Basic.lean | isGLB_Icc | [] | [
704,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/GroupTheory/Torsion.lean | CommMonoid.primaryComponent.exists_orderOf_eq_prime_pow | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.185001\ninst✝ : CommMonoid G\np : ℕ\nhp : Fact (Nat.Prime p)\ng : { x // x ∈ primaryComponent G p }\n⊢ ∃ n, orderOf g = p ^ n",
"tactic": "simpa [primaryComponent] using g.property"
}
] | [
243,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean | SubMulAction.coe_one | [] | [
40,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_sup' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.308272\nβ : Type ?u.308275\nγ : Type ?u.308278\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nr : ι → ι → Prop\ninst✝ : IsWellOrder ι r\nf : ι → Ordinal\n⊢ bsup (type r) (bfamilyOfFamily' r f) = sup f",
"tactic": "simp only [... | [
1465,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.ne_of_false_of_true | [] | [
760,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Deprecated/Group.lean | MonoidHom.isGroupHom | [] | [
256,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.bijOn_sin | [] | [
642,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.map_sum | [] | [
1858,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1857,
1
] |
Mathlib/FieldTheory/Tower.lean | FiniteDimensional.finrank_mul_finrank | [
{
"state_after": "case pos\nF : Type u\nK : Type v\nA : Type w\ninst✝⁷ : Field F\ninst✝⁶ : DivisionRing K\ninst✝⁵ : AddCommGroup A\ninst✝⁴ : Algebra F K\ninst✝³ : Module K A\ninst✝² : Module F A\ninst✝¹ : IsScalarTower F K A\ninst✝ : FiniteDimensional F K\nhA : FiniteDimensional K A\n⊢ finrank F K * finrank K A... | [
133,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.eq_of_le_of_domain_eq | [] | [
230,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Topology/Category/TopCat/OpenNhds.lean | TopologicalSpace.OpenNhds.openEmbedding | [] | [
101,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.inv_tensor | [
{
"state_after": "case hom_inv_id\nC_1 : Type u\n𝒞 : Category C_1\ninst : MonoidalCategory C_1\nC : Type u\ninst_1 : Category C\ninst_2 : MonoidalCategory C\nW X Y Z : C\nf : W ⟶ X\ninst_3 : IsIso f\ng : Y ⟶ Z\ninst_4 : IsIso g\n⊢ (f ⊗ g) ≫ (inv f ⊗ inv g) = 𝟙 (W ⊗ Y)",
"state_before": "C✝ : Type u\n𝒞 : ... | [
211,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.abs_log_sub_add_sum_range_le | [
{
"state_after": "x : ℝ\nh : abs x < 1\nn : ℕ\nF : ℝ → ℝ := fun x => ∑ i in Finset.range n, x ^ (i + 1) / (↑i + 1) + log (1 - x)\n⊢ abs (∑ i in Finset.range n, x ^ (i + 1) / (↑i + 1) + log (1 - x)) ≤ abs x ^ (n + 1) / (1 - abs x)",
"state_before": "x : ℝ\nh : abs x < 1\nn : ℕ\n⊢ abs (∑ i in Finset.range n, ... | [
268,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.fg_closure_singleton | [] | [
75,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | LinearEquiv.finrank_eq | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁹ : Ring K\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module K V\nV₂ : Type v'\ninst✝⁶ : AddCommGroup V₂\ninst✝⁵ : Module K V₂\nR : Type u_1\nM : Type u_2\nM₂ : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup M₂\ninst✝¹ : Module R M\ninst✝ : Modul... | [
227,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coe_inf | [] | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_le_coe_of_le_coe | [
{
"state_after": "case intro\nα : Type ?u.104939\nβ : Type ?u.104942\na✝ b✝ c d : ℝ≥0∞\nr p q b a : ℝ≥0\nh : ↑a ≤ ↑b\n⊢ ENNReal.toReal ↑a ≤ ↑b",
"state_before": "α : Type ?u.104939\nβ : Type ?u.104942\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\nb : ℝ≥0\nh : a ≤ ↑b\n⊢ ENNReal.toReal a ≤ ↑b",
"tactic": "lif... | [
724,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.coe_linearMapAt | [] | [
239,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | strictMonoOn_mul_self | [] | [
549,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.eq_pow_of_mul_eq_pow_bit1_right | [
{
"state_after": "no goals",
"state_before": "a b c : ℤ\nhab : IsCoprime a b\nk : ℕ\nh : a * b = c ^ bit1 k\n⊢ b * a = ?m.184097 hab h ^ bit1 k",
"tactic": "rwa [mul_comm] at h"
}
] | [
410,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.isPwo_iUnion_support | [] | [
1422,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1421,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_lt_tan_of_lt_of_lt_pi_div_two | [
{
"state_after": "x y : ℝ\nhx₁ : -(π / 2) < x\nhy₂ : y < π / 2\nhxy : x < y\nhx0 : x ≤ 0\nhy0 : y ≤ 0\n⊢ tan (-y) < tan (-x)",
"state_before": "x y : ℝ\nhx₁ : -(π / 2) < x\nhy₂ : y < π / 2\nhxy : x < y\nhx0 : x ≤ 0\nhy0 : y ≤ 0\n⊢ -tan y < -tan x",
"tactic": "rw [← tan_neg, ← tan_neg]"
},
{
"sta... | [
986,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.dense_induction | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.37249\nP : Type ?u.37252\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nS : Substructure L M\ns✝ : Set M\np : M → Prop\nx : M\ns : Set M\nhs : LowerAdjoint.toFun (closure L) s = ⊤\nHs : ∀ (x : M), x ∈ s → p x\nHfun : ∀ {n : ℕ} (f :... | [
363,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Group/Defs.lean | one_mul | [] | [
458,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toMatrix_transpose_apply | [] | [
70,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Num/Prime.lean | PosNum.minFac_to_nat | [
{
"state_after": "case one\n\n⊢ ↑(minFac one) = Nat.minFac ↑one\n\ncase bit1\nn : PosNum\n⊢ ↑(minFac (bit1 n)) = Nat.minFac ↑(bit1 n)\n\ncase bit0\na✝ : PosNum\n⊢ ↑(minFac (bit0 a✝)) = Nat.minFac ↑(bit0 a✝)",
"state_before": "n : PosNum\n⊢ ↑(minFac n) = Nat.minFac ↑n",
"tactic": "cases' n with n"
},
... | [
85,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_sum | [
{
"state_after": "case h\nα : Type u_2\nβ : Type ?u.1758361\nγ : Type ?u.1758364\nδ : Type ?u.1758367\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nι : Type u_1\nm : MeasurableSpace α\nμ : ι → Measure α\nf : α → ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(withDensity (sum μ) f) s = ↑↑(sum fun n => withDensity (μ n... | [
1583,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1580,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.eventually_ge_atTop | [] | [
208,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_succ_row_zero | [
{
"state_after": "m : Type ?u.2165579\nn✝ : Type ?u.2165582\ninst✝⁴ : DecidableEq n✝\ninst✝³ : Fintype n✝\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nn : ℕ\nA : Matrix (Fin (Nat.succ n)) (Fin (Nat.succ n)) R\n⊢ ∑ i : Fin (Nat.succ n), (-1) ^ ↑i * Aᵀ i 0 * det (submatrix Aᵀ (↑(Fi... | [
752,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
747,
1
] |
Mathlib/Algebra/Homology/ImageToKernel.lean | homology.condition | [] | [
191,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
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