file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.map_surjective | [
{
"state_after": "case h1\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\nhf : Surjective ↑f\ni : σ →₀ ℕ\nfr : S₁\n⊢ ∃ a, ↑(map f) a = ↑(monomial i) fr\n\ncase h2... | [
1304,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.pos_iff | [] | [
132,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
11
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_and | [] | [
1143,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.comp_continuousLinearEquivAt_eq_coord_change | [
{
"state_after": "case h.h\nR : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝¹⁰ : NontriviallyNormedField R\ninst✝⁹ : (x : B) → AddCommMonoid (E x)\ninst✝⁸ : (x : B) → Module R (E x)\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace R F\ninst✝⁵ : TopologicalSpace B\ninst✝⁴ : TopologicalSpace ... | [
542,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Order/OrderIsoNat.lean | RelEmbedding.not_wellFounded_of_decreasing_seq | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\nf : (fun x x_1 => x > x_1) ↪r r\n⊢ Nonempty ((fun x x_1 => x > x_1) ↪r r)",
"state_before": "α : Type u_1\nr : α → α → Prop\ninst✝ : IsStrictOrder α r\nf : (fun x x_1 => x > x_1) ↪r r\n⊢ ¬WellFounded r",
"tactic": "rw [wellFoun... | [
103,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_Ico | [] | [
729,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Topology/Separation.lean | QuotientMap.of_surjective_continuous | [] | [
1344,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_mul_I | [
{
"state_after": "x y : ℂ\nh : I * sin (x * I) = -sinh x\n⊢ sin (x * I) = sinh x * I",
"state_before": "x y : ℂ\n⊢ sin (x * I) = sinh x * I",
"tactic": "have h : I * sin (x * I) = -sinh x := by\n rw [mul_comm, ← sinh_mul_I]\n ring_nf\n simp"
},
{
"state_after": "x y : ℂ\nh : I * sin (x * I) =... | [
838,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_a_ne_zero' | [] | [
391,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.pointReflection_involutive | [] | [
795,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.eq_cyclotomic_iff | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nhpos : 0 < n\nP : R[X]\n✝ : Nontrivial R\n⊢ P = cyclotomic n R ↔ P * ∏ i in Nat.properDivisors n, cyclotomic i R = X ^ n - 1",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nn : ℕ\nhpos : 0 < n\nP : R[X]\n⊢ P = cyclotomic n R ↔ P * ∏ i in Nat.pr... | [
556,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.Coprime.gcd_mul_right_cancel | [
{
"state_after": "m n k : ℕ+\n⊢ Coprime k n → gcd (k * m) n = gcd m n",
"state_before": "m n k : ℕ+\n⊢ Coprime k n → gcd (m * k) n = gcd m n",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m n k : ℕ+\n⊢ Coprime k n → gcd (k * m) n = gcd m n",
"tactic": "apply... | [
214,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/List/Cycle.lean | List.prev_cons_cons_eq' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx y z : α\nh : x ∈ y :: z :: l\nhx : x = y\n⊢ prev (y :: z :: l) x h = getLast (z :: l) (_ : z :: l ≠ [])",
"tactic": "rw [prev, dif_pos hx]"
}
] | [
220,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_toIcoMod | [] | [
746,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Topology/Separation.lean | compl_singleton_mem_nhdsSet_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\nx : α\ns : Set α\n⊢ {x}ᶜ ∈ 𝓝ˢ s ↔ ¬x ∈ s",
"tactic": "rw [isOpen_compl_singleton.mem_nhdsSet, subset_compl_singleton_iff]"
}
] | [
677,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_one_iff_eq | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.153618\nt : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite ∅) _auto✝\n⊢ ncard ∅ ≤ 1 ↔ ∅ = ∅ ∨ ∃ a, ∅ = {a}\n\ncase inr.intro\nα : Type u_1\nβ : Type ?u.153618\ns t : Set α\na b x✝ y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\nx : α\nhx :... | [
681,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.count_ne_zero_iff_dvd | [
{
"state_after": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\na p : α\nha0 : a ≠ 0\nhp : Irreducible p\ninst✝ : Nontrivial α\n⊢ count (Associates.mk p) (... | [
1715,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1703,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.coeff_mul_degree_add_degree | [
{
"state_after": "case refine'_1\nR : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np✝ q✝ : R[X]\nι : Type ?u.653636\np q : R[X]\n⊢ ∀ (b : ℕ × ℕ),\n b ∈ Nat.antidiagonal (natDegree p + natDegree q) →\n b ≠ (natDegree p, natDegree q) → coeff p b.fst * coeff q b.snd = 0\n\ncase refine'_2\n... | [
925,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Data/Set/Basic.lean | Set.nonempty_of_not_subset | [] | [
483,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Polynomial/IntegralNormalization.lean | Polynomial.integralNormalization_eval₂_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : CommSemiring S\np : R[X]\nf : R →+* S\nz : S\nhz : eval₂ f z p = 0\ninj : ∀ (x : R), ↑f x = 0 → x = 0\n⊢ ∑ n in support p, ↑f (coeff (integralNormalization p) n) * (z * ↑f (leadingCoeff p)) ... | [
147,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_mul_distrib_aux | [
{
"state_after": "F : Type ?u.217198\nι : Type ?u.217201\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.217210\nf✝ : α → β → β\nop : α → α → α\ninst✝¹ : Monoid β\ninst✝ : Monoid γ\ns : Finset α\nf g : α → β\ncomm_ff : Set.Pairwise ↑s fun x y => Commute (f x) (f y)\ncomm_gg : Set.Pairwise ↑s fun x y => Commute (g x) (... | [
388,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.preimage | [] | [
1717,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1715,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_congr | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S₁\np q : MvPolynomial σ R\nf : R →+* S₁\ng : σ → S₁\nf₁ : R →+* S₁\ng₁ : σ → S₁\np₁ : MvPolynomial σ R\n⊢ ↑(eval₂Hom f₁ g₁) p₁ = ↑(eval₂Ho... | [
1035,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Std/Data/Int/DivMod.lean | Int.div_eq_of_eq_mul_right | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH1 : b ≠ 0\nH2 : a = b * c\n⊢ div a b = c",
"tactic": "rw [H2, Int.mul_div_cancel_left _ H1]"
}
] | [
742,
92
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
741,
11
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.comp_mono | [] | [
362,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | lt_one_div_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.159623\nα : Type u_1\nβ : Type ?u.159629\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nha : a < 0\nhb : b < 0\n⊢ a < 1 / b ↔ b < 1 / a",
"tactic": "simpa using lt_inv_of_neg ha hb"
}
] | [
832,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Init/Propext.lean | iff_eq_eq | [] | [
35,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.closure_subset | [] | [
446,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/RingTheory/JacobsonIdeal.lean | Ideal.map_jacobson_of_bijective | [] | [
204,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffOn.csin | [] | [
429,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.comp_tsnd | [
{
"state_after": "t : Type u → Type u → Type u\ninst✝⁵ : Bitraversable t\nβ : Type u\nF G : Type u → Type u\ninst✝⁴ : Applicative F\ninst✝³ : Applicative G\ninst✝² : IsLawfulBitraversable t\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα β₀ β₁ β₂ : Type u\ng : β₀ → F β₁\ng' : β₁ → G β₂\nx : t α β₀... | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | left_le_toIcoMod | [] | [
99,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_union_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.122422\ns t : Set α\na b x y : α\nf : α → β\nh : Disjoint s t\nhs : autoParam (Set.Finite s) _auto✝\nht : autoParam (Set.Finite t) _auto✝\n⊢ ncard (s ∪ t) = ncard s + ncard t",
"tactic": "classical\nrw [ncard_eq_toFinset_card _ hs, ... | [
491,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_neg | [] | [
745,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.comap_abs_nhds_zero | [] | [
148,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Computability/Ackermann.lean | ack_two | [
{
"state_after": "case zero\n\n⊢ ack 2 zero = 2 * zero + 3\n\ncase succ\nn : ℕ\nIH : ack 2 n = 2 * n + 3\n⊢ ack 2 (succ n) = 2 * succ n + 3",
"state_before": "n : ℕ\n⊢ ack 2 n = 2 * n + 3",
"tactic": "induction' n with n IH"
},
{
"state_after": "no goals",
"state_before": "case zero\n\n⊢ ack... | [
94,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
src/lean/Init/Prelude.lean | PLift.down_up | [] | [
760,
71
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
760,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | zpow_neg_one | [] | [
301,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Order/WellFounded.lean | Function.argmin_le | [] | [
223,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.incl_idealRange | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
1143,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1139,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.comap | [] | [
857,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.hom_ext' | [] | [
1431,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | measurable_mul_op | [] | [
789,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_nat_add | [] | [
247,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Algebra/Order/Hom/Basic.lean | le_map_div_add_map_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.16670\nF : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.16682\nδ : Type ?u.16685\ninst✝³ : Group α\ninst✝² : AddCommSemigroup β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b c : α\n⊢ ↑f (a / c) ≤ ↑f (a / b) + ↑f (b / c)",
"tacti... | [
154,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.exists_boundary_dart | [
{
"state_after": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nS : Set V\nuS✝ : u ∈ S\nvS✝ : ¬v ∈ S\nu✝ : V\nuS : u✝ ∈ S\nvS : ¬u✝ ∈ S\n⊢ ∃ d, d ∈ darts nil ∧ d.fst ∈ S ∧ ¬d.snd ∈ S\n\ncase cons\nV : Type u\nV' : Type v\nV'' : Type w\nG... | [
1262,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.IsEquivalence.ofIso_trans | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF G H : C ⥤ D\ne : F ≅ G\ne' : G ≅ H\nhF : IsEquivalence F\n⊢ mk' (inverse F) ((unitIso ≪≫ hcomp e (Iso.refl (inverse F))) ≪≫ hcomp e' (Iso.refl (inverse F)))\n (hcomp (Iso.refl (inverse F)) e'.symm ≪≫ hcomp (Iso.refl (inv... | [
641,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_zero | [] | [
2557,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2556,
1
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.ble_eq_false | [
{
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}
] | [
672,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
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Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.comp_tfst | [
{
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81,
55
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.symm_bijective | [] | [
354,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
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Mathlib/RingTheory/NonZeroDivisors.lean | eq_zero_of_ne_zero_of_mul_left_eq_zero | [] | [
119,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Std/Data/String/Lemmas.lean | String.Pos.ne_of_lt | [] | [
121,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
121,
1
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Mathlib/Analysis/NormedSpace/Basic.lean | interior_sphere | [
{
"state_after": "no goals",
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160,
67
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158,
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_mul | [] | [
158,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Std/Logic.lean | Decidable.not_and | [] | [
600,
81
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599,
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] |
Mathlib/Data/MvPolynomial/Supported.lean | MvPolynomial.supported_strictMono | [] | [
135,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Data/Nat/Factors.lean | Nat.factors_add_two | [
{
"state_after": "no goals",
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}
] | [
121,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
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Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.comap_normalizer | [
{
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86,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_nhds_eq | [] | [
1851,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1850,
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Mathlib/Data/List/Rotate.lean | List.rotate_eq_rotate' | [
{
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},
{
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116,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Finset.Nat.antidiagonalTuple_zero_zero | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongEpi_comp | [
{
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106,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Order/Basic.lean | GE.ge.le | [] | [
324,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
11
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Mathlib/Order/SymmDiff.lean | himp_bihimp | [
{
"state_after": "no goals",
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"tactic": "rw [bihimp, himp_inf_distrib, himp_himp, himp_himp]"
}
] | [
291,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
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Mathlib/Data/Rat/Cast.lean | Rat.cast_inj | [
{
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203,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
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Mathlib/Analysis/Convex/Join.lean | convexJoin_comm | [
{
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46,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsLimit.lift_comp_conePointsIsoOfNatIso_inv | [
{
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337,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
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Mathlib/Algebra/Group/Basic.lean | div_eq_one | [
{
"state_after": "no goals",
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}
] | [
816,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
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Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.multiplicity_le | [
{
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193,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.reflTransSymmAux_mem_I | [
{
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"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ ... | [
83,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_inv_int | [
{
"state_after": "case ofNat\nF : Type ?u.33624\nι : Type ?u.33627\nα : Type u_1\nβ : Type ?u.33633\ninst✝ : DivisionRing α\nn : ℕ\n⊢ ↑(↑(Int.ofNat n))⁻¹ = (↑(Int.ofNat n))⁻¹\n\ncase negSucc\nF : Type ?u.33624\nι : Type ?u.33627\nα : Type u_1\nβ : Type ?u.33633\ninst✝ : DivisionRing α\nn : ℕ\n⊢ ↑(↑(Int.negSucc ... | [
167,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_le_one | [] | [
267,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | modelWithCornersSelf_coe_symm | [] | [
388,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_one_div_one_add_sq | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, 1 / (1 + x ^ 2)) = arctan b - arctan a",
"tactic": "simp only [one_div, integral_inv_one_add_sq]"
}
] | [
553,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
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Mathlib/Data/Seq/Computation.lean | Computation.LiftRel.swap | [] | [
1052,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1050,
1
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Mathlib/CategoryTheory/Types.lean | CategoryTheory.FunctorToTypes.inv_hom_id_app_apply | [] | [
186,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.iInf_Prop | [
{
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1249,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.frontier_thickening_disjoint | [
{
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"state_before": "ι : Sort ?u.92543\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpac... | [
965,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | aux | [
{
"state_after": "no goals",
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"tact... | [
152,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
9
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.boundary_one | [
{
"state_after": "case h\nX : Type u\ninst✝ : TopologicalSpace X\nn : ℕ\nx✝ : X\nx : I^ 1\n⊢ x ∈ boundary 1 ↔ x ∈ {0, 1}",
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"tactic": "ext x"
},
{
"state_after": "case h\nX : Type u\ninst✝ : Topological... | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_eq_of_eq_mul_right | [
{
"state_after": "no goals",
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"tactic": "rw [H2, Int.mul_ediv_cancel_left _ H1]"
}
] | [
745,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
744,
11
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_eq | [
{
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"state_before":... | [
113,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Init/Function.lean | Function.Injective.comp | [] | [
67,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/List/Basic.lean | List.enum_singleton | [] | [
3893,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3892,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.rowLen_transpose | [
{
"state_after": "no goals",
"state_before": "μ : YoungDiagram\ni : ℕ\n⊢ rowLen (transpose μ) i = colLen μ i",
"tactic": "simp [rowLen, colLen]"
}
] | [
375,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | IsCyclic.exponent_eq_card | [
{
"state_after": "case intro\nα : Type u\na : α\ninst✝² : Group α\ninst✝¹ : IsCyclic α\ninst✝ : Fintype α\ng : α\nhg : ∀ (x : α), x ∈ Subgroup.zpowers g\n⊢ exponent α = Fintype.card α",
"state_before": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : IsCyclic α\ninst✝ : Fintype α\n⊢ exponent α = Fintype.card ... | [
571,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Algebra/Order/Module.lean | bddAbove_smul_iff_of_neg | [] | [
245,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_zero_succ' | [] | [
105,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Part.lean | Part.get_mem | [] | [
108,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/List/Forall2.lean | List.rel_reverse | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.140328\nδ : Type ?u.140331\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\na✝ : α\nb✝ : β\nl₁✝ : List α\nl₂✝ : List β\nh₁ : R a✝ b✝\nh₂ : Forall₂ R l₁✝ l₂✝\n⊢ Forall₂ R (reverse l₁✝ ++ [a✝]) (reverse l₂✝ ++ [b✝])",
"state_before": "α : Type... | [
260,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_union_congr_of_subset | [
{
"state_after": "α : Type u_1\nβ : Type ?u.36188\nγ : Type ?u.36191\nδ : Type ?u.36194\nι : Type ?u.36197\nR : Type ?u.36200\nR' : Type ?u.36203\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t t₁ t₂ : Set α\nhs : s₁ ⊆ s₂\nhsμ : ↑↑μ s₂ ≤ ↑↑μ s₁\nht : t₁ ⊆ t₂\nhtμ : ↑↑μ t₂ ≤ ↑↑μ t₁\n⊢ ↑↑μ (⋃ (b : Bool), b... | [
356,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.nthHomSeq_mul | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nR : Type u_1\ninst✝ : NonAssocSemiring R\nf : (k : ℕ) → R →+* ZMod (p ^ k)\nf_compat : ∀ (k1 k2 : ℕ) (hk : k1 ≤ k2), RingHom.comp (ZMod.castHom (_ : p ^ k1 ∣ p ^ k2) (ZMod (p ^ k1))) (f k2) = f k1\nr s : R\nε : ℚ\nhε : ε > 0\n⊢ ∃ i,\n ∀ (j : ℕ), j ≥ i →... | [
567,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | tendsto_uniformity_iff_dist_tendsto_zero | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.214516\nι✝ : Type ?u.214519\ninst✝ : PseudoMetricSpace α\nι : Type u_1\nf : ι → α × α\np : Filter ι\n⊢ Tendsto ((fun p => dist p.fst p.snd) ∘ f) p (𝓝 0) ↔ Tendsto (fun x => dist (f x).fst (f x).snd) p (𝓝 0)",
"state_before": "α : Type u\nβ : Type v\nX ... | [
1465,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.generateFrom_setOf_isOpen | [] | [
220,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Filter.Tendsto.nnrpow | [] | [
469,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | RingTopology.ext | [] | [
310,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | Filter.EventuallyEq.derivWithin_eq | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nhs : f₁ =ᶠ[𝓝[s] x] f\n... | [
606,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.congr | [] | [
1222,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | Basis.ext_alternating | [
{
"state_after": "R : Type ?u.1290808\ninst✝¹⁶ : Semiring R\nM : Type ?u.1290814\ninst✝¹⁵ : AddCommMonoid M\ninst✝¹⁴ : Module R M\nN : Type ?u.1290846\ninst✝¹³ : AddCommMonoid N\ninst✝¹² : Module R N\nP : Type ?u.1290876\ninst✝¹¹ : AddCommMonoid P\ninst✝¹⁰ : Module R P\nM' : Type ?u.1290906\ninst✝⁹ : AddCommGro... | [
1222,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
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