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/GroupWithZero/Basic.lean | eq_zero_of_zero_eq_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.2729\nM₀ : Type u_1\nG₀ : Type ?u.2735\nM₀' : Type ?u.2738\nG₀' : Type ?u.2741\nF : Type ?u.2744\nF' : Type ?u.2747\ninst✝ : MulZeroOneClass M₀\nh : 0 = 1\na : M₀\n⊢ a = 0",
"tactic": "rw [← mul_one a, ← h, mul_zero]"
}
] | [
114,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.bound_of_shell | [
{
"state_after": "case pos\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.2539023\nE : Type u_3\nEₗ : Type ?u.2539029\nF : Type u_4\nFₗ : Type ?u.2539035\nG : Type ?u.2539038\nGₗ : Type ?u.2539041\n𝓕 : Type ?u.2539044\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedAddCommGroup G... | [
1411,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_union_Ico | [
{
"state_after": "case inl.inl\nα : Type u_1\nβ : Type ?u.116141\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab : a ≤ b\nhcd : c ≤ d\nh₁ : a ≤ d\nh₂ : c ≤ b\n⊢ Ico a b ∪ Ico c d = Ico (min a c) (max b d)\n\ncase inl.inr\nα : Type u_1\nβ : Type ?u.116141\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nhab... | [
1529,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1525,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_of_nat | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ↑abs ↑n = ↑abs ↑↑n",
"tactic": "rw [ofReal_nat_cast]"
}
] | [
965,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Topology/LocalAtTarget.lean | embedding_iff_embedding_of_iSup_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set β\nι : Type ?u.40608\nU : ι → Opens β\nhU : iSup U = ⊤\nh : Continuous f\n⊢ Inducing f ∧ Function.Injective f ↔\n ∀ (i : ι), Inducing (restrictPreimage (U i).carrier f) ∧ Function.Injecti... | [
148,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.inf_basis_neBot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45066\nγ : Type ?u.45069\nι : Sort u_2\nι' : Sort u_3\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nhl : HasBasis l p s\nhl' : HasBasis l' p' s'\n⊢ (∀ {i : PProd ι ι'}, p i.fs... | [
633,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | neg_iff_neg_of_mul_pos | [] | [
580,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec3_dotProduct' | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\na₀ a₁ a₂ b₀ b₁ b₂ : α\n⊢ ![a₀, a₁, a₂] ⬝ᵥ ![b₀, b₁, b₂] = a₀ * b₀ + a₁ * b₁ + a₂ * b₂",
"tactic": "rw [cons_dotProduct_cons, cons_dotProduct_co... | [
502,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_eq_of_lt | [
{
"state_after": "case hnc\na b : Nat\nh₀ : a < b\n⊢ ¬(0 < b ∧ b ≤ a)",
"state_before": "a b : Nat\nh₀ : a < b\n⊢ a / b = 0",
"tactic": "rw [div_eq a, if_neg]"
},
{
"state_after": "case hnc\na b : Nat\nh₀ : a < b\nh₁ : 0 < b ∧ b ≤ a\n⊢ False",
"state_before": "case hnc\na b : Nat\nh₀ : a < b... | [
295,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
292,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_image_fst | [
{
"state_after": "case a\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.11252\ns s' : Finset α\nt t' : Finset β\na : α\nb : β\ninst✝ : DecidableEq α\nht : Finset.Nonempty t\ni : α\n⊢ i ∈ image Prod.fst (s ×ˢ t) ↔ i ∈ s",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.11252\ns s' : Finset α\nt t' : Finse... | [
80,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | orthonormal_span | [] | [
1967,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1963,
1
] |
Mathlib/Order/WithBot.lean | WithTop.le_coe | [] | [
857,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Algebra/Star/Prod.lean | Prod.star_def | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.coe_union | [] | [
1832,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1831,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrixAlgEquiv_apply' | [] | [
758,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.mk_add_mk | [] | [
165,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Complex/Cardinality.lean | mk_complex | [
{
"state_after": "no goals",
"state_before": "⊢ (#ℂ) = 𝔠",
"tactic": "rw [mk_congr Complex.equivRealProd, mk_prod, lift_id, mk_real, continuum_mul_self]"
}
] | [
29,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | IsLocalMax.fderiv_eq_zero | [] | [
210,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq | [] | [
138,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsFiltered.sup_objs_exists | [
{
"state_after": "case empty\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsFiltered C\n⊢ ∃ S, ∀ {X : C}, X ∈ ∅ → _root_.Nonempty (X ⟶ S)\n\ncase insert\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsFiltered C\nX : C\nO' : Finset C\nnm : ¬X ∈ O'\nh : ∃ S, ∀ {X : C}, X ∈ O' → _root_.Nonempty (X ⟶ S)\n⊢ ∃ S, ∀ {X_1 : ... | [
217,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_apply | [
{
"state_after": "case hq\nK : Type u\ninst✝³ : Field K\nR : Type u_1\nF : Type u_2\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : MonoidHomClass F K[X] R[X]\nφ : F\nhφ : K[X]⁰ ≤ Submonoid.comap φ R[X]⁰\nf : RatFunc K\n⊢ denom f ≠ 0",
"state_before": "K : Type u\ninst✝³ : Field K\nR : Type u_1\nF : Type... | [
1349,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add | [] | [
656,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.exists_eq_smul | [] | [
700,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Algebra/Field/Power.lean | zpow_bit1_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DivisionRing α\nn✝ : ℤ\na : α\nn : ℤ\n⊢ (-a) ^ bit1 n = -a ^ bit1 n",
"tactic": "rw [zpow_bit1', zpow_bit1', neg_mul_neg, neg_mul_eq_mul_neg]"
}
] | [
33,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Dynamics/Flow.lean | Flow.continuous | [] | [
122,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
11
] |
Std/Data/Nat/Gcd.lean | Nat.coprime.dvd_of_dvd_mul_left | [
{
"state_after": "no goals",
"state_before": "k m n : Nat\nH1 : coprime k m\nH2 : k ∣ m * n\n⊢ k ∣ n * m",
"tactic": "rwa [Nat.mul_comm]"
}
] | [
253,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
252,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biInter_eq_iInter | [] | [
903,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_mul_im | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nz : ℂ\n⊢ (↑r * z).im = r * z.im",
"tactic": "simp [ofReal']"
}
] | [
284,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Topology/Separation.lean | lim_eq_iff | [] | [
1036,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.dirac_apply_of_mem | [
{
"state_after": "α : Type u_1\nβ : Type ?u.326296\nγ : Type ?u.326299\nδ : Type ?u.326302\nι : Type ?u.326305\nR : Type ?u.326308\nR' : Type ?u.326311\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\ninst✝ : MeasurableSpace α\na... | [
1990,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1986,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.ascFactorial_pos | [] | [
329,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.SignedMeasure.toMeasureOfLEZero_toSignedMeasure | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.717548\nm : MeasurableSpace α\ns : SignedMeasure α\ni✝ j : Set α\nhs : restrict s Set.univ ≤ restrict 0 Set.univ\ni : Set α\n⊢ MeasurableSet i →\n ↑(Measure.toSignedMeasure (toMeasureOfLEZero s Set.univ (_ : MeasurableSet Set.univ) hs)) i = ↑(-s) i",
"s... | [
1411,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.inv_zero | [] | [
888,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
8
] |
Std/Data/Nat/Lemmas.lean | Nat.one_add | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ 1 + n = succ n",
"tactic": "simp [Nat.add_comm]"
}
] | [
321,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
321,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.sinh_lt_sinh | [] | [
701,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Tactic/Ring/RingNF.lean | Mathlib.Tactic.RingNF.nat_rawCast_1 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\n⊢ Nat.rawCast 1 = 1",
"tactic": "simp"
}
] | [
115,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_inter_distrib_right | [] | [
2091,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2090,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/WeaklyInitial.lean | CategoryTheory.hasInitial_of_weakly_initial_and_hasWideEqualizers | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasWideEqualizers C\nT : C\nhT : ∀ (X : C), Nonempty (T ⟶ X)\nendos : Type v := T ⟶ T\n⊢ HasInitial C",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : HasWideEqualizers C\nT : C\nhT : ∀ (X : C), Nonempty (T ⟶ X)\n⊢ HasInitial C",
"tac... | [
67,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.of_part | [
{
"state_after": "this : ∀ (f : ℕ →. ℕ), Partrec f → Partrec' fun v => f (Vector.head v)\nn : ℕ\nf : Vector ℕ n →. ℕ\nhf : _root_.Partrec f\ng : ℕ → Part ℕ := fun n₁ => Part.bind ↑(decode n₁) fun a => Part.map encode (f a)\n⊢ Partrec' f",
"state_before": "this : ∀ (f : ℕ →. ℕ), Partrec f → Partrec' fun v =>... | [
412,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.node3R_size | [
{
"state_after": "α : Type u_1\nl : Ordnode α\nx : α\nm : Ordnode α\ny : α\nr : Ordnode α\n⊢ (match l with\n | nil => 0\n | node sz l x r => sz) +\n (((match m with\n | nil => 0\n | node sz l x r => sz) +\n match r with\n | nil => 0\n |... | [
394,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_zero_measure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.922396\nγ : Type ?u.922399\nδ : Type ?u.922402\nm✝ : MeasurableSpace α\nμ ν : Measure α\nm : MeasurableSpace α\nf : α → ℝ≥0∞\n⊢ (∫⁻ (a : α), f a ∂0) ≤ ⊥",
"tactic": "simp [lintegral]"
}
] | [
646,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/Analysis/Convex/Slope.lean | convexOn_iff_slope_mono_adjacent | [] | [
202,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_eq_one | [
{
"state_after": "no goals",
"state_before": "p q : ℕ+ → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∃ n, p n\nn m : ℕ+\n⊢ PNat.find h = 1 ↔ p 1",
"tactic": "simp [find_eq_iff]"
}
] | [
106,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Order/Max.lean | not_isMin_of_lt | [] | [
320,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiff.continuous | [] | [
1472,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.ext_iff | [] | [
751,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/Order/WithBot.lean | WithBot.le_coe_unbot' | [] | [
385,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/List/Rotate.lean | List.isRotated_singleton_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nl l' : List α\nx : α\n⊢ [x] ~r l ↔ [x] = l",
"tactic": "rw [isRotated_comm, isRotated_singleton_iff, eq_comm]"
}
] | [
507,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | NormedAddGroupHom.IsQuotient.norm_lift | [
{
"state_after": "case intro\nM : Type u_1\nN : Type u_2\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nf : NormedAddGroupHom M N\nhquot : IsQuotient f\nε : ℝ\nhε : 0 < ε\nm : M\n⊢ ∃ m_1, ↑f m_1 = ↑f m ∧ ‖m_1‖ < ‖↑f m‖ + ε",
"state_before": "M : Type u_1\nN : Type u_2\ninst✝¹ : Semino... | [
390,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xn_succ_succ | [] | [
532,
24
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531,
1
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Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_mk | [] | [
94,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_eq_finrank_span_cols | [
{
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164,
97
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163,
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Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ioi_self_neBot' | [] | [
2392,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.isoCoproduct_inv | [
{
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500,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
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Mathlib/Data/List/MinMax.lean | List.minimum_singleton | [] | [
302,
6
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301,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.csinh | [] | [
510,
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508,
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Mathlib/Data/Stream/Init.lean | Stream'.nth_inits | [
{
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{
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719,
80
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714,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.congr_right | [] | [
319,
32
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317,
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Mathlib/Order/Bounds/Basic.lean | MonotoneOn.mem_lowerBounds_image_self | [] | [
1169,
38
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1168,
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.aestronglyMeasurable_const | [] | [
1152,
48
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1150,
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Std/Data/Array/Init/Lemmas.lean | Array.SatisfiesM_mapM' | [] | [
167,
93
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161,
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Mathlib/Analysis/Normed/Field/Basic.lean | nnnorm_prod | [] | [
714,
50
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713,
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Mathlib/Topology/MetricSpace/Basic.lean | abs_dist_sub_le | [] | [
270,
96
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268,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_lt_aleph0_iff | [
{
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1573,
97
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Mathlib/Deprecated/Subgroup.lean | Multiplicative.isNormalSubgroup_iff | [
{
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211,
48
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Continuous.comp_stronglyMeasurable | [] | [
372,
96
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369,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mod_zero | [
{
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}
] | [
1036,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.add_sub_self_right | [
{
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{
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] | [
540,
45
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539,
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Mathlib/Data/Finmap.lean | Finmap.ext_lookup | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\ns₁✝ s₂✝ : Finmap β\ns₁ s₂ : AList β\nh : ∀ (x : α), dlookup x s₁.entries = dlookup x s₂.entries\n⊢ ⟦s₁⟧ = ⟦s₂⟧",
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329,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
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Std/Data/Array/Init/Lemmas.lean | Array.SatisfiesM_foldlM | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nas : Array α\nmotive : Nat → β → Prop\ninit : β\nh0 : motive 0 init\nf : β → α → m β\nhf : ∀ (i : Fin (size as)) (b : β), motive i.val b → SatisfiesM (motive (i.val + 1)) (f b as[i])\n⊢ SatisfiesM (mo... | [
116,
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104,
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Mathlib/Topology/Sequences.lean | IsSeqCompact.isComplete | [
{
"state_after": "X : Type u_1\nY : Type ?u.18740\ninst✝¹ : UniformSpace X\ns : Set X\ninst✝ : IsCountablyGenerated (𝓤 X)\nhs : IsSeqCompact s\nl : Filter X\nhl : Cauchy l\nhls : l ≤ 𝓟 s\nthis : NeBot l\n⊢ ∃ x, x ∈ s ∧ l ≤ 𝓝 x",
"state_before": "X : Type u_1\nY : Type ?u.18740\ninst✝¹ : UniformSpace X\ns... | [
384,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
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Std/Data/Int/Lemmas.lean | Int.mul_ne_zero | [] | [
1307,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1306,
11
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Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | limsInf_eq_of_le_nhds | [] | [
188,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.mem_inf | [
{
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494,
23
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492,
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Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.lintegral_tendsto_of_countably_generated | [] | [
382,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
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Mathlib/LinearAlgebra/Basic.lean | pi_eq_sum_univ | [
{
"state_after": "case h\nR✝ : Type ?u.40332\nR₁ : Type ?u.40335\nR₂ : Type ?u.40338\nR₃ : Type ?u.40341\nR₄ : Type ?u.40344\nS : Type ?u.40347\nK : Type ?u.40350\nK₂ : Type ?u.40353\nM : Type ?u.40356\nM' : Type ?u.40359\nM₁ : Type ?u.40362\nM₂ : Type ?u.40365\nM₃ : Type ?u.40368\nM₄ : Type ?u.40371\nN : Type ... | [
157,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_sup_le_and_aux_left | [] | [
912,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
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Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.mem_inf | [] | [
155,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atTop_prod_self | [] | [
1475,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1473,
1
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Mathlib/Topology/Sets/Closeds.lean | TopologicalSpace.Closeds.coe_sup | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Dense.eq_zero_of_inner_right | [
{
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"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.903722\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\nx y : E\ninst✝ : CompleteSpace E\nhK : Dense ↑... | [
969,
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Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.coe_id | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/Order/Monotone/Basic.lean | StrictMono.ite' | [
{
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604,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
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Mathlib/Data/List/Join.lean | List.drop_take_succ_join_eq_get | [
{
"state_after": "α : Type u_1\nβ : Type ?u.9242\nL : List (List α)\ni : Fin (length L)\nthis : take (↑i) (map length L) = take (↑i) (map length (take (↑i + 1) L))\n⊢ drop (sum (take (↑i) (map length L))) (take (sum (take (↑i + 1) (map length L))) (join L)) = get L i",
"state_before": "α : Type u_1\nβ : Typ... | [
143,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_false | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.99177\nι : Type ?u.99180\ninst✝ : CompleteLattice α\nf : Filter β\nu : β → α\n⊢ (blimsup u f fun x => False) = ⊥",
"tactic": "simp [blimsup_eq]"
}
] | [
641,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_smul | [] | [
401,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
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] |
Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.mapRange.linearEquiv_trans | [
{
"state_after": "no goals",
"state_before": "ι : Type u_5\nR : Type u_1\nS : Type ?u.248835\nM : ι → Type ?u.248840\nN : Type ?u.248843\ndec_ι : DecidableEq ι\ninst✝¹⁰ : Semiring R\ninst✝⁹ : (i : ι) → AddCommMonoid (M i)\ninst✝⁸ : (i : ι) → Module R (M i)\ninst✝⁷ : AddCommMonoid N\ninst✝⁶ : Module R N\nβ :... | [
249,
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245,
1
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Mathlib/Algebra/Star/Basic.lean | star_star_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semigroup R\ninst✝ : StarSemigroup R\nx y : R\n⊢ star (star x * y) = star y * x",
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}
] | [
143,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Parity.lean | Odd.sub_even | [
{
"state_after": "F : Type ?u.104075\nα : Type u_1\nβ : Type ?u.104081\nR : Type ?u.104084\ninst✝ : Ring α\na b : α\nn : ℕ\nha : Odd a\nhb : Even b\n⊢ Odd (a + -b)",
"state_before": "F : Type ?u.104075\nα : Type u_1\nβ : Type ?u.104081\nR : Type ?u.104084\ninst✝ : Ring α\na b : α\nn : ℕ\nha : Odd a\nhb : Ev... | [
445,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_trunc | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn m : σ →₀ ℕ\nφ : MvPowerSeries σ R\n⊢ MvPolynomial.coeff m (↑(trunc R n) φ) = if m < n then ↑(coeff R m) φ else 0",
"tactic": "simp [trunc, coeff_truncFun]"
}
] | [
704,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_eq_mul | [
{
"state_after": "ι : Type ?u.375985\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : α → β\na b : α\nhn : a ≠ b\nh₀ : ∀ (c : α), c ∈ s → c ≠ a ∧ c ≠ b → f c = 1\nha : ¬a ∈ s → f a = 1\nhb : ¬b ∈ s → f b = 1\nthis : DecidableEq α\n⊢ ∏ x in s... | [
849,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_concat | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\np : Walk G u v\nh : Adj G v w\n⊢ edges (concat p h) = List.concat (edges p) (Quotient.mk (Sym2.Rel.setoid V) (v, w))",
"tactic": "simp [edges]"
... | [
750,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAtFilter.tendsto_nhds | [] | [
715,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
8
] |
Mathlib/Data/Finite/Card.lean | Finite.cast_card_eq_mk | [] | [
72,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/FieldTheory/Finiteness.lean | IsNoetherian.coeSort_finsetBasisIndex | [] | [
91,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Algebra/CharP/Basic.lean | charP_of_prime_pow_injective | [
{
"state_after": "case intro\nR✝ : Type ?u.957555\ninst✝³ : NonAssocRing R✝\ninst✝² : Fintype R✝\nn✝ : ℕ\nR : Type u_1\ninst✝¹ : Ring R\ninst✝ : Fintype R\np : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nhn : Fintype.card R = p ^ n\nhR : ∀ (i : ℕ), i ≤ n → ↑(p ^ i) = 0 → i = n\nc : ℕ\nhc : CharP R c\n⊢ CharP R (p ^ n)",... | [
675,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.id_apply | [] | [
753,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.reindex_updateRow | [] | [
2912,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2909,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | iteratedFDeriv_add_apply | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\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 : Normed... | [
1246,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.rightUnitor_hom_hom | [
{
"state_after": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX : Action V G\n⊢ ((𝟙 X.V ⊗ 𝟙 (𝟙_ V)) ≫ (ρ_ X.V).hom) ≫ 𝟙 X.V = (ρ_ X.V).hom",
"state_before": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX : Action V G\n⊢ (ρ_ ... | [
543,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
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