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/Fin/Basic.lean | Fin.succAbove_pred | [
{
"state_after": "case h\nn m : ℕ\nx y : Fin (n + 1)\nh : x < y\nhy : optParam (y ≠ 0) (_ : y ≠ 0)\n⊢ x ≤ ↑castSucc (pred y hy)",
"state_before": "n m : ℕ\nx y : Fin (n + 1)\nh : x < y\nhy : optParam (y ≠ 0) (_ : y ≠ 0)\n⊢ ↑(succAbove x) (pred y hy) = y",
"tactic": "rw [succAbove_above, succ_pred]"
},... | [
2142,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2139,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_induction₂ | [
{
"state_after": "case refine'_1\nF : Type ?u.501259\nR : Type u_2\nA : Type u_1\nB : Type ?u.501268\ninst✝⁹ : CommSemiring R\ninst✝⁸ : StarRing R\ninst✝⁷ : Semiring A\ninst✝⁶ : Algebra R A\ninst✝⁵ : StarRing A\ninst✝⁴ : StarModule R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : StarRing B\ninst✝ : Sta... | [
526,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/LinearAlgebra/Ray.lean | exists_nonneg_right_iff_sameRay | [
{
"state_after": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhy : y ≠ 0\n⊢ (∃ r, 0 ≤ r ∧ x = r • y) ↔ SameRay R y x",
"state_before": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\... | [
752,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_casesOn | [] | [
598,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_sup | [] | [
508,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_self_lt_top_iff | [
{
"state_after": "α : Type ?u.93966\nβ : Type ?u.93969\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ a = 0 → a < ⊤",
"state_before": "α : Type ?u.93966\nβ : Type ?u.93969\na✝ b c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\n⊢ a * a < ⊤ ↔ a < ⊤",
"tactic": "rw [ENNReal.mul_lt_top_iff, and_self, or_self, or_iff_left_iff... | [
610,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_one_le_of_lt | [] | [
1252,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1252,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.iUnion_Ioo_of_tendsto | [] | [
472,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_eq_arg_add_pi_iff | [
{
"state_after": "case inl\nx : ℂ\nhi : x.im < 0\n⊢ arg (-x) = arg x + π ↔ x.im < 0 ∨ x.im = 0 ∧ 0 < x.re\n\ncase inr.inl\nx : ℂ\nhi : x.im = 0\n⊢ arg (-x) = arg x + π ↔ x.im < 0 ∨ x.im = 0 ∧ 0 < x.re\n\ncase inr.inr\nx : ℂ\nhi : 0 < x.im\n⊢ arg (-x) = arg x + π ↔ x.im < 0 ∨ x.im = 0 ∧ 0 < x.re",
"state_bef... | [
414,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Finsupp.smul_sum | [] | [
83,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/LinearAlgebra/TensorPower.lean | TensorPower.cast_trans | [] | [
130,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg | [
{
"state_after": "no goals",
"state_before": "x : ℝ*\n⊢ InfiniteNeg x ↔ Infinitesimal x⁻¹ ∧ x⁻¹ < 0",
"tactic": "rw [← infinitePos_neg, infinitePos_iff_infinitesimal_inv_pos, inv_neg, neg_pos, infinitesimal_neg]"
}
] | [
751,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_congr_imp | [] | [
818,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_bot | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.109715\n𝕜 : Type ?u.109718\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑(edgeSet G)\ninst✝¹ : Fintype ↑(edgeSet G₁)\ninst✝ : Fintype ↑(edgeSet G₂)\n... | [
923,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.toList_eq_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.31041\nγ : Type ?u.31044\ns : Multiset α\n⊢ toList s = [] ↔ s = 0",
"tactic": "rw [← coe_eq_zero, coe_toList]"
}
] | [
463,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.dist_affineCombination | [
{
"state_after": "V : Type ?u.16219\nP : Type ?u.16222\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nι : Type ?u.16493\ns : Finset ι\nw₁ w₂ : ι → ℝ\np : ι → P\nh₁ : ∑ i in s, w₁ i = 1\nh₂ : ∑ i in s, w₂ i = 1\na₁ : (fun a => P) w₁\n⊢ Sort ?u... | [
110,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Pi.hasSum | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.798357\nγ : Type ?u.798360\nδ : Type ?u.798363\nι : Type u_3\nπ : α → Type u_2\ninst✝¹ : (x : α) → AddCommMonoid (π x)\ninst✝ : (x : α) → TopologicalSpace (π x)\nf : ι → (x : α) → π x\ng : (x : α) → π x\n⊢ HasSum f g ↔ ∀ (x : α), HasSum... | [
1314,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1312,
1
] |
Mathlib/Order/Filter/ZeroAndBoundedAtFilter.lean | Filter.BoundedAtFilter.smul | [] | [
106,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.lt_succ_sqrt' | [] | [
80,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_add_nat | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.213247\nα : Type u_1\nβ : Type ?u.213253\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\nn : ℕ\n⊢ ⌈a + ↑n⌉ = ⌈a⌉ + ↑n",
"tactic": "rw [← Int.cast_ofNat, ceil_add_int]"
}
] | [
1149,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.AbsolutelyContinuous.refl | [] | [
2381,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2380,
11
] |
Mathlib/Algebra/Group/Basic.lean | div_right_inj | [] | [
791,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.ae_empty_or_univ_of_image_ae_le' | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : MeasureTheory.Measure α\nhf : Ergodic f\nhs : MeasurableSet s\nh_fin : ↑↑μ s ≠ ⊤\nhs' : s ≤ᶠ[ae μ] f ⁻¹' s\n⊢ s =ᶠ[ae μ] ∅ ∨ s =ᶠ[ae μ] univ",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Meas... | [
160,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.universalHom_commutes | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝² : Semiring R\nS : Submonoid R\ninst✝¹ : OreSet S\nT : Type u_1\ninst✝ : Semiring T\nf : R →+* T\nfS : { x // x ∈ S } →* Tˣ\nhf : ∀ (s : { x // x ∈ S }), ↑f ↑s = ↑(↑fS s)\nr : R\n⊢ ↑(universalHom f fS hf) (↑numeratorHom r) = ↑f r",
"tacti... | [
819,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.sInf_coe | [
{
"state_after": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\nS : Set (LieSubalgebra R L)\n⊢ (⋂ (p : Submodule R L) (_ : p ∈ {x | ∃ s, s ∈ S... | [
502,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_apply_below | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni j : Fin (n + 1)\nh : j < i\nx : α i\np : (k : Fin n) → α (↑(succAbove i) k)\n⊢ insertNth i x p j = Eq.recOn (_ : ↑(succAbove i) (castLT j (_ : ↑j < n)) = j) (p (castLT j (_ : ↑j < n)))",
"tactic": "rw [insertN... | [
711,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Logic/Basic.lean | Decidable.and_forall_ne | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.15695\nα : Sort u_1\nκ : ι → Sort ?u.15697\np✝ q : α → Prop\ninst✝ : DecidableEq α\na : α\np : α → Prop\n⊢ (p a ∧ ∀ (b : α), b ≠ a → p b) ↔ ∀ (b : α), p b",
"tactic": "simp only [← @forall_eq _ p a, ← forall_and, ← or_imp, Decidable.em, forall_co... | [
754,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.int_cast_eq_int_cast_iff_dvd_sub | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nc : ℕ\n⊢ ↑a = ↑b ↔ ↑c ∣ b - a",
"tactic": "rw [ZMod.int_cast_eq_int_cast_iff, Int.modEq_iff_dvd]"
}
] | [
479,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.sum_pow_units | [
{
"state_after": "K : Type u_1\nR : Type ?u.484011\ninst✝² : Field K\ninst✝¹ : Fintype K\ninst✝ : Fintype Kˣ\ni : ℕ\nφ : Kˣ →* K :=\n { toOneHom := { toFun := fun x => ↑(x ^ i), map_one' := (_ : ↑(1 ^ i) = 1) },\n map_mul' := (_ : ∀ (x y : Kˣ), ↑((x * y) ^ i) = ↑(x ^ i) * ↑(y ^ i)) }\n⊢ ∑ x : Kˣ, ↑(x ^ i) =... | [
204,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.forall_pow_eq_one_iff | [
{
"state_after": "case intro\nK : Type u_1\nR : Type ?u.404549\ninst✝¹ : Field K\ninst✝ : Fintype K\ni : ℕ\nx : Kˣ\nhx : ∀ (x_1 : Kˣ), x_1 ∈ Subgroup.zpowers x\n⊢ (∀ (x : Kˣ), x ^ i = 1) ↔ q - 1 ∣ i",
"state_before": "K : Type u_1\nR : Type ?u.404549\ninst✝¹ : Field K\ninst✝ : Fintype K\ni : ℕ\n⊢ (∀ (x : Kˣ... | [
182,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.toFun_eq_coe | [] | [
741,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mk_self | [
{
"state_after": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type ?u.129008\ninst✝¹ : CommMonoid N\nP : Type ?u.129014\ninst✝ : CommMonoid P\na : { x // x ∈ S }\n⊢ 1 = mk (↑a) a",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type ?u.129008\ninst✝¹ : CommMonoid N\... | [
434,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.transpose_circulant | [
{
"state_after": "case a.h\nα : Type u_2\nβ : Type ?u.5768\nm : Type ?u.5771\nn : Type u_1\nR : Type ?u.5777\ninst✝ : AddGroup n\nv : n → α\ni✝ x✝ : n\n⊢ (circulant v)ᵀ i✝ x✝ = circulant (fun i => v (-i)) i✝ x✝",
"state_before": "α : Type u_2\nβ : Type ?u.5768\nm : Type ?u.5771\nn : Type u_1\nR : Type ?u.57... | [
84,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/ZMod/Defs.lean | ZMod.card | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ninst✝ : Fintype (ZMod n)\n⊢ Fintype.card (ZMod n) = n",
"tactic": "cases n with\n| zero => exact (not_finite (ZMod 0)).elim\n| succ n => convert Fintype.card_fin (n + 1) using 2"
},
{
"state_after": "no goals",
"state_before": "case zero\n... | [
114,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.Types.pushforwardFamily_compatible | [
{
"state_after": "C : Type u_3\ninst✝⁴ : Category C\nD : Type u_2\ninst✝³ : Category D\nE : Type ?u.49250\ninst✝² : Category E\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology E\nA : Type ?u.49302\ninst✝¹ : Category A\nG : C ⥤ D\nH : CoverDense K G\ninst✝ : Full G\nℱ : Dᵒᵖ ⥤ Typ... | [
197,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/CategoryTheory/Functor/LeftDerived.lean | CategoryTheory.Functor.leftDerived_map_eq | [
{
"state_after": "C : Type u\ninst✝¹² : Category C\nD : Type u_2\ninst✝¹¹ : Category D\ninst✝¹⁰ : Preadditive C\ninst✝⁹ : HasZeroObject C\ninst✝⁸ : HasEqualizers C\ninst✝⁷ : HasImages C\ninst✝⁶ : HasProjectiveResolutions C\ninst✝⁵ : Preadditive D\ninst✝⁴ : HasEqualizers D\ninst✝³ : HasCokernels D\ninst✝² : HasI... | [
127,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.symm_trans | [
{
"state_after": "case h.mk\nF✝ : Type ?u.209823\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nf₀ f₁ f₂ : C(X, Y)\nF : Homotopy f₀ f₁\nG : Homotopy f₁ f₂\nt : ↑I\nsnd✝ : X\n⊢ ↑(symm (trans F G... | [
283,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_rpow_eq_tsum | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < ENNReal.toReal p\nf : { x // x ∈ lp E p }\n⊢ (∑' (i : α), ‖↑f i‖ ^ ENNReal.toReal p) ^ (1 / ENNReal.toReal p * ENNReal.toReal p) =\n ∑' (i : α), ‖↑f i‖ ^ ENNReal.toReal p\n\ncase hx\nα : Type u_... | [
424,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousOn.inv | [] | [
255,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.16783\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\ninst✝ : DecidableEq β\n⊢ gcd (∅ ∪ s₂) f = GCDMonoid.gcd (gcd ∅ f) (gcd s₂ f)",
"tactic": "rw [empty_union, gcd_... | [
189,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.sndKernelFork_ι | [] | [
1699,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1698,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.mapAlgEquiv_refl | [] | [
138,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_eq_zpow_iff' | [] | [
442,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_sdiff_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.264321\nγ : Type ?u.264324\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b : α\ns t : Finset α\na : α\n⊢ erase (s \\ t) a = erase s a \\ erase t a",
"tactic": "simp_rw [erase_eq, sdiff_sdiff, sup_sdiff_eq_sup le_rfl, sup_comm]"
... | [
2274,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2273,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.testBit_succ | [
{
"state_after": "m : ℕ\nb : Bool\nn : ℕ\nthis : bodd (shiftr (shiftr (bit b n) 1) m) = bodd (shiftr n m)\n⊢ testBit (bit b n) (succ m) = testBit n m",
"state_before": "m : ℕ\nb : Bool\nn : ℕ\n⊢ testBit (bit b n) (succ m) = testBit n m",
"tactic": "have : bodd (shiftr (shiftr (bit b n) 1) m) = bodd (shi... | [
356,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_int_cast | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.656985\nT : Type ?u.656988\nR : Type u_1\ninst✝ : CommRing R\nr x y z✝ : R\na b c : ℍ[R]\nz : ℤ\n⊢ ↑normSq ↑z = ↑z ^ 2",
"tactic": "rw [← coe_int_cast, normSq_coe]"
}
] | [
1221,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | AddSubgroup.int_mul_mem | [
{
"state_after": "case h.e'_4\nR : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\nG : AddSubgroup R\nk : ℤ\ng : R\nh : g ∈ G\n⊢ ↑k * g = k • g",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\nG : AddSubgroup R\nk : ℤ\... | [
1409,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.deleteEdges_inter_edgeSet_right_eq | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.253463\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : Subgraph G\ns : Set (Sym2 V)\n⊢ deleteEdges G' (s ∩ edgeSet G') = deleteEdges G' s",
"tactic": "ext <;> simp (config := { contextual := true }) [imp_false]"
}
] | [
1107,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulLeftRight_apply | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBySet_span_singleton_eq | [] | [
293,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_bot | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.exists_mem_Ico₀ | [] | [
290,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_of_infinite_mulSupport | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.185720\nι : Type ?u.185723\nG : Type ?u.185726\nM : Type u_2\nN : Type ?u.185732\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\nhf : Set.Infinite (mulSupport f)\n⊢ (∏ᶠ (i : α), f i) = 1",
"tactic": "classical rw [finprod_d... | [
425,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.Bucket.update_update | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nself : Bucket α β\ni : USize\nd d' : AssocList α β\nh : USize.toNat i < Array.size self.val\nh' : USize.toNat i < Array.size (update self i d h).val\n⊢ { val := Array.set (Array.set self.val { val := USize.toNat i, isLt := h } d) { val := USize.toNat i, isLt := h' }... | [
31,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
29,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_eq_iff_eq' | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝¹ : CommMonoid N\nP : Type ?u.851307\ninst✝ : CommMonoid P\nf : LocalizationMap S N\nx₁ x₂ : M\ny₁ y₂ : { x // x ∈ S }\n⊢ mk' f x₁ y₁ = mk' f x₂ y₂ ↔ ↑(toMap f) (x₁ * ↑y₂) = ↑(toMap f) (x₂ ... | [
780,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.eq_of_add_eq_add_right | [
{
"state_after": "a b c : Cardinal\nh : b + a = b + c\nhb : b < ℵ₀\n⊢ a = c",
"state_before": "a b c : Cardinal\nh : a + b = c + b\nhb : b < ℵ₀\n⊢ a = c",
"tactic": "rw [add_comm a b, add_comm c b] at h"
},
{
"state_after": "no goals",
"state_before": "a b c : Cardinal\nh : b + a = b + c\nhb... | [
848,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
11
] |
Mathlib/LinearAlgebra/Ray.lean | neg_rayOfNeZero | [] | [
462,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | ae_eq_trim_of_measurable | [
{
"state_after": "G : Type ?u.2153121\nα✝ : Type ?u.2153124\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : Div G\nm✝ : MeasurableSpace α✝\nf✝ g✝ : α✝ → G\nμ✝ : MeasureTheory.Measure α✝\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝³ : MeasurableSpace E\ninst✝² : AddGroup E\nins... | [
416,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.list_indexOf₁ | [] | [
781,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.sup | [] | [
1553,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1551,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.coe_mkContinuous | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.int_mul | [] | [
370,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_ite_subset | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.93493\nι : Sort ?u.93496\nι' : Sort ?u.93499\nf✝ : ι → α\ns t : Set α\np : α → Prop\ninst✝ : DecidablePred p\nf g : α → β\n⊢ ∀ (y : α), (if p y then f y else g y) ∈ range f ∪ range g",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.93493\nι... | [
1097,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1093,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.pred_succAbove | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nx : Fin n\ny : Fin (n + 1)\nh : y ≤ ↑castSucc x\nh' : optParam (↑(succAbove y) x ≠ 0) (_ : ↑(succAbove y) x ≠ 0)\n⊢ pred (↑(succAbove y) x) h' = x",
"tactic": "simp only [succAbove_above _ _ h, pred_succ]"
}
] | [
2152,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2150,
1
] |
Mathlib/Data/Set/Basic.lean | Set.univ_subset_iff | [] | [
683,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Std/Data/Int/Lemmas.lean | Int.negSucc_mul_ofNat' | [] | [
60,
98
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
60,
15
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.closure_eq_mrange | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nA : Type ?u.77455\nB : Type ?u.77458\ninst✝ : Monoid M\ns : Set M\n⊢ closure s = mrange (↑FreeMonoid.lift Subtype.val)",
"tactic": "rw [FreeMonoid.mrange_lift, Subtype.range_coe]"
}
] | [
358,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/GroupTheory/GroupAction/Sum.lean | Sum.smul_inr | [] | [
54,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.componentComplMk_eq_of_adj | [
{
"state_after": "V : Type u\nG✝ : SimpleGraph V\nK L L' M : Set V\nG : SimpleGraph V\nv w : V\nvK : ¬v ∈ K\nwK : ¬w ∈ K\na : Adj G v w\n⊢ Reachable (induce (Kᶜ) G) { val := v, property := vK } { val := w, property := wK }",
"state_before": "V : Type u\nG✝ : SimpleGraph V\nK L L' M : Set V\nG : SimpleGraph ... | [
80,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | deriv.log | [] | [
129,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.sum_properDivisors_dvd | [
{
"state_after": "case zero\nh : ∑ x in properDivisors zero, x ∣ zero\n⊢ ∑ x in properDivisors zero, x = 1 ∨ ∑ x in properDivisors zero, x = zero\n\ncase succ\nn : ℕ\nh : ∑ x in properDivisors (succ n), x ∣ succ n\n⊢ ∑ x in properDivisors (succ n), x = 1 ∨ ∑ x in properDivisors (succ n), x = succ n",
"state... | [
377,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_mul_negOfNat | [
{
"state_after": "no goals",
"state_before": "m n : Nat\n⊢ ↑m * negOfNat n = negOfNat (m * n)",
"tactic": "cases n <;> rfl"
}
] | [
383,
18
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
382,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_fintype | [] | [
71,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_mul | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.mem_sum | [
{
"state_after": "ι : Type ?u.865375\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\nf : α → Multiset β\ns : Finset α\nb : β\n⊢ ∀ ⦃a : α⦄ {s : Finset α},\n ¬a ∈ s →\n (b ∈ ∑ x in s, f x ↔ ∃ a, a ∈ s ∧ b ∈ f a) → (b ∈ ∑ x in insert a s, f x ↔ ∃ a_3, a_3 ∈ insert a s ∧ b ∈ f... | [
1898,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1893,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.results_of_terminates' | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nT : Terminates s\na : α\nh : a ∈ s\n⊢ Results s (get s) (length s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nT : Terminates s\na : α\nh : a ∈ s\n⊢ Results s a (length s)",
"tactic": "rw [← get_eq_of_... | [
516,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | Algebra.IsIntegral.finite | [
{
"state_after": "R : Type u_1\nA : Type u_2\nB : Type ?u.621954\nS : Type ?u.621957\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\nh : Algebra.IsIntegral R A\nh' : FiniteType R A\nthis : RingHom.Finite (algebraMap R A... | [
442,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | RingHom.eq_natCast' | [] | [
293,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_sub' | [] | [
1235,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.val_mk | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand₀' | [] | [
209,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_eq_cons_Ioo | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.109231\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b c : α\nh : a < b\n⊢ Ico a b = cons a (Ioo a b) (_ : ¬a ∈ Ioo a b)",
"tactic": "classical rw [cons_eq_insert, Ioo_insert_left h]"
},
{
"state_after": "no goal... | [
630,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Lp.lean | MeasureTheory.Memℒp.finStronglyMeasurable_of_stronglyMeasurable | [
{
"state_after": "α : Type u_2\nG : Type u_1\np : ℝ≥0∞\nm m0 : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup G\nf : α → G\nhf : Memℒp f p\nhf_meas : StronglyMeasurable f\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nthis✝¹ : MeasurableSpace G := borel G\nthis✝ : BorelSpace G\n⊢ FinStronglyMeasurable f ... | [
58,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | mem_closure_iff_nhds_one | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\ninst✝ : TopologicalSpace α\nf : α → G\ns✝ : Set α\nx✝ : α\nx : G\ns : Set G\n⊢ (∀ (i : Set G), i ∈ 𝓝 1 → ∃ y, y ∈ s ∧ y ∈ {y | y / x ∈ id i}) ↔ ∀ (U : Set G), U ∈ 𝓝 1 →... | [
855,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.sized_shadow_iff | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns✝ t : Finset α\na : α\nk r : ℕ\nh : ¬∅ ∈ 𝒜\nh𝒜 : Set.Sized r ↑((∂ ) 𝒜)\ns : Finset α\nhs : s ∈ ↑𝒜\n⊢ card s = r + 1",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 : Finset (Finset α)\ns t : Finset α\na : α\nk r :... | [
123,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_eq_sInf_lsub | [
{
"state_after": "case refine'_1\nα : Type ?u.13677\nr : α → α → Prop\no : Ordinal\n⊢ ∀ (b : Cardinal), b ∈ {a | ∃ ι f, lsub f = o ∧ (#ι) = a} → cof o ≤ b\n\ncase refine'_2\nα : Type ?u.13677\nr : α → α → Prop\no : Ordinal\n⊢ cof o ∈ {a | ∃ ι f, lsub f = o ∧ (#ι) = a}",
"state_before": "α : Type ?u.13677\nr... | [
261,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_le_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.428121\nf : α → β\nhf : Injective f\ns t : Multiset α\n⊢ map f s ≤ map f t ↔ s ≤ t",
"tactic": "classical\n refine' ⟨fun h => le_iff_count.mpr fun a => _, map_le_map⟩\n simpa [count_map_eq_count' f _ hf] using le_iff... | [
2614,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2610,
1
] |
Mathlib/Data/Sum/Interval.lean | Finset.sumLift₂_eq_empty | [
{
"state_after": "case refine'_1\nα₁ : Type u_3\nα₂ : Type u_4\nβ₁ : Type u_5\nβ₂ : Type u_6\nγ₁ : Type u_1\nγ₂ : Type u_2\nf f₁ g₁ : α₁ → β₁ → Finset γ₁\ng f₂ g₂ : α₂ → β₂ → Finset γ₂\na : α₁ ⊕ α₂\nb : β₁ ⊕ β₂\nc : γ₁ ⊕ γ₂\nh : sumLift₂ f g a b = ∅\n⊢ (∀ (a₁ : α₁) (b₁ : β₁), a = inl a₁ → b = inl b₁ → f a₁ b₁ =... | [
93,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Sigma/Lex.lean | PSigma.Lex.mono | [
{
"state_after": "case left\nι : Sort u_1\nα : ι → Sort u_2\nr r₁✝ r₂✝ : ι → ι → Prop\ns s₁✝ s₂✝ : (i : ι) → α i → α i → Prop\nr₁ r₂ : ι → ι → Prop\ns₁ s₂ : (i : ι) → α i → α i → Prop\nhr : ∀ (a b : ι), r₁ a b → r₂ a b\nhs : ∀ (i : ι) (a b : α i), s₁ i a b → s₂ i a b\na₁✝ : ι\na : α a₁✝\na₂✝ : ι\nb : α a₂✝\nhij... | [
179,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | ContinuousLinearMap.intervalIntegral_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14415591\n𝕜 : Type u_1\nE : Type u_3\nF : Type u_2\nA : Type ?u.14415603\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : CompleteSpace E\ninst✝⁴ : NormedSpace ℝ E\na✝ b✝ : ℝ\nμ : MeasureTheory.Measure ℝ\nf : ℝ → E\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace ... | [
673,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Algebra/Regular/Basic.lean | IsRightRegular.mul | [] | [
112,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
src/lean/Init/Data/Array/DecidableEq.lean | Array.isEqvAux_self | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\na : Array α\ni : Nat\n⊢ (if h : i < size a then\n let_fun this := (_ : i < size a);\n decide (a[i] = a[i]) && isEqvAux a a (_ : size a = size a) (fun x y => decide (x = y)) (i + 1)\n else true) =\n true",
"state_before": "α : Type u_1\ni... | [
39,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
34,
1
] |
Mathlib/Analysis/Convex/Between.lean | affineSegment_vsub_const_image | [] | [
113,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_tensorProduct' | [
{
"state_after": "R : Type u_1\ninst✝⁹ : CommRing R\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nN : Type u_3\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R N\nι : Type ?u.584160\ninst✝⁴ : Module.Free R M\ninst✝³ : Module.Finite R M\ninst✝² : Module.Free R N\ninst✝¹ : Module.Finite R N\ninst✝ : Non... | [
277,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.normalizedFactors_mul | [
{
"state_after": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\nx y : α\nhx : x ≠ 0\nhy : y ≠ 0\nh : ↑normalize = Associates.out ∘ Associates.mk\n⊢ normalizedFactors (x * y) = normalizedFactors x + normalizedFactor... | [
687,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.nondegenerate_toBilin'_iff_det_ne_zero | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2956365\nM✝ : Type ?u.2956368\ninst✝¹⁹ : Semiring R\ninst✝¹⁸ : AddCommMonoid M✝\ninst✝¹⁷ : Module R M✝\nR₁ : Type ?u.2956404\nM₁ : Type ?u.2956407\ninst✝¹⁶ : Ring R₁\ninst✝¹⁵ : AddCommGroup M₁\ninst✝¹⁴ : Module R₁ M₁\nR₂ : Type ?u.2957016\nM₂ : Type ... | [
600,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | map_iInf | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.6894\nδ : Type ?u.6897\nι : Sort u_4\nκ : ι → Sort ?u.6905\ninst✝² : InfSet α\ninst✝¹ : InfSet β\ninst✝ : sInfHomClass F α β\nf : F\ng : ι → α\n⊢ ↑f (⨅ (i : ι), g i) = ⨅ (i : ι), ↑f (g i)",
"tactic": "sim... | [
140,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.tendsto_integral_approxOn_of_measurable_of_range_subset | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1279631\nE : Type ?u.1279634\nF : Type ?u.1279637\n𝕜 : Type ?u.1279640\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : CompleteSpace E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : SMulCommClass ℝ �... | [
1398,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1392,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.subtypeRestr_coe | [] | [
1374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1372,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.closure_iUnion_closure | [] | [
521,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.