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/GroupTheory/Nilpotent.lean | nilpotent_iff_finite_ascending_central_series | [
{
"state_after": "case mp\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ Group.IsNilpotent G → ∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤\n\ncase mpr\nG : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\n⊢ (∃ n H, IsAscendingCentralSeries H ∧ H n = ⊤) → Group.IsNilpotent G",
... | [
230,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_smul' | [] | [
132,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.hasDerivWithinAt_next | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nv : PicardLindelof E\nf : FunSpace v\ninst✝ : CompleteSpace E\nt : ↑(Icc v.tMin v.tMax)\nthis : Fact (↑t ∈ Icc v.tMin v.tMax)\n⊢ HasDerivWithinAt ((next f).toFun ∘ proj v) (PicardLindelof.toFun v (↑t) (toFun f t)) (Icc v.tM... | [
296,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.abs_toZNum | [] | [
1106,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorBundleCore.localTriv_symmL | [
{
"state_after": "case h\nR : Type u_2\nB : Type u_1\nF : Type u_3\nE : B → Type ?u.445706\ninst✝⁸ : NontriviallyNormedField R\ninst✝⁷ : (x : B) → AddCommMonoid (E x)\ninst✝⁶ : (x : B) → Module R (E x)\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace R F\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpa... | [
816,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Order/LocallyFinite.lean | WithBot.Ioo_coe_coe | [] | [
1184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.le_of_dvd | [] | [
1265,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/Data/List/Perm.lean | List.Subperm.filter | [
{
"state_after": "case intro.intro\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\np : α → Bool\nl l' xs : List α\nhp : xs ~ l\nh : xs <+ l'\n⊢ List.filter p l <+~ List.filter p l'",
"state_before": "α : Type uu\nβ : Type vv\nl₁ l₂ : List α\np : α → Bool\nl l' : List α\nh : l <+~ l'\n⊢ List.filter p l <+~ List.f... | [
457,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Topology/ContinuousFunction/Algebra.lean | ContinuousMap.coe_nat_cast | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Logic/Basic.lean | Classical.some_spec₂ | [] | [
989,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.isWf_support | [] | [
102,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_lt_iff | [] | [
701,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | List.Nat.nodup_antidiagonalTuple | [
{
"state_after": "case zero\nn✝ n : ℕ\n⊢ Nodup (antidiagonalTuple Nat.zero n)\n\ncase succ\nn✝ k : ℕ\nih : ∀ (n : ℕ), Nodup (antidiagonalTuple k n)\nn : ℕ\n⊢ Nodup (antidiagonalTuple (Nat.succ k) n)",
"state_before": "k n : ℕ\n⊢ Nodup (antidiagonalTuple k n)",
"tactic": "induction' k with k ih generaliz... | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.generateFrom_eq | [
{
"state_after": "α : Type u_1\nd : DynkinSystem α\ns : Set (Set α)\nhs : IsPiSystem s\n⊢ generate s ≤ ofMeasurableSpace (generateFrom s)",
"state_before": "α : Type u_1\nd : DynkinSystem α\ns : Set (Set α)\nhs : IsPiSystem s\n⊢ ofMeasurableSpace\n (toMeasurableSpace (generate s)\n (_ : ∀ (t₁ t₂... | [
730,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_of_le_of_one_le' | [] | [
798,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryFan.IsLimit.hom_ext | [] | [
245,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/FiniteField.lean | ZMod.trace_pow_card | [
{
"state_after": "n : Type u_1\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nM : Matrix n n (ZMod p)\nh : trace (M ^ Fintype.card (ZMod p)) = trace M ^ Fintype.card (ZMod p)\n⊢ trace (M ^ p) = trace M ^ p",
"state_before": "n : Type u_1\ninst✝² : DecidableEq n\ninst✝¹ : Fin... | [
65,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Finset.Nonempty.cSup_eq_max' | [] | [
45,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.tendsto_setToL1 | [] | [
1259,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/Data/Finset/Sym.lean | Finset.sym_union | [] | [
225,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
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.502155\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... | [
250,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Box.splitUpper_def | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nM : Type ?u.18967\nn : ℕ\nI : Box ι\ni✝ : ι\nx✝ : ℝ\ny : ι → ℝ\ninst✝ : DecidableEq ι\ni : ι\nx : ℝ\nh : x ∈ Ioo (lower I i) (upper I i)\nh' : optParam (∀ (j : ι), update I.lower i x j < upper I j) (_ : ∀ (x_1 : ι), update I.lower i x x_1 < upper I... | [
136,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_ge_of_const_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.290238\nE : Type ?u.290241\nF : Type ?u.290244\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\ns t : Set α\nhf✝ : IntegrableOn f s\nhg : IntegrableOn g s\nc : ℝ\nhs : MeasurableSet s\nhμs : ↑↑μ s ≠ ⊤\nhf : ∀ (x : α), x ∈ s → c ≤ f x\nhfint : IntegrableOn (fun ... | [
717,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | BilinForm.toQuadraticForm_smul | [] | [
676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_symm | [] | [
560,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_empty | [] | [
766,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Topology/Maps.lean | Function.Injective.embedding_induced | [] | [
199,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/ModelTheory/Order.lean | FirstOrder.Language.realize_noBotOrder_iff | [
{
"state_after": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝ : LE M\n⊢ (∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 0 ≤ Fin.snoc (Fin.snoc default a) a_1 1) ↔ NoBotOrder M",
"state_before": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝ : LE M\n⊢ M ⊨ noBotOrderSentence Language.order... | [
254,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq | [] | [
425,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_mul_omega | [
{
"state_after": "a b : Ordinal\nm n : ℕ\nha : ↑m < ω\nhb : ↑n < ω\n⊢ ↑m * ↑n < ω",
"state_before": "a b : Ordinal\nm n : ℕ\nha : ↑m < ω\nhb : ↑n < ω\n⊢ (fun x x_1 => x * x_1) ↑m ↑n < ω",
"tactic": "dsimp only"
},
{
"state_after": "a b : Ordinal\nm n : ℕ\nha : ↑m < ω\nhb : ↑n < ω\n⊢ ↑(m * n) < ω... | [
344,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_bot | [] | [
232,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/RingTheory/DedekindDomain/Basic.lean | Ring.DimensionLEOne.integralClosure | [] | [
73,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
8
] |
Mathlib/Data/Erased.lean | Erased.bind_def | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutationsAux2_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nt : α\nts : List α\nr : List β\nys : List α\nf : List α → β\n⊢ (permutationsAux2 t ts [] ys f).snd ++ r = (permutationsAux2 t ts r ys f).snd",
"tactic": "induction ys generalizing f <;> simp [*]"
}
] | [
80,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Analysis/Convex/Combination.lean | convex_iff_sum_mem | [
{
"state_after": "R : Type u_1\nE : Type u_2\nF : Type ?u.108718\nι : Type ?u.108721\nι' : Type ?u.108724\nα : Type ?u.108727\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\nins... | [
220,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_add | [
{
"state_after": "case h\nθ₁ : Angle\nx✝ : ℝ\n⊢ cos (θ₁ + ↑x✝) = cos θ₁ * cos ↑x✝ - sin θ₁ * sin ↑x✝",
"state_before": "θ₁ θ₂ : Angle\n⊢ cos (θ₁ + θ₂) = cos θ₁ * cos θ₂ - sin θ₁ * sin θ₂",
"tactic": "induction θ₂ using Real.Angle.induction_on"
},
{
"state_after": "case h.h\nx✝¹ x✝ : ℝ\n⊢ cos (↑x... | [
440,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_min | [
{
"state_after": "a b c : Nat\nx✝ : a ≤ b ∧ a ≤ c\nh₁ : a ≤ b\nh₂ : a ≤ c\n⊢ a ≤ if b ≤ c then b else c",
"state_before": "a b c : Nat\nx✝ : a ≤ b ∧ a ≤ c\nh₁ : a ≤ b\nh₂ : a ≤ c\n⊢ a ≤ min b c",
"tactic": "rw [Nat.min_def]"
},
{
"state_after": "no goals",
"state_before": "a b c : Nat\nx✝ : ... | [
183,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
181,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.range_succAbove | [] | [
2170,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2169,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lt_lift_iff | [] | [
1137,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1132,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.HasZeroObject.to_zero_ext | [] | [
259,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | bit1_injective | [
{
"state_after": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : NoZeroDivisors R\ninst✝ : CharZero R\na b : R\nh : bit0 a = bit0 b\n⊢ a = b",
"state_before": "R : Type u_1\ninst✝² : NonAssocRing R\ninst✝¹ : NoZeroDivisors R\ninst✝ : CharZero R\na b : R\nh : bit1 a = bit1 b\n⊢ a = b",
"tactic": "simp o... | [
132,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.eq_of_mul_eq_mul_right | [
{
"state_after": "n m k : Nat\nhm : 0 < m\nh : m * n = m * k\n⊢ n = k",
"state_before": "n m k : Nat\nhm : 0 < m\nh : n * m = k * m\n⊢ n = k",
"tactic": "rw [Nat.mul_comm n m, Nat.mul_comm k m] at h"
},
{
"state_after": "no goals",
"state_before": "n m k : Nat\nhm : 0 < m\nh : m * n = m * k\... | [
469,
85
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
468,
1
] |
Std/Data/List/Basic.lean | List.dropLast_eq_dropLastTR | [
{
"state_after": "case h.h\nα : Type u_1\nl : List α\n⊢ dropLast l = dropLastTR l",
"state_before": "⊢ @dropLast = @dropLastTR",
"tactic": "funext α l"
},
{
"state_after": "no goals",
"state_before": "case h.h\nα : Type u_1\nl : List α\n⊢ dropLast l = dropLastTR l",
"tactic": "simp [drop... | [
217,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
216,
10
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | ball_sub_closedBall | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.1069697\nE : Type u_1\ninst✝³ : NormedField 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nx y z : E\nδ ε : ℝ\nhε : 0 < ε\nhδ : 0 ≤ δ\na b : E\n⊢ Metric.ball a ε - Metric.closedBall b δ = Metric.ball (a - ... | [
365,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mk_injective | [] | [
803,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | ContDiff.cexp | [] | [
159,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_nonneg | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.122679\nα : Type u_1\nβ : Type ?u.122685\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ 0 ≤ ⌊a⌋ ↔ 0 ≤ a",
"tactic": "rw [le_floor, Int.cast_zero]"
}
] | [
664,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.singletonMulHom_apply | [] | [
506,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isRefl_neg | [] | [
892,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | DifferentiableOn.hasDerivAt | [] | [
449,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivAtFilter.isBigO_sub | [] | [
291,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.Measure.integral_comp_inv_mul_right | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.97935\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : MeasurableSpace E\ninst✝⁵ : BorelSpace E\ninst✝⁴ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝³ : IsAddHaarMeasure μ\nF : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : Norme... | [
127,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.subset_span_trans | [] | [
178,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.colimit_topology | [] | [
411,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Dense.eq_of_sub_mem_orthogonal | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.890931\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 ↑K\nhK : Kᗮ = ⊥\nh : x - y ∈ Kᗮ\... | [
948,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
946,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.num_mk | [
{
"state_after": "no goals",
"state_before": "n d : ℤ\n⊢ (n /. d).num = Int.sign d * n / ↑(Int.gcd n d)",
"tactic": "rcases d with ((_ | _) | _) <;>\nrw [←Int.div_eq_ediv_of_dvd] <;>\nsimp [divInt, mkRat, Rat.normalize, Nat.succPNat, Int.sign, Int.gcd, -Nat.cast_succ,\n Int.zero_ediv, Int.ofNat_dvd_lef... | [
67,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Trivialization.linearEquivAt_apply | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Topology/LocallyConstant/Basic.lean | IsLocallyConstant.isOpen_fiber | [] | [
75,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.fderivWithin | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.65006\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.65101\ni... | [
142,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousWithinAt.integral_sub_linear_isLittleO_ae | [] | [
1004,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
995,
1
] |
Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.comp_app | [] | [
73,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_le_mul_of_nonpos_of_nonneg | [] | [
375,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/Data/Option/Basic.lean | Option.elim_none_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.20379\nδ : Type ?u.20382\nf : Option α → β\no : Option α\n⊢ Option.elim o (f none) (f ∘ some) = f o",
"tactic": "cases o <;> rfl"
}
] | [
407,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_one | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.coe_sumAddMonoidHom | [] | [
274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.IsClosable.closureIsClosable | [] | [
152,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.trans_le | [] | [
577,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Data/Int/Basic.lean | Int.succ_pred | [] | [
155,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Preadditive/Opposite.lean | CategoryTheory.op_sum | [] | [
101,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/RingTheory/Ideal/AssociatedPrime.lean | IsAssociatedPrime.isPrime | [] | [
61,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Algebra/Order/Kleene.lean | add_le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22650\nι : Type ?u.22653\nπ : ι → Type ?u.22658\ninst✝ : IdemSemiring α\na b c : α\n⊢ a + b ≤ c ↔ a ≤ c ∧ b ≤ c",
"tactic": "simp"
}
] | [
165,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_pair_le_of_left_mem | [] | [
1363,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.support_filter | [
{
"state_after": "case a\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\np : ι → Prop\ninst✝ : DecidablePred p\nf : Π₀ (i : ι), β i\ni : ι\n⊢ i ∈ support (filter p f) ↔ i ∈ Finset.f... | [
1256,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1255,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_mul | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsSymm.sub | [] | [
920,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
919,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_succ_eq_blsub | [] | [
1854,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1852,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.induction_on_min | [] | [
1645,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
1
] |
Mathlib/Algebra/DirectSum/Internal.lean | SetLike.Homogeneous.smul | [] | [
353,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Combinatorics/SetFamily/Shadow.lean | Finset.exists_subset_of_mem_shadow | [] | [
143,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_prod | [] | [
51,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Order/SupIndep.lean | Finset.supIndep_iff_disjoint_erase | [] | [
96,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_of_lt_add_one | [] | [
1256,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1256,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_inter_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.186600\nγ : Type ?u.186603\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t t₁ t₂ u v : Finset α\na✝ b a : α\ns : Finset α\nH : a ∈ s\n⊢ insert a ∅ ∩ s = insert a ∅",
"tactic": "rw [insert_inter_of_mem H, empty_inter]"
}
] | [
1676,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1675,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_eq_iterate | [
{
"state_after": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.135983\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝ x : 𝕜\n⊢ iteratedDeriv n f x = (deriv^[n]) f x",
... | [
302,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.inv_diagonal | [
{
"state_after": "l : Type ?u.340020\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nv : n → α\n⊢ Ring.inverse (diagonal v) = diagonal (Ring.inverse v)",
"state_before": "l : Type ?u.340020\nm : Type u\nn : Type u'\nα : Type v\ninst✝²... | [
576,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.fst | [] | [
205,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.coe_copy | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.attach_empty | [] | [
2417,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2416,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.antisymm_symm | [] | [
170,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_lt_card_fiber_of_mul_lt_card_of_maps_to | [] | [
248,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ContDiffAt.localInverse_apply_image | [] | [
785,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_inner_le_norm | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2478434\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : E\n⊢ ‖inner x y‖ ≤ sqrt (↑re (inner x x)) * sqrt (↑re (inner y y))",
... | [
1098,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Algebra/MonoidAlgebra/Division.lean | AddMonoidAlgebra.modOf_apply_add_self | [] | [
149,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | derivWithin.comp | [] | [
196,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_congr | [] | [
575,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
574,
1
] |
Mathlib/Order/Hom/Set.lean | compl_strictAnti | [] | [
156,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Terminal.lean | CategoryTheory.Limits.hasInitial_of_hasInitial_of_preservesColimit | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nG : C ⥤ D\nX : C\ninst✝¹ : HasInitial C\ninst✝ : PreservesColimit (Functor.empty C) G\nF : Discrete PEmpty ⥤ D\nthis : HasColimit (Functor.empty D)\n⊢ HasColimit F",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : T... | [
182,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.subsingleton_quotient_iff_eq_top | [
{
"state_after": "case mp\nR : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' : Submodule R M\n⊢ Subsingleton (M ⧸ p) → p = ⊤\n\ncase mpr\nR : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' : ... | [
288,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_castLT | [
{
"state_after": "case h\nn m : ℕ\nx y : Fin (n + 1)\nh : x < y\nhx : optParam (↑x < n) (_ : ↑x < n)\n⊢ ↑castSucc (castLT x hx) < y",
"state_before": "n m : ℕ\nx y : Fin (n + 1)\nh : x < y\nhx : optParam (↑x < n) (_ : ↑x < n)\n⊢ ↑(succAbove y) (castLT x hx) = x",
"tactic": "rw [succAbove_below, castSucc... | [
2135,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2132,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : StrictOrderedCommRing R\nM : Type u_3\nN : Type u_4\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R M\ninst✝³ : Module R N\nι : Type u_2\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ninst✝ : Nontrivial R\ne : Basis ι R ... | [
157,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
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