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/Order/Hom/Lattice.lean | InfTopHom.coe_inf | [] | [
1000,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/LinearAlgebra/Matrix/Symmetric.lean | Matrix.isSymm_transpose_mul_self | [] | [
65,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_add | [
{
"state_after": "case a.h\nl : Type ?u.140829\nm : Type u_2\nn : Type u_3\no : Type u_4\np : Type ?u.140841\nq : Type ?u.140844\nm' : o → Type ?u.140849\nn' : o → Type ?u.140854\np' : o → Type ?u.140859\nR : Type ?u.140862\nS : Type ?u.140865\nα : Type u_1\nβ : Type ?u.140871\ninst✝¹ : DecidableEq o\ninst✝ : A... | [
426,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieEquiv.ofSubalgebras_symm_apply | [] | [
829,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_coe_set | [] | [
988,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
986,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.exists_intermediate_Set' | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\nβ : Type ?u.132165\ns t : Set α\na b x y : α\nf : α → β\nm : ℕ\nhs : ncard s ≤ m\nht : m ≤ ncard t\nh : s ⊆ t\nr : Set α\nhsr : s ⊆ r\nhrt : r ⊆ t\nhc : ncard r = m - ncard s + ncard s\n⊢ ∃ r, s ⊆ r ∧ r ⊆ t ∧ ncard r = m",
"state_before": "α : Type u_1... | [
596,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.int_lcm_helper | [
{
"state_after": "x y : ℤ\n⊢ Int.lcm x y = Nat.lcm (Int.natAbs x) (Int.natAbs y)",
"state_before": "x y : ℤ\nx' y' d : ℕ\nhx : Int.natAbs x = x'\nhy : Int.natAbs y = y'\nh : Nat.lcm x' y' = d\n⊢ Int.lcm x y = d",
"tactic": "subst_vars"
},
{
"state_after": "no goals",
"state_before": "x y : ℤ... | [
70,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Computability/Ackermann.lean | ack_lt_iff_left | [] | [
234,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder | [
{
"state_after": "case intro\np : ℝ\nhp : Fact (0 < p)\nu : AddCircle p\nhu : IsOfFinAddOrder u\nhu' : u ≠ 0\nn : ℕ\nhn : ‖u‖ = p * (↑n / ↑(addOrderOf u))\n⊢ p ≤ addOrderOf u • ‖u‖",
"state_before": "p : ℝ\nhp : Fact (0 < p)\nu : AddCircle p\nhu : IsOfFinAddOrder u\nhu' : u ≠ 0\n⊢ p ≤ addOrderOf u • ‖u‖",
... | [
274,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | NonarchAddGroupSeminorm.zero_apply | [] | [
570,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | StrictMono.mul_const' | [] | [
1409,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1408,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.support_curry | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.552201\nι : Type ?u.552204\nM : Type u_3\nM' : Type ?u.552210\nN : Type ?u.552213\nP : Type ?u.552216\nG : Type ?u.552219\nH : Type ?u.552222\nR : Type ?u.552225\nS : Type ?u.552228\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\ninst✝ : DecidableEq... | [
1286,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.mem_atTop | [] | [
55,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LocalHomeomorph.hasStrictFDerivAt_symm | [] | [
419,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.coe_sup | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.length_edges | [
{
"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 : V\np : Walk G u v\n⊢ List.length (edges p) = length p",
"tactic": "simp [edges]"
}
] | [
781,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.HasBiproduct.mk | [] | [
272,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Real/CauSeq.lean | IsCauSeq.cauchy₂ | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf g : ℕ → β\nhf : IsCauSeq abv f\nε : α\nε0 : 0 < ε\ni : ℕ\nhi : ∀ (j : ℕ), j ≥ i → abv (f j - f i) < ε / 2\nj : ℕ\nij : j ≥ i\nk : ℕ\nik : k ≥ i\n⊢ abv (f j - f k) < ε",
"... | [
110,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | upperClosure_smul | [] | [
277,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.pow_log_le_self | [] | [
123,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/String/Basic.lean | List.toList_inv_asString | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_congr_right | [] | [
826,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.isCauSeq_im | [
{
"state_after": "no goals",
"state_before": "f : CauSeq ℂ ↑abs\nε : ℝ\nε0 : ε > 0\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → ↑abs (↑f j - ↑f i) < ε\nj : ℕ\nij : j ≥ i\n⊢ abs' ((fun n => (↑f n).im) j - (fun n => (↑f n).im) i) ≤ ↑abs (↑f j - ↑f i)",
"tactic": "simpa using abs_im_le_abs (f j - f i)"
}
] | [
1245,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_lt_of_top_le | [
{
"state_after": "no goals",
"state_before": "n m l : ℕ\nhml : m ≤ l\nk : ℕ\nhk : k ∈ Ico n m\n⊢ decide (k < l) = true",
"tactic": "simp only [(lt_of_lt_of_le (mem.1 hk).2 hml), decide_True]"
}
] | [
161,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_extend_by_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1844\nγ : Type ?u.1847\nι : Type u_2\ninst✝² : DecidableEq ι\ninst✝¹ : Fintype ι\ninst✝ : CommMonoid α\ns : Finset ι\nf : ι → α\n⊢ (∏ i : ι, if i ∈ s then f i else 1) = ∏ i in s, f i",
"tactic": "rw [← prod_filter, filter_mem_eq_int... | [
59,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Subsingleton.eq_singleton_of_mem | [] | [
2341,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2340,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.continuous | [] | [
186,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
11
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.coe_linearMap_maxTrivLinearMapEquivLieModuleHom_symm | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.82316\nγ : Type ?u.82319\nι : Sort ?u.82322\nκ : ι → Sort ?u.82327\ninst✝ : LE α\ns t : UpperSet α\na : α\nS : Set (UpperSet α)\n⊢ ↑(compl (sSup S)) = ↑(⨆ (s : UpperSet α) (_ : s ∈ S), compl s)",
"tactic": "simp only [coe_compl, coe... | [
838,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
11
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Iic | [] | [
56,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Finset/NoncommProd.lean | Finset.noncommProd_union_of_disjoint | [
{
"state_after": "case intro.intro\nF : Type ?u.199818\nι : Type ?u.199821\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.199830\nf✝ : α → β → β\nop : α → α → α\ninst✝² : Monoid β\ninst✝¹ : Monoid γ\ninst✝ : DecidableEq α\nt : Finset α\nf : α → β\nsl : List α\nsl' : List.Nodup sl\nh : Disjoint (List.toFinset sl) t\nc... | [
373,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.mono_of_kernel_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : Preadditive C\nP Q R : C\nf✝ f' : P ⟶ Q\ng✝ g' : Q ⟶ R\nX Y : C\nf : X ⟶ Y\ninst✝ : HasLimit (parallelPair f 0)\nw : kernel.ι f = 0\nP✝ : C\ng : P✝ ⟶ X\nh : g ≫ f = 0\n⊢ g = 0",
"tactic": "rw [← kernel.lift_ι f g h, ... | [
246,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | Filter.HasBasis.mem_separationRel | [] | [
113,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/Basic.lean | isClosed_setOf_clusterPt | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nf : Filter α\n⊢ IsClosed (⋂ (i : α → Prop), {x | (¬∀ᶠ (x : α) in 𝓝 x, i x) ∨ ∃ᶠ (x : α) in f, i x})",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α... | [
1287,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.toNNReal_pos | [
{
"state_after": "no goals",
"state_before": "r : ℝ\n⊢ 0 < toNNReal r ↔ 0 < r",
"tactic": "simp [← NNReal.coe_lt_coe, lt_irrefl]"
}
] | [
617,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Algebra/Group/WithOne/Defs.lean | WithZero.coe_one | [] | [
228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ext_iff | [] | [
137,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.int_cast_imJ | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | closedBall_prod_same | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.262111\nι : Type ?u.262114\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nx : α\ny : β\nr : ℝ\nz : α × β\n⊢ z ∈ closedBall x r ×ˢ closedBall y r ↔ z ∈ closedBall (x, y) r",
"tactic": "simp [Prod.dist_eq]"
}
... | [
1770,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1768,
1
] |
Mathlib/Order/Ideal.lean | Order.Ideal.inter_nonempty | [
{
"state_after": "case intro\nP : Type u_1\ninst✝¹ : LE P\nI✝ J✝ s t : Ideal P\nx y : P\ninst✝ : IsDirected P fun x x_1 => x ≥ x_1\nI J : Ideal P\na : P\nha : a ∈ ↑I\n⊢ Set.Nonempty (↑I ∩ ↑J)",
"state_before": "P : Type u_1\ninst✝¹ : LE P\nI✝ J✝ s t : Ideal P\nx y : P\ninst✝ : IsDirected P fun x x_1 => x ≥ ... | [
196,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_lt_iff_lt_toReal | [
{
"state_after": "case intro\nα : Type ?u.810494\nβ : Type ?u.810497\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ\nha : 0 ≤ a\nb : ℝ≥0\n⊢ ENNReal.ofReal a < ↑b ↔ a < ENNReal.toReal ↑b",
"state_before": "α : Type ?u.810494\nβ : Type ?u.810497\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ\nb : ℝ≥0∞\nha : 0 ≤ a\nhb : b ≠ ⊤\n... | [
2146,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2143,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.coeff_coe_units_zero_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nu : R[X]ˣ\n⊢ coeff (↑u) (natDegree ↑u) ≠ 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nu : R[X]ˣ\n⊢ coeff... | [
984,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | AddCommGroupCat.asHom_apply | [] | [
346,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Std/Data/String/Lemmas.lean | String.nil_append | [] | [
489,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
489,
9
] |
Mathlib/Data/Matrix/DMatrix.lean | DMatrix.add_apply | [] | [
136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/CategoryTheory/FintypeCat.lean | FintypeCat.Skeleton.is_skeletal | [
{
"state_after": "X Y : Skeleton\nx✝ : IsIsomorphic X Y\nh : X ≅ Y\na : Fin (len X)\n⊢ (fun x => (h.inv { down := x }).down) ((fun x => (h.hom { down := x }).down) a) = a",
"state_before": "X Y : Skeleton\nx✝ : IsIsomorphic X Y\nh : X ≅ Y\n⊢ Function.LeftInverse (fun x => (h.inv { down := x }).down) fun x =... | [
172,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/List/Card.lean | List.card_subset_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.43987\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nbs : List α\nx✝ : [] ⊆ bs\n⊢ card [] ≤ card bs",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Sort ?u.43987\ninst✝¹ : Decidable... | [
136,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/FieldTheory/Adjoin.lean | PowerBasis.equivAdjoinSimple_symm_aeval | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nL : Type u_2\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\npb : PowerBasis K L\nf : K[X]\n⊢ ↑(AlgEquiv.symm (equivAdjoinSimple pb)) (↑(aeval pb.gen) f) = ↑(aeval (AdjoinSimple.gen K pb.gen)) f",
"tactic": "rw [equivAdjoinSimple, equ... | [
1300,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.lower_ne_upper | [] | [
95,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.AEStronglyMeasurable.mono_measure | [] | [
1232,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1230,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.stream_succ | [
{
"state_after": "case zero\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\nh : Int.fract v ≠ 0\n⊢ IntFractPair.stream v (Nat.zero + 1) = IntFractPair.stream (Int.fract v)⁻¹ Nat.zero\n\ncase succ\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn✝ : ℕ\nh... | [
144,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.empty_isTransitive | [] | [
48,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.coe_lt_coe | [] | [
142,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | HasFDerivAt.cpow | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : E → ℂ\nf' g' : E →L[ℂ] ℂ\nx : E\ns : Set E\nc : ℂ\nhf : HasFDerivAt f f' x\nhg : HasFDerivAt g g' x\nh0 : 0 < (f x).re ∨ (f x).im ≠ 0\n⊢ HasFDerivAt (fun x => f x ^ g x) ((g x * f x ^ (g... | [
96,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.ofEq_rfl | [
{
"state_after": "case h.a\nR : Type u_2\nR₁ : Type ?u.1814068\nR₂ : Type ?u.1814071\nR₃ : Type ?u.1814074\nR₄ : Type ?u.1814077\nS : Type ?u.1814080\nK : Type ?u.1814083\nK₂ : Type ?u.1814086\nM : Type u_1\nM' : Type ?u.1814092\nM₁ : Type ?u.1814095\nM₂ : Type ?u.1814098\nM₃ : Type ?u.1814101\nM₄ : Type ?u.181... | [
2041,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2041,
1
] |
Mathlib/Order/Compare.lean | ofDual_compares_ofDual | [
{
"state_after": "case lt\nα : Type u_1\nβ : Type ?u.11173\ninst✝ : LT α\na b : αᵒᵈ\n⊢ Compares lt (↑ofDual a) (↑ofDual b) ↔ Compares lt b a\n\ncase eq\nα : Type u_1\nβ : Type ?u.11173\ninst✝ : LT α\na b : αᵒᵈ\n⊢ Compares eq (↑ofDual a) (↑ofDual b) ↔ Compares eq b a\n\ncase gt\nα : Type u_1\nβ : Type ?u.11173\n... | [
167,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iInter_mul_subset | [] | [
520,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Submodule.toSubalgebra_toSubmodule | [] | [
583,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.right_triangle_components | [] | [
202,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.swap_mul_involutive | [] | [
558,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.to₂ | [] | [
559,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.not_not_eq | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ {a b : Bool}, ¬(!a) = b ↔ a = b",
"tactic": "decide"
}
] | [
216,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_sq_add_sin_sq | [
{
"state_after": "case h\nx✝ : ℝ\n⊢ cos ↑x✝ ^ 2 + sin ↑x✝ ^ 2 = 1",
"state_before": "θ : Angle\n⊢ cos θ ^ 2 + sin θ ^ 2 = 1",
"tactic": "induction θ using Real.Angle.induction_on"
},
{
"state_after": "no goals",
"state_before": "case h\nx✝ : ℝ\n⊢ cos ↑x✝ ^ 2 + sin ↑x✝ ^ 2 = 1",
"tactic":... | [
446,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.ext | [] | [
793,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_pure | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.9264\nα : Type u_1\nβ : Type ?u.9270\nX : Type ?u.9273\nY : Type ?u.9276\nx : α\n⊢ 𝓝 (pure x) = 𝓟 {⊥, pure x}",
"tactic": "rw [← principal_singleton, nhds_principal, principal_singleton, Iic_pure]"
}
] | [
132,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/InverseDeriv.lean | Real.contDiffAt_arccos_iff | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nn : ℕ∞\n⊢ ContDiffAt ℝ n arccos x ↔ n = 0 ∨ x ≠ -1 ∧ x ≠ 1",
"tactic": "refine' Iff.trans ⟨fun h => _, fun h => _⟩ contDiffAt_arcsin_iff <;>\n simpa [arccos] using (@contDiffAt_const _ _ _ _ _ _ _ _ _ _ (π / 2)).sub h"
}
] | [
194,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Algebra/Category/ModuleCat/Biproducts.lean | ModuleCat.binaryProductLimitCone_cone_π_app_right | [] | [
71,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/FieldTheory/MvPolynomial.lean | MvPolynomial.quotient_mk_comp_C_injective | [
{
"state_after": "σ : Type u\nK : Type v\ninst✝ : Field K\nI : Ideal (MvPolynomial σ K)\nhI : I ≠ ⊤\nx : K\nhx : ↑(RingHom.comp (Ideal.Quotient.mk I) C) x = 0\n⊢ x = 0",
"state_before": "σ : Type u\nK : Type v\ninst✝ : Field K\nI : Ideal (MvPolynomial σ K)\nhI : I ≠ ⊤\n⊢ Function.Injective ↑(RingHom.comp (I... | [
47,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_of_add_bdd_below_left | [] | [
734,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasStrictDerivAt.smul_const | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nf✝ f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\n𝕜' : Type u_1\ninst✝... | [
93,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Data/Int/DivMod.lean | Int.neg_dvd | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ -a ∣ b ↔ a ∣ b",
"tactic": "constructor <;> exact fun ⟨k, e⟩ =>\n ⟨-k, by simp [e, Int.neg_mul, Int.mul_neg, Int.neg_neg]⟩"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nx✝ : a ∣ b\nk : Int\ne : b = a * k\n⊢ b = -a * -... | [
605,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
603,
11
] |
Mathlib/Analysis/NormedSpace/Completion.lean | UniformSpace.Completion.norm_toComplL | [] | [
79,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.revAt_le | [] | [
81,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearEquiv.comp_contDiffWithinAt_iff | [] | [
331,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_diagonal | [] | [
116,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Ioi | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ioi a = Ioi ↑a",
"tactic": "rw [← preimage_coe_Ioi, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Ioi_subset_Ioi bot_le)]"
}
] | [
208,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_prod_pow_eq_self | [
{
"state_after": "n : ℕ\nhn : n ≠ 0\n⊢ (Finsupp.prod (↑Multiset.toFinsupp ↑(factors n)) fun x x_1 => x ^ x_1) = n",
"state_before": "n : ℕ\nhn : n ≠ 0\n⊢ (Finsupp.prod (factorization n) fun x x_1 => x ^ x_1) = n",
"tactic": "rw [factorization_eq_factors_multiset n]"
},
{
"state_after": "n : ℕ\nh... | [
109,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.AnalyticSet.iInter | [
{
"state_after": "case intro\nα : Type u_2\ninst✝² : TopologicalSpace α\nι : Type u_1\ninst✝¹ : Countable ι\ninst✝ : T2Space α\ns : ι → Set α\nhs : ∀ (n : ι), AnalyticSet (s n)\ni₀ : ι\n⊢ AnalyticSet (⋂ (n : ι), s n)",
"state_before": "α : Type u_2\ninst✝² : TopologicalSpace α\nι : Type u_1\nhι : Nonempty ι... | [
186,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RepresentationTheory/Basic.lean | Representation.dualTensorHom_comm | [
{
"state_after": "case a.h.h.h\nk : Type u_1\nG : Type u_4\nV : Type u_2\nW : Type u_3\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Group G\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\ninst✝¹ : AddCommMonoid W\ninst✝ : Module k W\nρV : Representation k G V\nρW : Representation k G W\ng : G\nx✝² : Module.Dual k V\nx✝¹ ... | [
465,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.coe_symm_toEquiv | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mem_brange | [] | [
1177,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.eq_of_mono_coequalizer | [] | [
1077,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | hasFDerivAt_fst | [] | [
158,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Sigma/Basic.lean | sigma_mk_injective | [] | [
110,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_univ | [] | [
968,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_lineMap_right | [] | [
765,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.toBlock_inverse_mul_toBlock_eq_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.126037\nm : Type u_2\nn : Type ?u.126043\no : Type ?u.126046\nm' : α → Type ?u.126051\nn' : α → Type ?u.126056\nR : Type v\ninst✝⁶ : CommRing R\nM N : Matrix m m R\nb : m → α\ninst✝⁵ : DecidableEq m\ninst✝⁴ : Fintype m\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\ninst... | [
268,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Nat/Periodic.lean | Nat.filter_multiset_Ico_card_eq_of_periodic | [
{
"state_after": "n a : ℕ\np : ℕ → Prop\ninst✝ : DecidablePred p\npp : Periodic p a\n⊢ Multiset.count True (map p (Ico n (n + a))) = Multiset.count True (map (p ∘ fun x => x % a) (Ico n (n + a)))",
"state_before": "n a : ℕ\np : ℕ → Prop\ninst✝ : DecidablePred p\npp : Periodic p a\n⊢ ↑card (filter p (Ico n (... | [
56,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/RingTheory/WittVector/Defs.lean | WittVector.sub_coeff | [] | [
364,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideEqualizer.hom_ext | [] | [
643,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | OpenEmbedding.singleton_smoothManifoldWithCorners | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : Nonempty M\nf :... | [
742,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/CategoryTheory/Shift/Basic.lean | CategoryTheory.shift_equiv_triangle | [] | [
497,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/PNat/Find.lean | PNat.find_min | [] | [
67,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_diagonal | [
{
"state_after": "ι : Type ?u.281006\nι' : Type ?u.281009\nα : Type u_1\nβ : Type ?u.281015\nγ : Type ?u.281018\ninst✝ : SemilatticeInf α\n⊢ Tendsto (fun a => (a, a)) atBot (atBot ×ˢ atBot)",
"state_before": "ι : Type ?u.281006\nι' : Type ?u.281009\nα : Type u_1\nβ : Type ?u.281015\nγ : Type ?u.281018\ninst... | [
1432,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.mem_inf | [] | [
129,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.VectorsProdEqOne.rotate_length | [] | [
451,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Fintype/Card.lean | Finite.exists_ne_map_eq_of_infinite | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.81981\nβ✝ : Type ?u.81984\nγ : Type ?u.81987\nα : Sort u_1\nβ : Sort u_2\ninst✝¹ : Infinite α\ninst✝ : Finite β\nf : α → β\n⊢ ∃ x y, x ≠ y ∧ f x = f y",
"tactic": "simpa only [Injective, not_forall, not_imp, and_comm] using not_injective_infinit... | [
1153,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/GroupTheory/Coset.lean | rightCoset_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Semigroup α\ns : Set α\na b : α\n⊢ s *r a *r b = s *r (a * b)",
"tactic": "simp [leftCoset, rightCoset, (image_comp _ _ _).symm, Function.comp, mul_assoc]"
}
] | [
134,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_one | [] | [
276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_eq_singleton_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.71894\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ Icc a b = {c} ↔ a = c ∧ b = c",
"tactic": "rw [← coe_eq_singleton, coe_Icc, Set.Icc_eq_singleton_iff]"
}
] | [
533,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.