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/Analysis/Normed/Order/UpperLower.lean | IsUpperSet.thickening' | [
{
"state_after": "α : Type u_1\nι : Type ?u.23\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsUpperSet s\nε : ℝ\n⊢ IsUpperSet (ball 1 ε * s)",
"state_before": "α : Type u_1\nι : Type ?u.23\ninst✝ : NormedOrderedGroup α\ns : Set α\nhs : IsUpperSet s\nε : ℝ\n⊢ IsUpperSet (thickening ε s)",
"tactic": "rw... | [
40,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
11
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_le | [] | [
450,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : CommSemiring R\np : R[X]\nn : ℕ\n⊢ ↑derivative (p ^ Nat.zero) = ↑C ↑Nat.zero * p ^ (Nat.zero - 1) * ↑derivative p",
"tactic": "rw [pow_zero, derivative_one, Nat.cast_zero, C... | [
487,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_le_of_forall_sum_le | [] | [
598,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/RingTheory/IntegralDomain.lean | sum_hom_units | [
{
"state_after": "case inl\nR : Type u_2\nG : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\ninst✝² : Group G\ninst✝¹ : Fintype G\nf : G →* R\ninst✝ : Decidable (f = 1)\nh : f = 1\n⊢ ∑ g : G, ↑f g = ↑(Fintype.card G)\n\ncase inr\nR : Type u_2\nG : Type u_1\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\ninst✝² ... | [
289,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.hasSum_conj | [] | [
486,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Algebra/Star/Basic.lean | IsUnit.star | [] | [
558,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/ModelTheory/Encoding.lean | FirstOrder.Language.BoundedFormula.listDecode_encode_list | [
{
"state_after": "L : Language\nM : Type w\nN : Type ?u.139469\nP : Type ?u.139472\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nl : List ((n : ℕ) × BoundedFormula L α n)\nh :\n ∀ (φ : (n : ℕ) × BoundedFormula L α n) (l : List ((k : ℕ) × Term L (α ⊕ Fin k) ⊕ ... | [
292,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Init/Algebra/Classes.lean | trichotomous | [] | [
276,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_swap_mul_swap | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y z : α\nh : ¬(x = y ∨ x = z ∨ False) ∧ ¬(y = z ∨ False)\n⊢ support (swap x y * swap y z) = {x, y, z}",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nx y z : α\nh : List.Nodup... | [
470,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | addRothNumber_Ico | [
{
"state_after": "case inl\nF : Type ?u.153476\nα : Type ?u.153479\nβ : Type ?u.153482\n𝕜 : Type ?u.153485\nE : Type ?u.153488\ns : Finset ℕ\nk n a b : ℕ\nh : b ≤ a\n⊢ ↑addRothNumber (Ico a b) = ↑rothNumberNat (b - a)\n\ncase inr\nF : Type ?u.153476\nα : Type ?u.153479\nβ : Type ?u.153482\n𝕜 : Type ?u.153485\... | [
510,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Set/Basic.lean | Set.diff_eq_compl_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t✝ t₁ t₂ u s t : Set α\n⊢ s \\ t = tᶜ ∩ s",
"tactic": "rw [diff_eq, inter_comm]"
}
] | [
1814,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.subgroup_eq_top_of_subsingleton | [
{
"state_after": "G : Type u\ninst✝¹ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH✝ : Type v\ninst✝ : Group H✝\nφ : G →* H✝\nH : Subgroup G\nh : Subsingleton (G ⧸ H)\nx : G\nx✝ : x ∈ ⊤\nthis : 1⁻¹ * x ∈ H\n⊢ x ∈ H",
"state_before": "G : Type u\ninst✝¹ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N... | [
673,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.coe_mk | [] | [
729,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_iInf_map_of_injective | [] | [
408,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_mono' | [] | [
104,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | HomotopyCategory.quotient_obj_as | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.totalize_of_le | [] | [
190,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | coe_comp_nnnorm' | [] | [
894,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.expand_WF.foldl | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : BEq α\ninst✝ : Hashable α\nrank : α → Nat\nl : List (α × β)\ni : Nat\nhl₁ : ∀ [inst : PartialEquivBEq α] [inst : LawfulHashable α], List.Pairwise (fun a b => ¬(a.fst == b.fst) = true) l\nhl₂ : ∀ (x : α × β), x ∈ l → rank x.fs... | [
141,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
113,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_le_one_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.88530\nα : Type u_1\nβ : Type ?u.88536\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh1 : 0 < a\nh2 : a ≤ 1\n⊢ 1 ≤ 1 / a",
"tactic": "rwa [le_one_div (@zero_lt_one α _ _ _ _ _) h1, one_div_one]"
}
] | [
486,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Topology/PathConnected.lean | joinedIn_univ | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.615739\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.615754\nF : Set X\n⊢ JoinedIn univ x y ↔ Joined x y",
"tactic": "simp [JoinedIn, Joined, exists_true_iff_nonempty]"
}
] | [
869,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | add_tsub_assoc_of_le | [] | [
218,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.leftInvOn | [] | [
241,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
11
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_add | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.886766\n𝕜 : Type ?u.886769\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
864,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Data/PFun.lean | PFun.mem_core | [] | [
472,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Data/Multiset/Functor.lean | Multiset.lift_coe | [] | [
94,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_lt_prod_of_subset' | [
{
"state_after": "ι : Type u_1\nα : Type ?u.129835\nβ : Type ?u.129838\nM : Type u_2\nN : Type ?u.129844\nG : Type ?u.129847\nk : Type ?u.129850\nR : Type ?u.129853\ninst✝ : OrderedCancelCommMonoid M\nf g : ι → M\ns t : Finset ι\nh : s ⊆ t\ni : ι\nht : i ∈ t\nhs : ¬i ∈ s\nhlt : 1 < f i\nhle : ∀ (j : ι), j ∈ t →... | [
492,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.isTranscendenceBasis_iff | [
{
"state_after": "case mp\nι✝ : Type ?u.1377649\nι' : Type ?u.1377652\nR✝ : Type ?u.1377655\nK : Type ?u.1377658\nA✝ : Type ?u.1377661\nA' : Type ?u.1377664\nA'' : Type ?u.1377667\nV : Type u\nV' : Type ?u.1377672\nx✝ : ι✝ → A✝\ninst✝¹⁰ : CommRing R✝\ninst✝⁹ : CommRing A✝\ninst✝⁸ : CommRing A'\ninst✝⁷ : CommRin... | [
539,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_of_seq_tendsto | [] | [
1831,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1829,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.add | [] | [
159,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.Quotient.nontrivial | [] | [
153,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
11
] |
Mathlib/Order/PFilter.lean | Order.PFilter.principal_le_principal_iff | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\ninst✝ : Preorder P\nx y : P\nF s t : PFilter P\np q : P\n⊢ principal q ≤ principal p ↔ p ≤ q",
"tactic": "simp"
}
] | [
127,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Measurable.nat_ceil | [] | [
92,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Topology/NhdsSet.lean | monotone_nhdsSet | [] | [
126,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.symm_map_nhds_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.68858\nδ : Type ?u.68861\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nh : α ≃ₜ β\nx : α\n⊢ map (↑(Homeomorph.symm h)) (𝓝 (↑h x)) = 𝓝 x",
"tactic"... | [
380,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_ball_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.189193\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t : Set α\n⊢ x ∈ ball y ε ↔ y ∈ ball x ε",
"tactic": "rw [mem_ball', mem_ball]"
}
] | [
568,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.eq_zero_of_add_eq_zero | [] | [
324,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
323,
1
] |
Mathlib/Order/RelIso/Group.lean | RelIso.coe_one | [] | [
34,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Matrix/Rank.lean | Matrix.rank_submatrix | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.188785\nm : Type u_1\nn : Type u_3\no : Type ?u.188794\nR : Type u_2\nm_fin : Fintype m\ninst✝³ : Fintype n\ninst✝² : Fintype o\ninst✝¹ : CommRing R\ninst✝ : Fintype m\nA : Matrix m m R\ne₁ e₂ : n ≃ m\n⊢ rank (submatrix A ↑e₁ ↑e₂) = rank A",
"tac... | [
125,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.zero_im | [] | [
146,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.isSplittingField_iSup | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_3\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nα : E\nι : Type u_1\nt : ι → IntermediateField F E\np : ι → F[X]\ns : Finset ι\nh0 : ∏ i in s, p i ≠ 0\nh : ∀ (i : ι), i ∈ s → IsSplittingField F { x // x ∈ t i } (p i)\nK : IntermediateField F E :=... | [
561,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
src/lean/Init/Prelude.lean | Fin.ne_of_val_ne | [] | [
1759,
39
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1758,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | Polynomial.coe_add | [
{
"state_after": "case h\nσ : Type ?u.4308129\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ : R[X]\nn✝ : ℕ\n⊢ ↑(PowerSeries.coeff R n✝) ↑(φ + ψ) = ↑(PowerSeries.coeff R n✝) (↑φ + ↑ψ)",
"state_before": "σ : Type ?u.4308129\nR : Type u_1\ninst✝ : CommSemiring R\nφ ψ : R[X]\n⊢ ↑(φ + ψ) = ↑φ + ↑ψ",
"tactic": "... | [
2569,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2567,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.add_limZero | [
{
"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 : CauSeq β abv\nhf : LimZero f\nhg : LimZero g\nε : α\nε0 : ε > 0\ni : ℕ\nH : ∀ (j : ℕ), j ≥ i → abv (↑f j) < ε / 2 ∧ abv (↑g j) < ε / 2\nj : ℕ\nij : j ≥ i\nH₁ : abv (↑f j)... | [
422,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Logic/Nonempty.lean | nonempty_prod | [] | [
65,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.isUnit_iff | [
{
"state_after": "case mp\nF : Type ?u.300168\nα : Type u_1\nβ : Type ?u.300174\nγ : Type ?u.300177\nδ : Type ?u.300180\nε : Type ?u.300183\ninst✝ : DivisionMonoid α\nf g : Filter α\n⊢ IsUnit f → ∃ a, f = pure a ∧ IsUnit a\n\ncase mpr\nF : Type ?u.300168\nα : Type u_1\nβ : Type ?u.300174\nγ : Type ?u.300177\nδ ... | [
781,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
773,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.mul_eq_mul_of_div_eq_div | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.64657\nG : Type ?u.64660\nα : Type u_1\nM : Type ?u.64666\nN : Type ?u.64669\ninst✝ : DivisionCommMonoid α\na✝ b c✝ d : α\nhb : IsUnit b\nhd : IsUnit d\na c : α\nh : a / b = c / d\n⊢ a * d = c * b",
"tactic": "rw [← mul_one a, ← hb.div_self, ← mu... | [
491,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
11
] |
Mathlib/Order/Lattice.lean | sup_le_sup_right | [] | [
238,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | dvd_of_mul_left_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : CommSemigroup α\na b c : α\nh : a * b ∣ c\nd : α\nceq : c = a * b * d\n⊢ b * (a * d) = c",
"tactic": "simp [ceq]"
}
] | [
184,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/LinearAlgebra/Projection.lean | LinearMap.range_eq_of_proj | [] | [
52,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_sub | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Directed.lean | Monotone.directed_ge | [] | [
155,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivWithinAt.const_mul | [] | [
470,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_binop | [
{
"state_after": "case intro.intro.intro\nα : Type u_1\ninst✝ : MeasurableSpace α\nm m₁ m₂ m₃ : OuterMeasure α\nop : ℝ≥0∞ → ℝ≥0∞ → ℝ≥0∞\nh : ∀ (s : Set α), ↑m₁ s = op (↑m₂ s) (↑m₃ s)\ns t : Set α\n_hst : s ⊆ t\n_ht : MeasurableSet t\nhtm :\n ∀ (i : Fin (Nat.succ (Nat.succ (Nat.succ 0)))),\n ↑(Matrix.vecCons... | [
1741,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1737,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | one_le_inv_of_le_one | [] | [
1274,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_one_right_eq_X_pow | [
{
"state_after": "case zero\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ ↑(monomial Nat.zero) 1 = X ^ Nat.zero\n\ncase succ\nR : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nih : ↑(monomial n) 1 = X ^ n\n⊢ ↑(monomial (Nat.succ n)) 1 = X ^ Nat.succ n",
"state_before":... | [
561,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Analysis/SpecialFunctions/ImproperIntegrals.lean | integrableOn_Ioi_rpow_of_lt | [
{
"state_after": "a : ℝ\nha : a < -1\nc : ℝ\nhc : 0 < c\nhd : ∀ (x : ℝ), x ∈ Ici c → HasDerivAt (fun t => t ^ (a + 1) / (a + 1)) (x ^ a) x\n⊢ IntegrableOn (fun t => t ^ a) (Ioi c)",
"state_before": "a : ℝ\nha : a < -1\nc : ℝ\nhc : 0 < c\n⊢ IntegrableOn (fun t => t ^ a) (Ioi c)",
"tactic": "have hd : ∀ (... | [
76,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.snd_mem_divisors_of_mem_antidiagonal | [
{
"state_after": "n : ℕ\nx : ℕ × ℕ\nh : x.fst * x.snd = n ∧ n ≠ 0\n⊢ x.snd ∈ divisors n",
"state_before": "n : ℕ\nx : ℕ × ℕ\nh : x ∈ divisorsAntidiagonal n\n⊢ x.snd ∈ divisors n",
"tactic": "rw [mem_divisorsAntidiagonal] at h"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nx : ℕ × ℕ... | [
239,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_pow_atTop_nhdsWithin_0_of_lt_1 | [] | [
118,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.liftIco_continuous | [
{
"state_after": "𝕜 : Type u_2\nB : Type u_1\ninst✝⁴ : LinearOrderedAddCommGroup 𝕜\ninst✝³ : TopologicalSpace 𝕜\ninst✝² : OrderTopology 𝕜\np a : 𝕜\nhp : Fact (0 < p)\ninst✝¹ : Archimedean 𝕜\ninst✝ : TopologicalSpace B\nf : 𝕜 → B\nhf : f a = f (a + p)\nhc : ContinuousOn f (Icc a (a + p))\n⊢ Continuous\n ... | [
653,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.preimage_Iic | [
{
"state_after": "case h\nF : Type ?u.76506\nα : Type u_1\nβ : Type ?u.76512\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn : ℕ\na : α\nha : 0 ≤ a\nx✝ : ℕ\n⊢ x✝ ∈ Nat.cast ⁻¹' Iic a ↔ x✝ ∈ Iic ⌊a⌋₊",
"state_before": "F : Type ?u.76506\nα : Type u_1\nβ : Type ?u.76512\ninst✝¹ : LinearO... | [
435,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.empty.nonempty_embedding_iff | [] | [
951,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.aux_cobounded_eq | [] | [
439,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Rel.lean | Set.preimage_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.40784\nf : α → β\ns : Set β\n⊢ f ⁻¹' s = Rel.preimage (Function.graph f) s",
"tactic": "simp [Set.preimage, Function.graph, Rel.preimage, Rel.inv, flip, Rel.image]"
}
] | [
279,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.star_eq_inv' | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.coe_image_of_subset | [
{
"state_after": "case h\nα : Type u_1\ns t : Set α\nh : t ⊆ s\nx : α\n⊢ x ∈ val '' {x | ↑x ∈ t} ↔ x ∈ t",
"state_before": "α : Type u_1\ns t : Set α\nh : t ⊆ s\n⊢ val '' {x | ↑x ∈ t} = t",
"tactic": "ext x"
},
{
"state_after": "case h\nα : Type u_1\ns t : Set α\nh : t ⊆ s\nx : α\n⊢ (∃ x_1, x_1 ... | [
1388,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | refl_mem_uniformity | [] | [
439,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Order/Basic.lean | Prod.lt_iff | [
{
"state_after": "case refine'_1\nι : Type ?u.107734\nα : Type u\nβ : Type v\nγ : Type w\nπ : ι → Type ?u.107745\nr : α → α → Prop\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na a₁ a₂ : α\nb b₁ b₂ : β\nx y : α × β\nh : x < y\n⊢ x.fst < y.fst ∧ x.snd ≤ y.snd ∨ x.fst ≤ y.fst ∧ x.snd < y.snd\n\ncase refine'_2\nι : Ty... | [
1243,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
1
] |
Mathlib/Data/Set/Semiring.lean | Set.up_one | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Order/LocallyFinite.lean | Multiset.mem_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.33502\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrderTop α\na x : α\n⊢ x ∈ Ici a ↔ a ≤ x",
"tactic": "rw [Ici, ← Finset.mem_def, Finset.mem_Ici]"
}
] | [
588,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.ext | [] | [
107,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.qRight_one_left | [
{
"state_after": "θ : ↑I\n⊢ 1 * (1 + ↑θ) ≤ 2 * ↑1",
"state_before": "θ : ↑I\n⊢ 1 * (1 + ↑(1, θ).snd) ≤ 2 * ↑(1, θ).fst",
"tactic": "dsimp only"
},
{
"state_after": "θ : ↑I\n⊢ ↑θ + 1 ≤ 1 + 1",
"state_before": "θ : ↑I\n⊢ 1 * (1 + ↑θ) ≤ 2 * ↑1",
"tactic": "rw [coe_one, one_mul, mul_one, add... | [
202,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.card_support_le_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.137292\nγ : Type ?u.137295\nι : Type ?u.137298\nM : Type u_2\nM' : Type ?u.137304\nN : Type ?u.137307\nP : Type ?u.137310\nG : Type ?u.137313\nH : Type ?u.137316\nR : Type ?u.137319\nS : Type ?u.137322\ninst✝¹ : Zero M\na a' : α\nb : M\... | [
504,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_C | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na✝ b : R\nn : ℕ\ninst✝ : Semiring R\na : R\n⊢ ↑derivative (↑C a) = 0",
"tactic": "simp [derivative_apply]"
}
] | [
126,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.one_ne_zero | [] | [
427,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
426,
11
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.symm_apply_mk_proj | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.8645\nB : Type u_2\nF : Type u_3\nE : B → Type ?u.8656\nZ : Type u_1\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne : Pretrivialization F proj\nx✝ x : Z\nex : x ∈ e.source\n⊢ ↑(LocalEquiv.symm e.toLocalEquiv) (proj x, (↑e x... | [
180,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.chain_mono | [] | [
984,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/RingTheory/MatrixAlgebra.lean | matrixEquivTensor_apply_std_basis | [
{
"state_after": "R : Type u\ninst✝⁴ : CommSemiring R\nA : Type v\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\ni j : n\nx : A\nt : ∀ (p : n × n), i = p.fst ∧ j = p.snd ↔ p = (i, j)\n⊢ ↑(matrixEquivTensor R A n) (stdBasisMatrix i j x) = x ⊗ₜ[R] stdBasisMatrix... | [
174,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.coe_sinOrderIso_apply | [] | [
921,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.max_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : PseudoEMetricSpace α\nf g : α → ℝ\nKf Kg : ℝ≥0\nhf : LipschitzWith Kf f\na : ℝ\n⊢ LipschitzWith Kf fun x => max (f x) a",
"tactic": "simpa only [max_eq_left (zero_le Kf)] using hf.max (LipschitzWith.con... | [
452,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Order/Monotone/Basic.lean | antitone_nat_of_succ_le | [] | [
995,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/RingTheory/FiniteType.lean | modulePolynomialOfEndo.isScalarTower | [
{
"state_after": "R : Type ?u.731560\ninst✝² : CommRing R\nM : Type ?u.731566\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf : M →ₗ[R] M\nthis : Module R[X] M := modulePolynomialOfEndo f\n⊢ SMul R[X] M",
"state_before": "R : Type ?u.731560\ninst✝² : CommRing R\nM : Type ?u.731566\ninst✝¹ : AddCommGroup M\n... | [
659,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.invRev | [] | [
624,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_add_le_tsub_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.19397\ninst✝⁴ : Preorder α\ninst✝³ : AddCommSemigroup α\ninst✝² : Sub α\ninst✝¹ : OrderedSub α\na b c d : α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\n⊢ a + b ≤ a + (c + (b - c))",
"state_before": "α : Type u_1\nβ : Type ?u.19397\nins... | [
186,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_eq_prod_X_pow_sub_one_pow_moebius | [
{
"state_after": "case inl\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ ↑(algebraMap R[X] (RatFunc R)) (cyclotomic 0 R) =\n ∏ i in Nat.divisorsAntidiagonal 0, ↑(algebraMap R[X] (RatFunc R)) (X ^ i.snd - 1) ^ ↑μ i.fst\n\ncase inr\nn : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nhpos... | [
481,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.move_ok | [
{
"state_after": "case nil\np : Γ' → Bool\nk₁ k₂ : K'\nq : Λ'\ns✝ : Option Γ'\nL₁ : List Γ'\no : Option Γ'\nL₂ : List Γ'\nS✝ : K' → List Γ'\nh₁ : k₁ ≠ k₂\ne✝ : splitAtPred p (S✝ k₁) = (L₁, o, L₂)\ns : Option Γ'\nS : K' → List Γ'\ne : splitAtPred p (S k₁) = ([], o, L₂)\n⊢ Reaches₁ (TM2.step tr) { l := some (Λ'.m... | [
1384,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Data/List/Sublists.lean | List.sublists'_singleton | [] | [
41,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Ordered.modify | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\ncmp : α → α → Ordering\nf : α → α\nt : RBNode α\nh : Ordered cmp t\nc✝ : RBColor\nl✝ : RBNode α\nv✝ : α\nr✝ : RBNode α\nx✝ : Path α\nH : OnRoot (fun x => cmpEq cmp (f x) x) (node c✝ l✝ v✝ r✝, x✝).fst\neq : RBNode.zoom cut t Path.root = (node c✝ l✝ v✝ r✝, x✝)\n... | [
388,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
383,
11
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integrable_iff_cauchy_basis | [
{
"state_after": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝¹ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\ninst✝ :... | [
234,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.isPartition_single_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nh : J ≤ I\n⊢ IsPartition (single I J h) ↔ J = I",
"tactic": "simp [isPartition_iff_iUnion_eq]"
}
] | [
726,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | UniformEquicontinuous.closure | [] | [
447,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | HasSum.compl_add | [] | [
368,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.ext | [] | [
77,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSet.exists_measurable_proj | [] | [
1150,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1145,
1
] |
Mathlib/Order/Filter/Cofinite.lean | Set.infinite_iff_frequently_cofinite | [] | [
90,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousAt_biInf | [] | [
1032,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1029,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_comap_comap_eq | [] | [
247,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection | [] | [
476,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Order/BoundedOrder.lean | max_eq_top | [] | [
873,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.