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/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_symm | [] | [
1693,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.abs_def | [] | [
946,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_subtypePerm | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nf : Perm α\np : α → Prop\ninst✝ : DecidablePred p\nh₁ : ∀ (x : α), p x ↔ p (↑f x)\nh₂ : ∀ (x : α), ↑f x ≠ x → p x\nl : { l // List.prod l = subtypePerm f h₁ ∧ ∀ (g : Perm { x // p x }), g ∈ l → IsSwap g } :=\n Trunc.out (trun... | [
675,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.isEquivalent_atTop_lead | [
{
"state_after": "case pos\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nh : P = 0\n⊢ (fun x => eval x P) ~[atTop] fun x => leadingCoeff P * x ^ natDegree P\n\ncase neg\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nh :... | [
57,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.coe_toIntLinearEquiv | [] | [
853,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.map_eq | [] | [
65,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_neg | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na : PadicSeq p\n⊢ ∀ (k : ℕ), padicNorm p (↑(-a) k) = padicNorm p (↑a k)",
"tactic": "simp"
}
] | [
426,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq | [
{
"state_after": "case h.e'_2\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nhp : Monic p\nhroots : ↑Multiset.card (roots p) = natDegree p\n⊢ Multiset.prod (Multiset.map (fun a => X - ↑C a) (roots p)) =\n ↑C (leadingCoeff p) * Multiset.prod (Multiset... | [
1134,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | strictConvexOn_univ_of_deriv2_pos | [] | [
1274,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.root_isInv | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝² : CommRing R\nf : R[X]\ninst✝¹ : CommRing S\ni : R →+* S\na : S\nh : eval₂ i a f = 0\ninst✝ : Algebra R S\nhfx : ↑(aeval a) f = 0\nr : R\n⊢ ↑(of (↑C r * X - 1)) r * root (↑C r * X - 1) = 1",
"tactic": "convert sub_e... | [
355,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.card_le_degree_of_subset_roots | [] | [
599,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Icc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nh : 0 < c\n⊢ (fun x x_1 => x * x_1) c ⁻¹' Icc a b = Icc (a / c) (b / c)",
"tactic": "simp [← Ici_inter_Iic, h]"
}
] | [
637,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | norm_pow_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.132724\nγ : Type ?u.132727\nι : Type ?u.132730\ninst✝¹ : SeminormedRing α\ninst✝ : NormOneClass α\na : α\nn : ℕ\n⊢ ‖a ^ Nat.zero‖ ≤ ‖a‖ ^ Nat.zero",
"tactic": "simp only [Nat.zero_eq, pow_zero, norm_one, le_rfl]"
}
] | [
383,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus | [
{
"state_after": "case hsep\nC : Type u\ninst✝⁷ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝⁶ : Category D\ninst✝⁵ : ConcreteCategory D\ninst✝⁴ : PreservesLimits (forget D)\ninst✝³ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\ninst✝² : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer... | [
455,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.withDensityᵥ_add' | [] | [
101,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_hom | [
{
"state_after": "ι : Type ?u.22722\nα : Type ?u.22725\nM : Type u_1\nN : Type u_3\nP : Type ?u.22734\nM₀ : Type ?u.22737\nG : Type ?u.22740\nR : Type ?u.22743\ninst✝³ : Monoid M\ninst✝² : Monoid N\ninst✝¹ : Monoid P\nl✝ l₁ l₂ : List M\na : M\nl : List M\nF : Type u_2\ninst✝ : MonoidHomClass F M N\nf : F\n⊢ fol... | [
105,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | compact_open_separated_mul_right | [
{
"state_after": "case refine_1\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen U\nhKU : K ⊆ U\n⊢ ∃ V, V ∈ 𝓝 1 ∧ ∅ * V ⊆ U\n\ncase refine_2\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\n... | [
1552,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1535,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.orderOf_r | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\ni : ZMod n\n⊢ orderOf (r ↑(ZMod.val i)) = n / Nat.gcd n (ZMod.val i)",
"state_before": "n : ℕ\ninst✝ : NeZero n\ni : ZMod n\n⊢ orderOf (r i) = n / Nat.gcd n (ZMod.val i)",
"tactic": "conv_lhs => rw [← ZMod.nat_cast_zmod_val i]"
},
{
"state_after": "no g... | [
186,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Set/Pointwise/Finite.lean | Set.Infinite.of_smul_set | [] | [
114,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.lt_ord | [] | [
1377,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Algebra/Order/Monoid/Defs.lean | bit0_pos | [] | [
91,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
15
] |
Mathlib/Data/List/Basic.lean | List.map_diff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.428249\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ : List α\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → β\nfinj : Injective f\nl₁ l₂ : List α\n⊢ map f (List.diff l₁ l₂) = List.diff (map f l₁) (map f l₂)",
"tactic": "simp ... | [
3785,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3783,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.differentiableAt | [] | [
53,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.monotone_map | [] | [
306,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Submonoid.subsemiringClosure_coe | [] | [
859,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.not_empty_hom | [] | [
1510,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1509,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_right | [] | [
2134,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2133,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_summable_of_mem_ball | [] | [
219,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.not_le | [] | [
192,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
11
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_smul | [] | [
1511,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1509,
1
] |
Std/Data/List/Lemmas.lean | List.modifyNthTail_length | [] | [
741,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
737,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_two | [] | [
214,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.coe_scalar | [] | [
1250,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Std/Data/List/Init/Lemmas.lean | List.take_append_drop | [] | [
131,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
128,
9
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_div_distrib | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.215706\nι : Type ?u.215709\nG : Type u_1\nM : Type ?u.215715\nN : Type ?u.215718\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\nf✝ g✝ : α → M\na b : α\ns t : Set α\ninst✝ : DivisionCommMonoid G\nf g : α → G\nhf : Set.Finite (mulSupport ... | [
626,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | HasFTaylorSeriesUpToOn.differentiableAt | [] | [
307,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/List/Sigma.lean | List.NodupKeys.eq_of_fst_eq | [] | [
124,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_self_eq | [] | [
1273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.int_cast_fst | [] | [
315,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.ext | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.309065\nδ : Type ?u.309068\ninst✝³ : MeasurableSpace α\nμ ν : Measure α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf g : α →ₘ[μ] β\nh : ↑f =ᵐ[μ] ↑g\n⊢ f = g",
"tactic": "rwa ... | [
176,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.π_comp_cokernelComparison | [] | [
1139,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Data/List/Basic.lean | List.getD_eq_getD_get? | [
{
"state_after": "case inl\nι : Type ?u.504470\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : α\nxs : List α\nd : α\nn✝ n : ℕ\nh : n < length l\n⊢ getD l n d = Option.getD (get? l n) d\n\ncase inr\nι : Type ?u.504470\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nx : ... | [
4447,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4444,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.comap_monotone | [
{
"state_after": "ι : Sort ?u.208589\n𝕜 : Type ?u.208592\nV : Type u\nW : Type v\nX : Type w\nG✝ : SimpleGraph V\nG'✝ : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nf : V ↪ W\nG G' : SimpleGraph W\nh : G ≤ G'\nv✝ w✝ : V\nha : Adj (SimpleGraph.comap (↑f) G) v✝ w✝\n⊢ Adj (SimpleGraph.comap (↑f) G') v✝ w✝",
"s... | [
1266,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1264,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_toSubfield | [] | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.not_empty_toList | [] | [
3378,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3377,
1
] |
Mathlib/LinearAlgebra/Matrix/Polynomial.lean | Polynomial.leadingCoeff_det_X_one_add_C | [
{
"state_after": "case inl\nn : Type u_1\nα : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : CommRing α\nA : Matrix n n α\nh✝ : Subsingleton α\n⊢ leadingCoeff (det (X • 1 + Matrix.map A ↑C)) = 1\n\ncase inr\nn : Type u_1\nα : Type u_2\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\ninst✝ : CommRing ... | [
113,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_map₂_distrib_left | [] | [
335,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Data/Multiset/Sections.lean | Multiset.coe_sections | [
{
"state_after": "α : Type u_1\na : List α\nl : List (List α)\n⊢ Sections ↑(↑a :: List.map (fun l => ↑l) l) =\n ↑(List.map (fun l => ↑l) (List.bind (List.sections l) fun s => List.map (fun a => a :: s) a))",
"state_before": "α : Type u_1\na : List α\nl : List (List α)\n⊢ Sections ↑(List.map (fun l => ↑l)... | [
52,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.kerLift_injective | [] | [
1049,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1048,
1
] |
Mathlib/Topology/NoetherianSpace.lean | TopologicalSpace.noetherianSpace_iff_opens | [
{
"state_after": "α : Type u_1\nβ : Type ?u.411\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\n⊢ (∀ (k : Opens α), CompleteLattice.IsCompactElement k) ↔ ∀ (s : Opens α), IsCompact ↑s",
"state_before": "α : Type u_1\nβ : Type ?u.411\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\n⊢ Noeth... | [
60,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_neg | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.207706\nα : Type u_1\nβ : Type ?u.207712\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz✝ : ℤ\na : α\nz : ℤ\n⊢ ⌈-a⌉ ≤ z ↔ -⌊a⌋ ≤ z",
"tactic": "rw [neg_le, ceil_le, le_floor, Int.cast_neg, neg_le]"
}
] | [
1104,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.biUnion_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns✝¹ : Finset α\nt✝ : Finset β\na✝ : α\nb c : β\ninst✝ : DecidableEq γ\ns✝ : Finset α\nt : α → Finset β\nf : β → γ\nthis : DecidableEq α\na : α\ns : Finset α\nx✝ : ¬a ∈ s\nih : image ... | [
636,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
633,
1
] |
Mathlib/SetTheory/Ordinal/CantorNormalForm.lean | Ordinal.zero_CNF | [
{
"state_after": "no goals",
"state_before": "o : Ordinal\nho : o ≠ 0\n⊢ CNF 0 o = [(0, o)]",
"tactic": "simp [CNF_ne_zero ho]"
}
] | [
96,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.forall_mem_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37873\nγ : Type ?u.37876\ns t : Finset α\na b : α\nh : ¬a ∈ s\np : α → Prop\n⊢ (∀ (x : α), x ∈ cons a s h → p x) ↔ p a ∧ ∀ (x : α), x ∈ s → p x",
"tactic": "simp only [mem_cons, or_imp, forall_and, forall_eq]"
}
] | [
855,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_list_le_max | [
{
"state_after": "case inl\nα : Type u\nh✝ : Finite α\n⊢ (#List α) ≤ max ℵ₀ (#α)\n\ncase inr\nα : Type u\nh✝ : Infinite α\n⊢ (#List α) ≤ max ℵ₀ (#α)",
"state_before": "α : Type u\n⊢ (#List α) ≤ max ℵ₀ (#α)",
"tactic": "cases finite_or_infinite α"
},
{
"state_after": "no goals",
"state_before... | [
1019,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1015,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Iic_prod | [] | [
1663,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_one | [
{
"state_after": "x✝ y z✝ x z : ℝ\nhx1 : 0 ≤ x\nhx2 : x < 1\nhz : 0 < z\n⊢ x ^ z < 1 ^ z",
"state_before": "x✝ y z✝ x z : ℝ\nhx1 : 0 ≤ x\nhx2 : x < 1\nhz : 0 < z\n⊢ x ^ z < 1",
"tactic": "rw [← one_rpow z]"
},
{
"state_after": "no goals",
"state_before": "x✝ y z✝ x z : ℝ\nhx1 : 0 ≤ x\nhx2 : ... | [
516,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.insert | [] | [
323,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
11
] |
Std/Data/List/Lemmas.lean | List.forIn_eq_bindList | [
{
"state_after": "case cons\nm : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → β → m (ForInStep β)\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : ∀ (init : β), forIn tail✝ init f = ForInStep.run <$> ForInStep.bindList f tail✝ (ForInStep.yield init)\ninit : β\n⊢ (do\n ... | [
1481,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1477,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_comp_subtypeL_eq_zero_iff | [
{
"state_after": "case h.e'_2.h.e'_4\n𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.813852\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK U V : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ U }\nh : ContinuousLi... | [
840,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.sInf_empty | [
{
"state_after": "no goals",
"state_before": "⊢ sInf ∅ = 0",
"tactic": "rw [← NNReal.coe_eq_zero, coe_sInf, Set.image_empty, Real.sInf_empty]"
}
] | [
512,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Order/Lattice.lean | sup_congr_right | [] | [
298,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_fract | [
{
"state_after": "F : Type ?u.161267\nα : Type u_1\nβ : Type ?u.161273\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ 0 ≤ fract a ∧ fract a < 1",
"state_before": "F : Type ?u.161267\nα : Type u_1\nβ : Type ?u.161273\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\... | [
922,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
921,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_neg | [] | [
324,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.pure_pow | [] | [
273,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_codRestrict_apply | [] | [
1016,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Data/Sign.lean | exists_signed_sum' | [
{
"state_after": "case intro.intro.intro.intro.intro.intro\nα✝ : Type ?u.152227\nα : Type u_1\ninst✝¹ : Nonempty α\ninst✝ : DecidableEq α\ns : Finset α\nf : α → ℤ\nn : ℕ\nh : ∑ i in s, Int.natAbs (f i) ≤ n\nβ : Type u_1\nw✝ : Fintype β\nsgn : β → SignType\ng : β → α\nhg : ∀ (b : β), g b ∈ s\nhβ : Fintype.card β... | [
534,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_def | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Order/UpperLower/Basic.lean | upperClosure_iUnion | [] | [
1444,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.ofList_cons | [] | [
145,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.le_iff | [] | [
436,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_norm_pow_norm_pow | [] | [
2031,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2029,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.image | [] | [
153,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | BoundedContinuousFunction.NNReal.toReal_lintegral_eq_integral | [
{
"state_after": "Ω : Type u_1\ninst✝² : MeasurableSpace Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nf : Ω →ᵇ ℝ≥0\nμ : Measure Ω\n⊢ ENNReal.toReal (∫⁻ (x : Ω), ↑(↑f x) ∂μ) = ENNReal.toReal (∫⁻ (a : Ω), ENNReal.ofReal ↑(↑f a) ∂μ)\n\nΩ : Type u_1\ninst✝² : MeasurableSpace Ω\ninst✝¹ : Topologic... | [
734,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/CategoryTheory/Localization/Construction.lean | CategoryTheory.Localization.Construction.morphismProperty_is_top | [
{
"state_after": "case h.h.h\nC : Type u_1\ninst✝¹ : Category C\nW : MorphismProperty C\nD : Type ?u.29447\ninst✝ : Category D\nG : C ⥤ D\nhG : MorphismProperty.IsInvertedBy W G\nP : MorphismProperty (MorphismProperty.Localization W)\nhP₁ : ∀ ⦃X Y : C⦄ (f : X ⟶ Y), P ((MorphismProperty.Q W).map f)\nhP₂ : ∀ ⦃X Y... | [
257,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.unrev_ok | [
{
"state_after": "no goals",
"state_before": "q : Λ'\ns : Option Γ'\nS : K' → List Γ'\n⊢ rev ≠ main",
"tactic": "decide"
}
] | [
1390,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.iSup_coe | [] | [
1923,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1922,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map₂_pure_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.28301\nβ : Type u_3\nβ' : Type ?u.28307\nγ : Type u_1\nγ' : Type ?u.28313\nδ : Type ?u.28316\nδ' : Type ?u.28319\nε : Type ?u.28322\nε' : Type ?u.28325\nm : α → β → γ\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nh✝ h₁ h₂ : Filter γ\ns s₁ s... | [
193,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/CompleteLattice.lean | sup_iSup_nat_succ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.180415\nβ₂ : Type ?u.180418\nγ : Type ?u.180421\nι : Sort ?u.180424\nι' : Sort ?u.180427\nκ : ι → Sort ?u.180432\nκ' : ι' → Sort ?u.180437\ninst✝ : CompleteLattice α\nf g s t : ι → α\na b : α\nu : ℕ → α\n⊢ (⨆ (x : ℕ) (_ : x ∈ {0} ∪ rang... | [
1669,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1665,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | normalizeScaleRoots_degree | [
{
"state_after": "case a\nR : Type u_1\nA : Type ?u.886014\nB : Type ?u.886017\nS : Type ?u.886020\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing A\ninst✝³ : CommRing B\ninst✝² : CommRing S\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nf : R →+* S\np : R[X]\nx : S\n⊢ degree (normalizeScaleRoots p) ≤ degree p\n\ncase a\n... | [
754,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.Limits.hasEqualizer_of_common_retraction | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA✝ B✝ : C\nf✝ g✝ : A✝ ⟶ B✝\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\ninst✝ : HasCoreflexiveEqualizers C\nA B : C\nf g : A ⟶ B\nr : B ⟶ A\nfr : f ≫ r = 𝟙 A\ngr : g ≫ r = 𝟙 A\nthis : IsCoreflexivePair f g := IsCoreflexivePair.mk' r f... | [
164,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_const_mul_le | [
{
"state_after": "α : Type u_1\nβ : Type ?u.935860\nγ : Type ?u.935863\nδ : Type ?u.935866\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\n⊢ (⨆ (i : α →ₛ ℝ≥0∞), r * ⨆ (_ : ↑i ≤ fun a => f a), SimpleFunc.lintegral i μ) ≤ ∫⁻ (a : α), r * f a ∂μ",
"state_before": "α : Type u_1\nβ : Type ?u.935... | [
716,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.partialSum_succ | [] | [
98,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Convex/Body.lean | ConvexBody.coe_add | [] | [
120,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/Order/Basic.lean | closure_Iio | [] | [
2236,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2235,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.limitEquivSections_apply | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Std/Logic.lean | And.imp | [] | [
150,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
150,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.rightUnitor_hom_apply | [] | [
237,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_finset_sum_measure | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nE : Type u_3\nF : Type ?u.1309166\n𝕜 : Type ?u.1309169\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : CompleteSpace E\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : SMulCommClass ℝ 𝕜 E\ninst✝⁴ : Nor... | [
1436,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1428,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_mul_pow_sub | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.24421\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : M\nm n : ℕ\nh : m ≤ n\n⊢ a ^ m * a ^ (n - m) = a ^ n",
"tactic": "rw [← pow_add, Nat.add_comm, Na... | [
166,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_iSup_of_directed | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\ninst✝² : NonAssocSemiring R\nM : Submonoid R\ninst✝¹ : NonAssocSemiring S✝\ninst✝ : NonAssocSemiring T\nι : Sort u_1\nhι : Nonempty ι\nS : ι → Subsemiring R\nhS : Directed (fun x x_1 => x ≤ x_1) S\nx : R\n⊢ x ∈ ↑(⨆ (i : ι), S... | [
1103,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/MeasureTheory/Function/Floor.lean | Measurable.floor | [] | [
36,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.equivOfEq_symm | [] | [
197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fintype.univ_of_isEmpty | [] | [
597,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.continuousOn_sin | [] | [
97,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Order/Kleene.lean | Pi.kstar_apply | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.algebraMap_eq_zero_iff | [] | [
428,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.rename_id | [] | [
98,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.norm_zero | [
{
"state_after": "no goals",
"state_before": "d : ℤ\n⊢ norm 0 = 0",
"tactic": "simp [norm]"
}
] | [
530,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | Pretrivialization.coe_linearMapAt | [
{
"state_after": "R : Type u_4\nB : Type u_1\nF : Type u_2\nE : B → Type u_3\ninst✝⁷ : Semiring R\ninst✝⁶ : TopologicalSpace F\ninst✝⁵ : TopologicalSpace B\ne✝ : Pretrivialization F TotalSpace.proj\nx : TotalSpace E\nb✝ : B\ny : E b✝\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module R F\ninst✝² : (x : B) → AddCommMono... | [
126,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.