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/Topology/Algebra/Order/Floor.lean | tendsto_floor_left_pure_ceil_sub_one | [
{
"state_after": "α : Type u_1\nβ : Type ?u.8173\nγ : Type ?u.8176\ninst✝³ : LinearOrderedRing α\ninst✝² : FloorRing α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\nx : α\n⊢ ↑⌈x⌉ < x + 1",
"state_before": "α : Type u_1\nβ : Type ?u.8173\nγ : Type ?u.8176\ninst✝³ : LinearOrderedRing α\ninst✝² ... | [
95,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Std/Logic.lean | iff_def' | [] | [
40,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_map' | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.902392\nγ : Type ?u.902395\nδ : Type ?u.902398\nm : MeasurableSpace α\nμ ν : Measure α\nβ : Type u_1\ninst✝ : MeasurableSpace β\nμ' : Measure β\nf : α →ₛ ℝ≥0∞\ng : β →ₛ ℝ≥0∞\nm' : α → β\neq : ∀ (a : α), ↑f a = ↑g (m' a)\nh : ∀ (s : Set β), MeasurableSet s → ↑↑μ' s = ... | [
1154,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_lt_prod' | [
{
"state_after": "case nil\nι : Type u_2\nα : Type ?u.85857\nM : Type u_1\nN : Type ?u.85863\nP : Type ?u.85866\nM₀ : Type ?u.85869\nG : Type ?u.85872\nR : Type ?u.85875\ninst✝⁷ : Monoid M\ninst✝⁶ : Monoid N\ninst✝⁵ : Monoid P\nl✝ l₁ l₂ : List M\na : M\ninst✝⁴ : Preorder M\ninst✝³ : CovariantClass M M (fun x x_... | [
322,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.ofWithBot_mono | [] | [
462,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/GroupTheory/SpecificGroups/Alternating.lean | Equiv.Perm.isThreeCycle_sq_of_three_mem_cycleType_five | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type ?u.96658\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nc g' : Perm (Fin 5)\nh : 3 ∈ cycleType (c * g')\nhd : Disjoint c g'\nleft✝ : IsCycle c\nh3 : Finset.card (support c) = 3\n⊢ IsThreeCycle (c * g' * (c * g'))",
"state_before": "α : Type ?u.9665... | [
210,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Algebra/CharP/Basic.lean | MonoidHom.map_iterate_frobenius | [] | [
377,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.tendsto_filterAt | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nβ : Type u\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : MeasureTheory.Measure α\ninst✝ : SigmaFinite μ\nx : α\ns : Set (Set α)\nhs : s ∈ VitaliFamily.filterAt (Besi... | [
1153,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.append_cons | [] | [
129,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.permCongr_apply | [] | [
442,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
9
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.extend_eq_at | [] | [
158,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Separation.lean | ConnectedSpace.infinite | [] | [
809,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.induced_eq | [] | [
233,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.beq_eq | [] | [
96,
134
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
96,
9
] |
Mathlib/Data/Finset/Basic.lean | Finset.forall_mem_union | [] | [
1359,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1357,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.IsOption.mk_left | [] | [
228,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableOn.congr_mono | [] | [
918,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
917,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | tsub_le_iff_tsub_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3403\ninst✝³ : Preorder α\ninst✝² : AddCommSemigroup α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\n⊢ a - b ≤ c ↔ a - c ≤ b",
"tactic": "rw [tsub_le_iff_left, tsub_le_iff_right]"
}
] | [
112,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.one_sub_X_sq_mul_derivative_T_eq_poly_in_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.69485\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\n⊢ (1 - X ^ 2) * ↑derivative (T R (n + 1)) = (1 - X ^ 2) * ((↑n + 1) * U R n)",
"tactic": "rw [T_derivative_eq_U]"
},
{
"state_after": "no goals",
"state_before": "R ... | [
211,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.one_fst | [] | [
252,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_X_sub_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✝ : CommRing R\nn k : ℕ\nc : R\n⊢ (↑derivative^[k]) ((X - ↑C c) ^ n) = ↑(∏ i in range k, (n - i)) * (X - ↑C c) ^ (n - k)",
"tactic": "rw [sub_eq_add_neg, ← C_neg, iterate_deriva... | [
677,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.comp_add | [
{
"state_after": "case h\nR₁ : Type u_5\nR₂ : Type u_3\nR₃ : Type u_4\ninst✝¹⁹ : Semiring R₁\ninst✝¹⁸ : Semiring R₂\ninst✝¹⁷ : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₃ : R₂ →+* R₃\nσ₁₃ : R₁ →+* R₃\nM₁ : Type u_6\ninst✝¹⁶ : TopologicalSpace M₁\ninst✝¹⁵ : AddCommMonoid M₁\nM'₁ : Type ?u.519412\ninst✝¹⁴ : TopologicalSpac... | [
821,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.image_closure | [] | [
754,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | lt_mul_of_lt_one_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.87400\ninst✝ : StrictOrderedRing α\na b c : α\nhb : b < 0\nh : a < 1\n⊢ b < a * b",
"tactic": "simpa only [one_mul] using mul_lt_mul_of_neg_right h hb"
}
] | [
704,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.isRight_inr | [] | [
107,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
9
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.lt_div_iff_mul_lt | [
{
"state_after": "case inl\na✝ b m n✝ k n a : ℕ\nhnd : 0 ∣ n\n⊢ a < n / 0 ↔ 0 * a < n\n\ncase inr\na✝ b m n✝ k n d : ℕ\nhnd : d ∣ n\na : ℕ\nhd0 : d > 0\n⊢ a < n / d ↔ d * a < n",
"state_before": "a✝ b m n✝ k n d : ℕ\nhnd : d ∣ n\na : ℕ\n⊢ a < n / d ↔ d * a < n",
"tactic": "rcases d.eq_zero_or_pos with (... | [
58,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/Analysis/Complex/Isometry.lean | LinearIsometry.im_apply_eq_im | [
{
"state_after": "f : ℂ →ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\nz : ℂ\nthis : ‖↑f z - 1‖ = ‖z - 1‖\n⊢ z + ↑(starRingEnd ℂ) z = ↑f z + ↑(starRingEnd ((fun x => ℂ) z)) (↑f z)",
"state_before": "f : ℂ →ₗᵢ[ℝ] ℂ\nh : ↑f 1 = 1\nz : ℂ\n⊢ z + ↑(starRingEnd ℂ) z = ↑f z + ↑(starRingEnd ((fun x => ℂ) z)) (↑f z)",
"tactic": "have ... | [
119,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr | [] | [
120,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_add_le | [] | [
274,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Icc' | [] | [
540,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_symmDiff | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.89359\nγ : Type ?u.89362\ns t : Set α\ninst✝³ : DecidableEq α\ninst✝² : Fintype ↑s\ninst✝¹ : Fintype ↑t\ninst✝ : Fintype ↑(s ∆ t)\na✝ : α\n⊢ a✝ ∈ toFinset (s ∆ t) ↔ a✝ ∈ toFinset s ∆ toFinset t",
"state_before": "α : Type u_1\nβ : Type ?u.89359\nγ : Type ?... | [
718,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_apply_fin | [] | [
76,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.iInter₂_mul_subset | [] | [
535,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_inv_nat_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.52437\nι : Type ?u.52440\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε✝ ε₁ ε₂ : ℝ\ns : Set α\nε : ℝ\nε0 : 0 < ε\nn : ℕ\nhn : 1 / (↑n + 1) < ε\n⊢ 1 / ↑(n + 1) ≤ ε",
"tactic": "exact_mod_cast hn.le"
}
] | [
760,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.natCoe_apply | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Finset/NatAntidiagonal.lean | Finset.Nat.filter_snd_eq_antidiagonal | [
{
"state_after": "n m : ℕ\nthis : (fun x => x.snd = m) ∘ Prod.swap = fun x => x.fst = m\n⊢ filter (fun x => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅",
"state_before": "n m : ℕ\n⊢ filter (fun x => x.snd = m) (antidiagonal n) = if m ≤ n then {(n - m, m)} else ∅",
"tactic": "have : (... | [
129,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.uniformContinuous_completionSeparationQuotientEquiv_symm | [] | [
666,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Topology/StoneCech.lean | ultrafilterBasis_is_basis | [
{
"state_after": "case intro.intro.intro\nα : Type u\na b : Set α\nu : Ultrafilter α\nua : u ∈ (fun s => {u | s ∈ u}) a\nub : u ∈ (fun s => {u | s ∈ u}) b\n⊢ ∃ t₃, t₃ ∈ ultrafilterBasis α ∧ u ∈ t₃ ∧ t₃ ⊆ (fun s => {u | s ∈ u}) a ∩ (fun s => {u | s ∈ u}) b",
"state_before": "α : Type u\n⊢ ∀ (t₁ : Set (Ultraf... | [
52,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasStrictDerivAt_lineMap | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 →ᵃ[𝕜] E\na b : E\nL : Filter 𝕜\ns : Set 𝕜\nx : 𝕜\n⊢ HasStrictDerivAt (↑(lineMap a b)) (b - a) x",
"tactic": "simpa using (li... | [
65,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Group/WithOne/Basic.lean | WithOne.map_coe | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.coe_comp | [] | [
593,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.coe_singletonOneHom | [] | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq'_pos | [
{
"state_after": "n : ℕ\n⊢ 0 < ↑(succ n)! / (Real.sqrt (2 * ↑(succ n)) * (↑(succ n) / exp 1) ^ succ n)",
"state_before": "n : ℕ\n⊢ 0 < stirlingSeq (succ n)",
"tactic": "unfold stirlingSeq"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 0 < ↑(succ n)! / (Real.sqrt (2 * ↑(succ n)) *... | [
187,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.ucs_eq_top_iff | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk✝ : ℕ\nN N₁ N₂ : LieSubmodule R L M\nk : ℕ\n⊢ lcs k ⊤ ≤ N ↔ LieModule.lowerCentralSeries R L... | [
422,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Std/Data/List/Lemmas.lean | List.nil_subset | [] | [
231,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
231,
9
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | Convex.mem_to_cone' | [
{
"state_after": "case refine'_1\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.167255\nG : Type ?u.167258\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nx : E\n⊢ (∃ c, 0 < c ∧ ∃ y, y ∈ s ∧ c • y = x) → ∃ c, 0 < c ∧ c • x ∈ s\n\ncase refine'_2\n𝕜 : Type u... | [
669,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Order/CompleteLattice.lean | le_iSup_of_le | [] | [
791,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousHull_eq_iSup | [
{
"state_after": "case intro.intro\nι : Type ?u.242952\nσ : Type ?u.242955\nR : Type ?u.242958\nA : Type ?u.242961\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nI : Ideal A\ni : ι\nx : A\n⊢ Homogeneous... | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Icc_eq_nhdsWithin_Iic | [
{
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594,
70
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593,
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_submatrix_eq_blockDiagonal | [] | [
646,
38
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643,
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Mathlib/CategoryTheory/Elements.lean | CategoryTheory.CategoryOfElements.comp_val | [] | [
81,
6
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79,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.X_inj | [] | [
295,
21
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294,
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.trans_mk | [] | [
179,
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175,
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Mathlib/GroupTheory/EckmannHilton.lean | EckmannHilton.mul | [
{
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68,
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Mathlib/Data/Nat/Log.lean | Nat.lt_pow_succ_log_self | [] | [
135,
39
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134,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.le_op_nnnorm | [
{
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469,
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466,
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Mathlib/Data/Nat/PSub.lean | Nat.psub_eq_sub | [] | [
104,
41
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103,
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Mathlib/Dynamics/Flow.lean | Flow.map_add | [] | [
128,
88
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128,
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Mathlib/Data/Nat/Lattice.lean | Set.biInter_lt_succ | [] | [
214,
23
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213,
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Mathlib/Data/Multiset/Fold.lean | Multiset.max_nat_le_of_forall_le | [] | [
137,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
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Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.insert | [
{
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73,
19
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Mathlib/Data/Complex/Basic.lean | Complex.normSq_neg | [
{
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}
] | [
648,
72
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648,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_erase_left | [
{
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] | [
553,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
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Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.memberSubfamily_inter | [
{
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81,
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_moveRight | [] | [
602,
22
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601,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.sup_h_of_disjoint | [
{
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382,
11
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377,
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Mathlib/Topology/Order.lean | IsClosed.mono | [] | [
248,
58
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247,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.isClique_iff | [] | [
53,
10
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Mathlib/Order/SuccPred/Limit.lean | Order.not_isPredLimit_of_noMin | [
{
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] | [
328,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
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Mathlib/Order/PrimeIdeal.lean | Order.Ideal.IsPrime.of_mem_or_mem | [
{
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141,
33
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133,
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Mathlib/Combinatorics/Hindman.lean | Ultrafilter.continuous_mul_left | [] | [
89,
98
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86,
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Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_diff | [] | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/BanachSteinhaus.lean | banach_steinhaus_iSup_nnnorm | [
{
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54
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.NeWord.toList_head? | [
{
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44
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529,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_le_power_right | [] | [
756,
68
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755,
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.subset_lieSpan | [
{
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615,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_mul_aleph0_eq | [] | [
586,
33
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585,
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Mathlib/Analysis/Convex/Body.lean | ConvexBody.ext | [] | [
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17
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11
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.iSup_eq_closure | [
{
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"tactic": "simp_rw [closure_iUni... | [
1273,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
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Std/Data/Int/Lemmas.lean | Int.le_toNat | [
{
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"tactic": "rw [← Int.ofNat_le, Int.toNat_of_nonneg h]"
}
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1381,
45
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1380,
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Mathlib/Data/Complex/Exponential.lean | Complex.exp_eq_exp_re_mul_sin_add_cos | [
{
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}
] | [
1090,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
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Mathlib/Order/CompleteLattice.lean | isGLB_sInf | [] | [
216,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
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Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_smul | [
{
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Mathlib/Logic/Relation.lean | Relation.ReflTransGen.cases_tail | [] | [
294,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.single_swap | [
{
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446,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.inseparable_iff | [
{
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425,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_le_ker_comp | [
{
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1351,
88
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1350,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | padicNormE.nonarchimedean' | [] | [
627,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Data/List/Basic.lean | List.nthLe_append | [] | [
1332,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
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Mathlib/Algebra/BigOperators/RingEquiv.lean | RingEquiv.map_list_prod | [] | [
26,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
11
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.continuousAt_of_comp_left | [
{
"state_after": "ι : Type ?u.43574\nB : Type u_2\nF : Type u_3\nE : B → Type ?u.43585\nZ : Type u_4\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nproj : Z → B\ninst✝² : TopologicalSpace Z\ninst✝¹ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx✝ : Z\nX : Type u_1\ninst✝ : Topologic... | [
553,
63
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547,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_zero_eq_constantCoeff_apply | [] | [
490,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
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Mathlib/Data/Finset/Preimage.lean | Finset.map_subset_iff_subset_preimage | [
{
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},
{
"state_after": "no ... | [
94,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.toOuterMeasure_top | [
{
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85
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Mathlib/Order/Filter/Bases.lean | Filter.mem_iff_inf_principal_compl | [
{
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690,
74
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686,
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.map_star | [
{
"state_after": "case h\nR : Type u\nA : Type v\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Ring A\ninst✝³ : Algebra R A\ninst✝² : InvolutiveStar R\ninst✝¹ : StarRing A\ninst✝ : StarModule R A\na : A\nx✝ : R\n⊢ x✝ ∈ σ (star a) ↔ x✝ ∈ star (σ a)",
"state_before": "R : Type u\nA : Type v\ninst✝⁵ : CommSemiring R\nins... | [
266,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
11
] |
Mathlib/RingTheory/GradedAlgebra/Basic.lean | GradedAlgebra.mem_support_iff | [] | [
240,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_half_lt_one | [] | [
534,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Std/Data/List/Init/Lemmas.lean | List.singleton_append | [] | [
54,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
54,
14
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.range_prod_eq | [] | [
1319,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1317,
1
] |
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