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/Computability/NFA.lean | NFA.evalFrom_singleton | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/CompleteLattice.lean | le_iSup₂_of_le | [] | [
808,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.ind | [] | [
318,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Topology/Sober.lean | isGenericPoint_def | [] | [
42,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/WellFoundedSet.lean | Finset.partiallyWellOrderedOn | [] | [
545,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
11
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Mathlib/LinearAlgebra/Dimension.lean | rank_fun_eq_lift_mul | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.533809\ninst✝¹⁴ : Ring K\ninst✝¹³ : StrongRankCondition K\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : Module K V\ninst✝¹⁰ : Module.Free K V\ninst✝... | [
1024,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Logic/Equiv/Fintype.lean | Function.Embedding.toEquivRange_eq_ofInjective | [
{
"state_after": "case H.a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\ne : Equiv.Perm α\nf : α ↪ β\nx✝ : α\n⊢ ↑(↑(toEquivRange f) x✝) = ↑(↑(Equiv.ofInjective ↑f (_ : Injective ↑f)) x✝)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\ne : E... | [
59,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.eq_of_associated_left | [] | [
340,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_biUnion_finset | [] | [
1597,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | eventually_nhds_norm_smul_sub_lt | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.15386\nγ : Type ?u.15389\nι : Type ?u.15392\ninst✝⁵ : NormedField α\ninst✝⁴ : SeminormedAddCommGroup β\nE : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace α E\nF : Type ?u.15423\ninst✝¹ : SeminormedAddCommGroup F\nins... | [
95,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Int/Parity.lean | Int.not_even_bit1 | [
{
"state_after": "no goals",
"state_before": "m n✝ n : ℤ\n⊢ ¬Even (bit1 n)",
"tactic": "simp [bit1, parity_simps]"
}
] | [
118,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.unpaired' | [] | [
445,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finsupp_lift_of_infinite | [
{
"state_after": "case a\nα : Type u\nβ : Type v\ninst✝² : Infinite α\ninst✝¹ : Zero β\ninst✝ : Nontrivial β\n⊢ (#α →₀ β) ≤ max (lift (#α)) (lift (#β))\n\ncase a\nα : Type u\nβ : Type v\ninst✝² : Infinite α\ninst✝¹ : Zero β\ninst✝ : Nontrivial β\n⊢ max (lift (#α)) (lift (#β)) ≤ (#α →₀ β)",
"state_before": "... | [
1046,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_iff_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45481\nγ : Type ?u.45484\nf : α → β\ns t u : Finset α\na b : α\n⊢ _root_.Disjoint s t ↔ ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ t → a ≠ b",
"tactic": "simp only [disjoint_left, imp_not_comm, forall_eq']"
}
] | [
923,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.Iso.toEquiv_comp | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | IsOpen.exists_iUnion_isClosed | [
{
"state_after": "case intro.intro\nι : Sort ?u.21246\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t : Set α\nΦ : α → β\nU : Set α\nhU : IsOpen U\na : ℝ≥0∞\na_pos : 0 < a\na_lt_one : a < 1\n⊢ ∃ F, (∀ (n : ℕ), IsClosed (F n)) ∧ (∀ (n : ℕ), F n ⊆ U) ∧ (⋃ (n : ℕ)... | [
229,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Topology/LocalExtr.lean | IsLocalMin.comp_continuousOn | [] | [
321,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_subset_union | [
{
"state_after": "case intro\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.220883\nG : Type ?u.220886\nι : Type ?u.220889\nπ : ι → Type ?u.220894\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nx✝ y✝ z x y : E\nc : 𝕜\n⊢ openSegment 𝕜 x y ⊆\n insert (↑(lineMap x y) c) (openSegment... | [
409,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.mem_comap | [] | [
293,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.iSup_lt_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.160773\nr : α → α → Prop\nι : Type u_1\nf : ι → Cardinal\nc : Cardinal\nhc : IsRegular c\nhι : (#ι) < c\n⊢ (#ι) < Ordinal.cof (ord c)",
"tactic": "rwa [hc.cof_eq]"
}
] | [
1110,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1108,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.IsDiag.map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nR : Type ?u.2825\nn : Type u_3\nm : Type ?u.2831\ninst✝¹ : Zero α\ninst✝ : Zero β\nA : Matrix n n α\nha : IsDiag A\nf : α → β\nhf : f 0 = 0\ni j : n\nh : i ≠ j\n⊢ Matrix.map A f i j = 0",
"state_before": "α : Type u_1\nβ : Type u_2\nR : Type ?u.2825\nn : Type u_... | [
82,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Algebra/Order/Kleene.lean | nsmul_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.18224\nι : Type ?u.18227\nπ : ι → Type ?u.18232\ninst✝ : IdemSemiring α\na✝ b c : α\nn : ℕ\nx✝ : n + 2 ≠ 0\na : α\n⊢ (n + 2) • a = a",
"tactic": "rw [succ_nsmul, nsmul_eq_self n.succ_ne_zero, add_idem]"
}
] | [
150,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.map_eq_iff | [] | [
169,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.snd_surjective | [] | [
90,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.zero_apply | [] | [
320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | odd_sq_dvd_geom_sum₂_sub | [
{
"state_after": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\na b x y : R\np : ℕ\nhp : Odd p\nh1 : ∀ (i : ℕ), ↑p ^ 2 ∣ (a + ↑p * b) ^ i - (a ^ (i - 1) * (↑p * b) * ↑i + a ^ i)\n⊢ ↑p ^ 2 ∣ ∑ i in range p, (a + ↑p * b) ^ i * a ^ (p - 1 - i) - ↑p * a ^ (p - 1)",
"state_before": "R : Type u_1\nn : ℕ\ninst✝ : CommR... | [
152,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_sigma_map | [] | [
1555,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.fg_iff_add_subgroup_fg | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.2420\nM : Type ?u.2423\ninst✝³ : Semiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\nG : Type u_1\ninst✝ : AddCommGroup G\nP : Submodule ℤ G\nx✝ : FG P\nS : Finset G\nhS : span ℤ ↑S = P\n⊢ AddSubgroup.closure ↑S = toAddSubgroup P",
"tactic... | [
68,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Set/Basic.lean | Set.monotoneOn_iff_monotone | [
{
"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 : Set α\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\n⊢ MonotoneOn f s ↔ Monotone fun a => f ↑a",
"tactic": "simp [Monotone, MonotoneOn]"
}
] | [
2653,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2651,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | SMul.comp.isScalarTower | [
{
"state_after": "M : Type ?u.9269\nN : Type ?u.9272\nG : Type ?u.9275\nA : Type ?u.9278\nB : Type ?u.9281\nα : Type ?u.9284\nβ : Type ?u.9287\nγ : Type ?u.9290\nδ : Type ?u.9293\ninst✝³ : SMul M α\ninst✝² : SMul M β\ninst✝¹ : SMul α β\ninst✝ : IsScalarTower M α β\ng : N → M\nthis : SMul N α\n⊢ Sort ?u.9343",
... | [
370,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.nondegenerate_toBilin'_iff_nondegenerate_toBilin | [] | [
548,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.pullback_map_self | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ninst✝¹ : HasPullbacks C\nf : X ⟶ Y\ninst✝ : Mono f\n⊢ ∀ (g : Subobject X), (pullback f).obj ((map f).obj g) = g",
"state_before": "C : Type u₁\ninst✝³ : Category C\nX Y Z : C\nD : Type u₂\ninst✝² : Category D\ni... | [
645,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/GroupTheory/FreeAbelianGroupFinsupp.lean | Finsupp.toFreeAbelianGroup_comp_toFinsupp | [
{
"state_after": "case H\nX : Type u_1\nx✝ : X\n⊢ ↑(AddMonoidHom.comp toFreeAbelianGroup toFinsupp) (of x✝) = ↑(AddMonoidHom.id (FreeAbelianGroup X)) (of x✝)",
"state_before": "X : Type u_1\n⊢ AddMonoidHom.comp toFreeAbelianGroup toFinsupp = AddMonoidHom.id (FreeAbelianGroup X)",
"tactic": "ext"
},
... | [
75,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.carrier_eq_coe | [] | [
253,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.inv_mk | [] | [
610,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.exists_isSubordinate_of_locallyFinite | [] | [
328,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.map_move | [
{
"state_after": "case mk\nΓ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nd : Dir\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ map f (move d { head := head✝, left := left✝, right := right✝ }) =\n move d (map f { head := head✝, left := left✝, right := right✝ })",
... | [
718,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_sub_lt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ abs (a - b) < c ↔ a - b < c ∧ b - a < c",
"tactic": "rw [@abs_lt α, neg_lt_sub_iff_lt_add', sub_lt_iff_lt_add', and_comm, sub_lt_iff_lt_add']"
}
] | [
289,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/FiniteField.lean | ZMod.charpoly_pow_card | [
{
"state_after": "n : Type u_1\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nM : Matrix n n (ZMod p)\nh : charpoly (M ^ Fintype.card (ZMod p)) = charpoly M\n⊢ charpoly (M ^ p) = charpoly M",
"state_before": "n : Type u_1\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\np : ℕ\ni... | [
53,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_inter_null_of_null_right | [] | [
344,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Data/List/Lemmas.lean | List.foldl_range_eq_of_range_eq | [] | [
82,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.prod_le_prod_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.175540\nι : Sort ?u.175543\nκ : ι → Sort ?u.175548\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : UpperSet α\nt t₁ t₂ : UpperSet β\nx : α × β\n⊢ ↑s₂ ⊆ ↑s₁ ∧ ↑t₂ ⊆ ↑t₁ ∨ ↑s₂ = ∅ ∨ ↑t₂ = ∅ ↔ s₁ ≤ s₂ ∧ t₁ ≤ t₂ ∨ s₂ = ⊤ ∨... | [
1625,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1624,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.exists_get?_of_mem | [
{
"state_after": "case h1\nα : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nh : a ∈ s\n⊢ ∀ (b : α) (s' : WSeq α), (a = b ∨ ∃ n, some a ∈ get? s' n) → ∃ n, some a ∈ get? (cons b s') n\n\ncase h2\nα : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\na : α\nh : a ∈ s\n⊢ ∀ (s : WSeq α), (∃ n, some a ∈ get? s n) → ... | [
1021,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.rpow_add_le_mul_rpow_add_rpow | [
{
"state_after": "case inl\nι : Type u\ns : Finset ι\nz₁ z₂ : ℝ≥0\nhp : 1 ≤ 1\n⊢ (z₁ + z₂) ^ 1 ≤ 2 ^ (1 - 1) * (z₁ ^ 1 + z₂ ^ 1)\n\ncase inr\nι : Type u\ns : Finset ι\nz₁ z₂ : ℝ≥0\np : ℝ\nhp : 1 ≤ p\nh'p : 1 < p\n⊢ (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p)",
"state_before": "ι : Type u\ns : Finset ι\n... | [
164,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Std/Data/String/Lemmas.lean | String.valid_next | [
{
"state_after": "no goals",
"state_before": "s : String\np : Pos\nh : Pos.Valid s p\nh₂ : p < endPos s\n⊢ Pos.Valid s (next s p)",
"tactic": "match s, p, h with\n| ⟨_⟩, ⟨_⟩, ⟨cs, [], rfl, rfl⟩ => simp at h₂\n| ⟨_⟩, ⟨_⟩, ⟨cs, c::cs', rfl, rfl⟩ =>\n rw [utf8ByteSize.go_eq, next_of_valid]\n simpa using ... | [
270,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
265,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Fintype.total_apply | [] | [
1059,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.compl_mem_coprodᵢ | [
{
"state_after": "no goals",
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"tactic": "simp only [Filter.coprodᵢ, mem_iSup, compl_mem_comap]"
}
] | [
210,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutComparison_map_desc | [
{
"state_after": "no goals",
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1495,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
1
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Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_apply_of_ne_of_ne | [
{
"state_after": "no goals",
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"tactic": "simp (config := { contextual := true }) [swap_apply_def]"
}
] | [
1573,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1572,
1
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_le_of_injective | [] | [
273,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.continuous_testAgainstNN_eval | [] | [
256,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
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Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.SpecialLinear.sl_bracket | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Analysis/Calculus/MeanValue.lean | image_norm_le_of_norm_deriv_right_le_deriv_boundary | [] | [
335,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Order/Monotone/Basic.lean | Function.monotone_eval | [] | [
342,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.mem_toSubsemigroup | [] | [
237,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
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Mathlib/Order/BooleanAlgebra.lean | inf_sdiff_right_comm | [
{
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"tactic": "rw [@inf_comm _ _ x, inf_comm, inf_sdiff_assoc]"
}
] | [
450,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
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Std/Data/Int/Lemmas.lean | Int.negOfNat_eq | [] | [
45,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_smul_index | [] | [
1631,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1629,
1
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Mathlib/Algebra/ContinuedFractions/ContinuantsRecurrence.lean | GeneralizedContinuedFraction.continuants_recurrence | [
{
"state_after": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn : ℕ\ninst✝ : DivisionRing K\ngp ppred pred : Pair K\nsucc_nth_s_eq : Stream'.Seq.get? g.s (n + 1) = some gp\nnth_conts_eq : continuantsAux g (n + 1) = ppred\nsucc_nth_conts_eq : continuantsAux g (n + 1 + 1) = pred\n⊢ continuants g (n + 2) = {... | [
49,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
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Mathlib/Data/List/BigOperators/Basic.lean | List.prod_eq_one | [
{
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532,
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528,
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Mathlib/Data/Sum/Order.lean | Sum.inr_strictMono | [] | [
197,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | IsUnit.ne_zero | [] | [
55,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
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Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Ico | [] | [
554,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
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Mathlib/CategoryTheory/Limits/Constructions/FiniteProductsOfBinaryProducts.lean | CategoryTheory.hasFiniteProducts_of_has_binary_and_terminal | [
{
"state_after": "J : Type v\ninst✝⁴ : SmallCategory J\nC : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasBinaryProducts C\ninst✝ : HasTerminal C\nn : ℕ\nK : Discrete (Fin n) ⥤ C\n⊢ HasLimit K",
"state_before": "J : Type v\ninst✝⁴ : SmallCategory J\nC : Type u\ninst✝³ : Category... | [
115,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
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Mathlib/Data/Fin/Basic.lean | Fin.castAdd_cast | [] | [
1166,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.coe_aeval_eq_eval | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_add_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1755617\nγ : Type ?u.1755620\nδ : Type ?u.1755623\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\ng : α → ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(withDensity μ (f + g)) s = ↑↑(withDensity μ f + withDensity μ g) s",
"state_before": "α ... | [
1566,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1561,
1
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Mathlib/CategoryTheory/Monoidal/Free/Coherence.lean | CategoryTheory.FreeMonoidalCategory.tensorFunc_obj_map | [
{
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"state_before": "C : Type u\nZ : F C\nn n' : (Discrete ∘ NormalMonoidalObject) C\nf : n ⟶ n'\n⊢ ((tensorFu... | [
183,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_of_not_ge | [] | [
1000,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
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Mathlib/Data/Rat/Lemmas.lean | Rat.num_den_mk | [
{
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"state_before": "q : ℚ\nn d : ℤ\nhd : d ≠ 0\nqdf : q = n /. d\n⊢ ∃ c, n = c * q.num ∧ d... | [
57,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/Algebra/Associated.lean | Associates.mk_eq_zero | [] | [
965,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.first_countable | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.848749\n𝕝 : Type ?u.848752\n𝕝₂ : Type ?u.848755\nE : Type u_2\nF : Type ?u.848761\nG : Type ?u.848764\nι : Type u_3\nι' : Type ?u.848770\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : Nonempty ι\ninst✝² : Countable ι... | [
770,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
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Std/Data/String/Lemmas.lean | String.all_iff | [
{
"state_after": "no goals",
"state_before": "s : String\np : Char → Bool\n⊢ all s p = true ↔ ∀ (c : Char), c ∈ s.data → p c = true",
"tactic": "simp [all_eq]"
}
] | [
725,
94
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
725,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_biInter | [] | [
264,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_inj | [] | [
291,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_inf_eq | [] | [
1238,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.comp_liftAddHom | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\nδ : Type u_1\ninst✝² : (i : ι) → AddZeroClass (β i)\ninst✝¹ : AddCommMonoid γ\ninst✝ : AddCommMonoid δ\ng : γ →+ δ\nf : (i : ι) → β i →+ γ\na : ι\n⊢ ↑(AddEquiv.symm ... | [
2050,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2045,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.linear_mk' | [] | [
190,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousAt_iInf | [] | [
1026,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_arg | [] | [
124,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/Filter.lean | Filter.isOpen_Iic_principal | [] | [
55,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_lt_top | [] | [
1415,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean | CategoryTheory.Limits.has_limits_of_finite_and_cofiltered | [] | [
102,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.lcm_congr | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.7148\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ : Finset β\nf✝ f g : β → α\nhfg : ∀ (a : β), a ∈ s₁ → f a = g a\n⊢ lcm s₁ f = lcm s₁ g",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.7148\ninst✝¹ : CancelComm... | [
106,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_assoc | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b c : X ⟶ Y\n⊢ a - -b + c = a + (b + c)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b c : X ⟶ Y\n⊢ a + b + c = a + (b + c)",
"tactic": "conv_lhs =>\n congr;... | [
425,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Module.isTorsionBySet_span_singleton_iff | [] | [
348,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Std/Data/List/Lemmas.lean | List.diff_append | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl₁ l₂ l₃ : List α\n⊢ List.diff l₁ (l₂ ++ l₃) = List.diff (List.diff l₁ l₂) l₃",
"tactic": "simp only [diff_eq_foldl, foldl_append]"
}
] | [
1523,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1522,
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Mathlib/Order/Heyting/Hom.lean | map_symmDiff | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.40368\nδ : Type ?u.40371\ninst✝² : CoheytingAlgebra α\ninst✝¹ : CoheytingAlgebra β\ninst✝ : CoheytingHomClass F α β\nf : F\na b : α\n⊢ ↑f (a ∆ b) = ↑f a ∆ ↑f b",
"tactic": "simp_rw [symmDiff, map_sup, map... | [
212,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_smul | [] | [
336,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.mem_iSup_of_directed | [
{
"state_after": "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 i) → ∃ i, x ∈ S i",
"state_b... | [
1098,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.units_zpow_left | [] | [
1146,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.withConstants_funMap_sum_inl | [] | [
512,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/List/Nodup.lean | List.count_eq_of_nodup | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na✝ b : α\ninst✝ : DecidableEq α\na : α\nl : List α\nd : Nodup l\nh : a ∈ l\n⊢ count a l = 1\n\ncase inr\nα : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na✝ b : α\ninst✝ : DecidableEq α\na : α\nl : List α\nd : N... | [
207,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_lt_sqrtTwoAddSeries | [
{
"state_after": "n : ℕ\nthis : π < (sqrt (2 - sqrtTwoAddSeries 0 n) / 2 + 1 / (2 ^ n) ^ 3 / 4) * 2 ^ (n + 2)\n⊢ (sqrt (2 - sqrtTwoAddSeries 0 n) / 2 + 1 / (2 ^ n) ^ 3 / 4) * 2 ^ (n + 2) =\n 2 ^ (n + 1) * sqrt (2 - sqrtTwoAddSeries 0 n) + 1 / 4 ^ n",
"state_before": "n : ℕ\nthis : π < (sqrt (2 - sqrtTwoA... | [
69,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.comp_add_le | [] | [
353,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.restrict_univ | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nι : Type ?u.1444502\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\ns t : Set β\na : α\n⊢ ↑(kernel.restrict κ (_ : MeasurableSet Set.univ)) a = ↑κ a",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.1444502\nmα : Me... | [
506,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_δ_self' | [
{
"state_after": "n : ℕ\ni : Fin (n + 2)\n⊢ δ i ≫ δ (↑Fin.castSucc i) = δ i ≫ δ (Fin.succ i)",
"state_before": "n : ℕ\ni : Fin (n + 2)\nj : Fin (n + 3)\nH : j = ↑Fin.castSucc i\n⊢ δ i ≫ δ j = δ i ≫ δ (Fin.succ i)",
"tactic": "subst H"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\ni... | [
255,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_mk | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanCompIso_app_left | [] | [
344,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_ite_empty_left | [
{
"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 : Set α\np : Prop\ninst✝ : Decidable p\nt : Set α\nx : α\n⊢ (∃ h, x ∈ t) ↔ ¬p ∧ x ∈ t",
"tactic": "simp"
}
] | [
2233,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2231,
1
] |
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