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/PartrecCode.lean | Nat.Partrec.Code.rec_prim | [
{
"state_after": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nc : α → Code\nhc : Primrec c\nz : α → σ\nhz : Primrec z\ns : α → σ\nhs : Primrec s\nl : α → σ\nhl : Primrec l\nr : α → σ\nhr : Primrec r\npr : α → Code → Code → σ → σ → σ\nhpr : Primrec fun a => pr a.fst a.snd.fst a.snd... | [
492,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_ne | [
{
"state_after": "case a\nα : Type ?u.412614\nβ : Type u_1\nγ : Type ?u.412620\np q : α → Prop\ninst✝³ : DecidablePred p\ninst✝² : DecidablePred q\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\ns : Finset β\nb a✝ : β\n⊢ a✝ ∈ filter (fun a => b ≠ a) s ↔ a✝ ∈ erase s b",
"state_before": "α : Type ?u.412614\n... | [
2942,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2938,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_const | [] | [
1048,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.smul_apply | [] | [
688,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isRefl | [] | [
343,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
11
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.mem_memberSubfamily | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\n⊢ (∃ a_1, (a_1 ∈ 𝒜 ∧ a ∈ a_1) ∧ erase a_1 a = s) ↔ insert a s ∈ 𝒜 ∧ ¬a ∈ s",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n𝒜 ℬ : Finset (Finset α)\ns : Finset α\na : α\n⊢ s ∈ memberSubfamily a 𝒜... | [
69,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.iSup_sInfGen_nonempty | [
{
"state_after": "case inl\nα : Type u_1\nm : Set (OuterMeasure α)\nh : Set.Nonempty m\n⊢ (⨆ (_ : Set.Nonempty ∅), sInfGen m ∅) = ⨅ (μ : OuterMeasure α) (_ : μ ∈ m), ↑μ ∅\n\ncase inr\nα : Type u_1\nm : Set (OuterMeasure α)\nh : Set.Nonempty m\nt : Set α\nht : Set.Nonempty t\n⊢ (⨆ (_ : Set.Nonempty t), sInfGen m... | [
1166,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1158,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousWithinAt.const_cpow | [] | [
134,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
8
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafify_hom_ext | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q : Cᵒᵖ ⥤ D\nη γ : sheafify J P ⟶ Q\nhQ : Presheaf.IsShe... | [
589,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat.mul | [
{
"state_after": "no goals",
"state_before": "p a b : ℕ\nhp : Fact (Nat.Prime p)\n⊢ a ≠ 0 → b ≠ 0 → padicValNat p (a * b) = padicValNat p a + padicValNat p b",
"tactic": "exact_mod_cast @padicValRat.mul p _ a b"
}
] | [
408,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_lt_top | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.96829\nβ : Type ?u.96832\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a < ⊤ → ∀ (n : ℕ), a ^ n < ⊤",
"tactic": "simpa only [lt_top_iff_ne_top] using pow_ne_top"
}
] | [
639,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
638,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.Results.val_unique | [] | [
533,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.eq_empty_of_ssubset_singleton | [] | [
802,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.add_hom | [] | [
408,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioc.coe_one | [] | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GeneralLinearGroup.ext_iff | [] | [
100,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.liftRel_nil | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) (destruct nil) (destruct nil)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\n⊢ LiftRel R nil nil",
"tactic": "rw [liftRel_destruct_iff]"
},
{
"state_af... | [
1095,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1092,
1
] |
Mathlib/Data/Rat/Floor.lean | Rat.num_lt_succ_floor_mul_den | [
{
"state_after": "q : ℚ\n⊢ ↑q.num < (↑⌊q⌋ + 1) * ↑q.den",
"state_before": "q : ℚ\n⊢ q.num < (⌊q⌋ + 1) * ↑q.den",
"tactic": "suffices (q.num : ℚ) < (⌊q⌋ + 1) * q.den by exact_mod_cast this"
},
{
"state_after": "q : ℚ\n⊢ ↑q.num < (q - fract q + 1) * ↑q.den",
"state_before": "q : ℚ\n⊢ ↑q.num < ... | [
131,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lxor'_comm | [] | [
185,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.zpow_add | [
{
"state_after": "case intro\nα : Type ?u.764582\nβ : Type ?u.764585\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nm n : ℤ\nx : ℝ≥0\nhx : ↑x ≠ 0\n⊢ ↑x ^ (m + n) = ↑x ^ m * ↑x ^ n",
"state_before": "α : Type ?u.764582\nβ : Type ?u.764585\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx : ℝ≥0∞\nhx : x ≠ 0\nh'x : x ≠ ⊤\nm n : ℤ\n⊢ x ^ (m + n)... | [
1938,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1934,
11
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.inter | [] | [
114,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Order/Lattice.lean | le_sup_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : LinearOrder α\na b c d : α\n⊢ a ≤ b ⊔ c ↔ a ≤ b ∨ a ≤ c",
"tactic": "exact ⟨fun h =>\n (le_total c b).imp\n (fun bc => by rwa [sup_eq_left.2 bc] at h)\n (fun bc => by rwa [sup_eq_right.2 bc] at h),\n fun h => h.elim le... | [
849,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | AddSubsemigroup.toSubsemigroup'_closure | [] | [
119,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_eq_centroid_image_of_inj_on | [
{
"state_after": "k : Type u_3\nV : Type u_4\nP : Type u_2\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.521615\ns₂ : Finset ι₂\np : ι → P\nhi : ∀ (i : ι), i ∈ s → ∀ (j : ι), j ∈ s → p i = p j → i = j\nps : Set P\ninst✝... | [
974,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.count_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.353095\nγ : Type ?u.353098\ninst✝ : DecidableEq α\na b : α\n⊢ count a {b} = if a = b then 1 else 0",
"tactic": "simp only [count_cons, ← cons_zero, count_zero, zero_add]"
}
] | [
2384,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2383,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | nnnorm_inner_le_nnnorm | [] | [
1102,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ (fun x => x - a) '' [[b, c]] = [[b - a, c - a]]",
"tactic": "simp [sub_eq_add_neg, add_comm]"
}
] | [
471,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/RingTheory/WittVector/IsPoly.lean | WittVector.IsPoly₂.ext | [
{
"state_after": "case mk'.intro\np : ℕ\nR S : Type u\nσ : Type ?u.744260\nidx : Type ?u.744263\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\nf g : ⦃R : Type u⦄ → [inst : CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\nhg : IsPoly₂ p g\nh : ∀ (R : Type u) [_Rcr : CommRing R] (x y : 𝕎 R) (n : ℕ), ↑(g... | [
614,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_distrib_right | [] | [
1066,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.zeroProdIso_inv_snd | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\n⊢ (limit.isoLimitCone { cone := BinaryFan.mk 0 (𝟙 X), isLimit := binaryFanZeroLeftIsLimit X }).inv ≫ prod.snd = 𝟙 X",
"state_before": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasZeroObject... | [
63,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Filter.Tendsto.uniformity_trans | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.47087\ninst✝ : UniformSpace α\nl : Filter β\nf₁ f₂ f₃ : β → α\nh₁₂ : Tendsto (fun x => (f₁ x, f₂ x)) l (𝓤 α)\nh₂₃ : Tendsto (fun x => (f₂ x, f₃ x)) l (𝓤 α)\ns : Set (α × α)\nhs : s ∈ 𝓤 α\n⊢ (fun x => (f₁ x, f₃ x)) ⁻¹' (s ○ s) ∈... | [
490,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Algebra/Group/Units.lean | val_div_eq_divp | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na b c : α\nu₁ u₂ : αˣ\n⊢ ↑(u₁ / u₂) = ↑u₁ /ₚ u₂",
"tactic": "rw [divp, division_def, Units.val_mul]"
}
] | [
526,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/Control/Fold.lean | Traversable.foldMap_hom | [] | [
290,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.mem_inv_smul_finset_iff₀ | [] | [
2044,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2043,
1
] |
Mathlib/Order/Basic.lean | gt_iff_lt | [] | [
350,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.zero_eq_coe | [] | [
344,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
20
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_of_forall_one_lt_le_mul | [
{
"state_after": "case intro\nα : Type u\ninst✝⁵ : LinearOrder α\ninst✝⁴ : DenselyOrdered α\ninst✝³ : Monoid α\ninst✝² : ExistsMulOfLE α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : ContravariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b : α\nh : ∀ (ε : α), 1... | [
77,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.elementarilyEquivalent_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type u_1\nP : Type ?u.269466\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\n⊢ M ≅[L] N ↔ ∀ (φ : Sentence L), M ⊨ φ ↔ N ⊨ φ",
"tactic": "simp only [Elementa... | [
797,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.exists_succ_get?_stream_of_gcf_of_get?_eq_some | [
{
"state_after": "case intro.intro\nK : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\ngp_n : Pair K\ns_nth_eq : Stream'.Seq.get? (of v).s n = some gp_n\nifp : IntFractPair K\nstream_succ_nth_eq : IntFractPair.stream v (n + 1) = some ifp\ngp_n_eq : { a := 1, b := ↑ifp.b } = gp_n\n⊢ ... | [
237,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Fin.succAbove_cycleRange | [
{
"state_after": "case zero\ni j : Fin Nat.zero\n⊢ ↑(succAbove (succ i)) (↑(cycleRange i) j) = ↑(swap 0 (succ i)) (succ j)\n\ncase succ\nn✝ : ℕ\ni j : Fin (Nat.succ n✝)\n⊢ ↑(succAbove (succ i)) (↑(cycleRange i) j) = ↑(swap 0 (succ i)) (succ j)",
"state_before": "n : ℕ\ni j : Fin n\n⊢ ↑(succAbove (succ i)) (... | [
273,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasDerivWithinAt.differentiableWithinAt | [] | [
386,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
384,
1
] |
Mathlib/Analysis/Convex/Slope.lean | ConcaveOn.slope_anti_adjacent | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\ns : Set 𝕜\nf : 𝕜 → 𝕜\nhf : ConcaveOn 𝕜 s f\nx y z : 𝕜\nhx : x ∈ s\nhz : z ∈ s\nhxy : x < y\nhyz : y < z\nthis : -(((-f) z - (-f) y) / (z - y)) ≤ -(((-f) y - (-f) x) / (y - x))\n⊢ (f z - f y) / (z - y) ≤ (f y - f x) / (y - x)",
"state_befor... | [
61,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.toFinsupp_apply | [
{
"state_after": "case ofFinsupp\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\ni : ℕ\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ ↑{ toFinsupp := toFinsupp✝ }.toFinsupp i = coeff { toFinsupp := toFinsupp✝ } i",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q f : R[X]\ni : ℕ\... | [
668,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_le_restrict_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.120092\nR : Type ?u.120095\nR' : Type ?u.120098\nms : Set (OuterMeasure α)\nm : OuterMeasure α\nβ : Type u_1\nma : OuterMeasure α\nmb : OuterMeasure β\nf : α → β\nh : ↑(map f) ma ≤ mb\ns : Set β\n⊢ ↑(↑(map f) ma) s ≤ ↑(↑(restrict (rang... | [
608,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
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Mathlib/Analysis/SpecialFunctions/Complex/Circle.lean | circle.injective_arg | [] | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_mul_monomial | [
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.inv_iff | [
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Mathlib/Data/Set/Prod.lean | Set.exists_prod_set | [
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Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.le_finestTopology | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_zero_one | [] | [
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Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.sub | [
{
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514,
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mul_mk'_eq_mk'_of_mul | [] | [
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Mathlib/Topology/VectorBundle/Constructions.lean | Trivialization.continuousLinearEquivAt_prod | [
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.equivalenceSelfOfHasFiniteBiproducts_inverse | [] | [
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Mathlib/Algebra/Periodic.lean | Function.Periodic.comp_addHom | [
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.le_graph_iff | [] | [
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Std/Data/Nat/Lemmas.lean | Nat.le_of_not_lt | [] | [
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Mathlib/Data/Fin/Tuple/Monotone.lean | StrictMono.vecCons | [] | [
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Mathlib/Data/Rat/NNRat.lean | NNRat.coe_sum | [] | [
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Mathlib/Topology/Inseparable.lean | specializes_iff_pure | [] | [
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.range_single_subset | [] | [
374,
42
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373,
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Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.le_topology_of_closedSieves_isSheaf | [
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270,
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Mathlib/Data/Complex/Exponential.lean | Real.exp_sub | [
{
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] | [
1173,
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Mathlib/LinearAlgebra/QuadraticForm/Prod.lean | QuadraticForm.anisotropic_of_pi | [
{
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Mathlib/Order/CompleteLattice.lean | iSup_le_iSup_of_subset | [] | [
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.hasGeneralizedEigenvalue_of_hasEigenvalue | [
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Mathlib/Order/BooleanAlgebra.lean | sdiff_unique | [
{
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.comap_id' | [
{
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1196,
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_replicate | [] | [
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Mathlib/Order/Hom/Set.lean | OrderIso.symm_preimage_preimage | [] | [
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Mathlib/Computability/TuringMachine.lean | Turing.tr_eval | [
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Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_filter_le_left | [
{
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223,
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Mathlib/Data/Nat/Parity.lean | Nat.even_pow' | [] | [
179,
35
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178,
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Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.equiv_symm | [] | [
181,
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180,
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Mathlib/SetTheory/Game/PGame.lean | PGame.leftMoves_add | [] | [
1476,
38
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1475,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.Normal.mem_comm | [
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1941,
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Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Cone.ofFork_π | [
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624,
68
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Mathlib/RingTheory/Adjoin/PowerBasis.lean | PowerBasis.repr_mul_isIntegral | [
{
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150,
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Mathlib/Topology/Algebra/Group/Basic.lean | Inducing.continuousInv | [] | [
413,
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410,
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Mathlib/Logic/Equiv/Option.lean | Equiv.optionSubtype_symm_apply_apply_coe | [] | [
243,
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241,
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Mathlib/Data/List/Sublists.lean | List.revzip_sublists' | [
{
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458,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPullback.inl_snd | [] | [
591,
43
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589,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.map_iff_of_equiv | [] | [
283,
100
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280,
11
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integralSum_neg | [
{
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Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.of_div_left | [] | [
607,
26
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606,
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Mathlib/Order/WithBot.lean | WithBot.ofDual_lt_iff | [] | [
1029,
10
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1027,
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.span_eq_top_iff_finite | [
{
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"tactic": "simp_rw [eq_... | [
216,
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213,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_mul_X_pow | [] | [
1021,
41
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1020,
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Mathlib/Order/Filter/Ultrafilter.lean | Filter.exists_ultrafilter_iff | [] | [
458,
73
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457,
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Mathlib/Order/Lattice.lean | inf_assoc | [] | [
503,
25
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502,
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.isOpen_basicOpen | [] | [
403,
25
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Mathlib/Topology/Homotopy/Contractible.lean | id_nullhomotopic | [
{
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69,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isAdjointPair_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝²⁰ : Semiring R\ninst✝¹⁹ : AddCommMonoid M\ninst✝¹⁸ : Module R M\nR₁ : Type ?u.1026415\nM₁ : Type ?u.1026418\ninst✝¹⁷ : Ring R₁\ninst✝¹⁶ : AddCommGroup M₁\ninst✝¹⁵ : Module R₁ M₁\nR₂ : Type ?u.1027027\nM₂ : Type ?u.1027030\ninst✝... | [
1043,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1042,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.coe_mul | [] | [
1726,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_bot | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.56692\nα : Type u_1\nβ : Type ?u.56698\nπ : ι → Type ?u.56703\ninst✝ : HeytingAlgebra α\na : α\n⊢ a ⇔ ⊥ = aᶜ",
"tactic": "simp [bihimp]"
}
] | [
369,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.triorthogonal_eq_orthogonal | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.883149\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace E\n⊢ topologicalClosure Kᗮ = Kᗮ",
"state_before": "�... | [
927,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image_image₂_right_anticomm | [] | [
505,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Analysis/Convex/Independent.lean | ConvexIndependent.subtype | [] | [
95,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
11
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.MeasurablySeparable.iUnion | [
{
"state_after": "α✝ : Type ?u.67309\ninst✝² : TopologicalSpace α✝\nι : Type u_1\ninst✝¹ : Countable ι\nα : Type u_2\ninst✝ : MeasurableSpace α\ns t : ι → Set α\nu : ι → ι → Set α\nhsu : ∀ (m n : ι), s m ⊆ u m n\nhtu : ∀ (m n : ι), Disjoint (t n) (u m n)\nhu : ∀ (m n : ι), MeasurableSet (u m n)\n⊢ MeasurablySep... | [
286,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformContinuous_toMul | [] | [
1452,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1451,
1
] |
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