file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.orthogonal_orthogonal | [
{
"state_after": "case h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.776857\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 { x // x ∈ K }\nv : E\n⊢ v ∈ Kᗮᗮ ↔ v ∈ K",
"... | [
777,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.lintegral_rpow_nnnorm_lt_top_of_snorm_lt_top | [
{
"state_after": "case hq0_lt\nα : Type u_1\nE : Type ?u.755518\nF : Type u_2\nG : Type ?u.755524\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nhfp : snorm... | [
156,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/List/Cycle.lean | List.prev_nthLe | [
{
"state_after": "case nil\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nn : ℕ\nh : Nodup []\nhn : n < length []\n⊢ prev [] (nthLe [] n hn) (_ : nthLe [] n hn ∈ []) =\n nthLe [] ((n + (length [] - 1)) % length []) (_ : (n + (length [] - 1)) % length [] < length [])\n\ncase cons\nα : Type u_1\ninst... | [
355,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.card_Icc | [
{
"state_after": "a b : ℕ+\n⊢ card (Icc a b) = card (Icc ↑a ↑b)",
"state_before": "a b : ℕ+\n⊢ card (Icc a b) = ↑b + 1 - ↑a",
"tactic": "rw [← Nat.card_Icc]"
},
{
"state_after": "a b : ℕ+\n⊢ card (Icc a b) = card (map (Function.Embedding.subtype fun n => 0 < n) (Icc a b))",
"state_before": "... | [
68,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | ContinuousMap.range_toLp | [
{
"state_after": "α : Type u_3\nE : Type u_2\nF : Type ?u.13639271\nG : Type ?u.13639274\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedAddCommGroup G\ninst✝⁷ : TopologicalSpace α\ninst✝⁶ : BorelSpace α\nin... | [
1713,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsCycle.transfer | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\nH : SimpleGraph V\nq : Walk G u u\nqc : IsCycle q\nhq : ∀ (e : Sym2 V), e ∈ edges q → e ∈ edgeSet H\n⊢ IsCycle (Walk.transfer q H hq)",... | [
1729,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1722,
11
] |
src/lean/Init/Prelude.lean | System.Platform.numBits_eq | [] | [
1739,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1738,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.strictMonoOn | [] | [
396,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
11
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasFDerivAtFilter.snd | [] | [
255,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
11
] |
Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.fst_openEmbedding_of_right_openEmbedding | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninst✝ : SmallCategory J\nX✝ Y✝ Z : TopCat\nX Y S : TopCat\nf : X ⟶ S\ng : Y ⟶ S\nH : OpenEmbedding ((forget TopCat).map g)\ne_2✝ : (forget TopCat).obj X = ↑X\n⊢ (forget TopCat).map pullback.fst =\n ↑(homeoOfIso (asIso pullback.fst)) ∘\n (forget TopCat).map (p... | [
331,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/Nat/Cast/Field.lean | Nat.cast_div_le | [
{
"state_after": "case zero\nα : Type u_1\ninst✝ : LinearOrderedSemifield α\nm : ℕ\n⊢ ↑(m / zero) ≤ ↑m / ↑zero\n\ncase succ\nα : Type u_1\ninst✝ : LinearOrderedSemifield α\nm n✝ : ℕ\n⊢ ↑(m / succ n✝) ≤ ↑m / ↑(succ n✝)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedSemifield α\nm n : ℕ\n⊢ ↑(m / n) ≤ ↑... | [
60,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.add_mul_right_left | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime (x + y * z) y",
"state_before": "R : Type u\ninst✝ : CommRing R\nx y : R\nh : IsCoprime x y\nz : R\n⊢ IsCoprime (x + z * y) y",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_be... | [
290,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivAt.ofReal_comp | [
{
"state_after": "no goals",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nE : Type ?u.149374\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → ℝ\nu : ℝ\nhf : HasDerivAt f u z\n⊢ HasDerivAt (fun y => ↑(f y)) (↑u) z",
"tactic": "simpa only [ofRealClm_apply, ofReal_one, real_smul, mul_one] usi... | [
147,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.ones_sizeUpTo | [
{
"state_after": "no goals",
"state_before": "n✝ : ℕ\nc : Composition n✝\nn i : ℕ\n⊢ sizeUpTo (ones n) i = min i n",
"tactic": "simp [sizeUpTo, ones_blocks, take_replicate]"
}
] | [
516,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.integrable_const | [] | [
327,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.div_opow_log_pos | [
{
"state_after": "case inl\no : Ordinal\nho : o ≠ 0\n⊢ 0 < o / 0 ^ log 0 o\n\ncase inr\nb o : Ordinal\nho : o ≠ 0\nhb : 0 < b\n⊢ 0 < o / b ^ log b o",
"state_before": "b o : Ordinal\nho : o ≠ 0\n⊢ 0 < o / b ^ log b o",
"tactic": "rcases eq_zero_or_pos b with (rfl | hb)"
},
{
"state_after": "no g... | [
435,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sigmaEquivProd_sigmaCongrRight | [
{
"state_after": "case H.mk\nα₁ : Type u_2\nβ₁ : Type u_1\nβ₂ : Type u_3\ne : α₁ → β₁ ≃ β₂\na : α₁\nb : β₁\n⊢ ↑((sigmaEquivProd α₁ β₁).symm.trans (sigmaCongrRight e)) (a, b) =\n ↑((prodCongrRight e).trans (sigmaEquivProd α₁ β₂).symm) (a, b)",
"state_before": "α₁ : Type u_2\nβ₁ : Type u_1\nβ₂ : Type u_3\n... | [
768,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Data/List/Basic.lean | List.head!_mem_self | [
{
"state_after": "ι : Type ?u.44810\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : Inhabited α\nl : List α\nh : l ≠ []\nh' : head! l ∈ head! l :: tail l\n⊢ head! l ∈ l",
"state_before": "ι : Type ?u.44810\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : Inha... | [
929,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ENNReal.continuousAt_rpow_const_of_pos | [
{
"state_after": "case pos\nx : ℝ≥0∞\ny : ℝ\nh : 0 < y\nhx : x = ⊤\n⊢ ContinuousAt (fun a => a ^ y) x\n\ncase neg\nx : ℝ≥0∞\ny : ℝ\nh : 0 < y\nhx : ¬x = ⊤\n⊢ ContinuousAt (fun a => a ^ y) x",
"state_before": "x : ℝ≥0∞\ny : ℝ\nh : 0 < y\n⊢ ContinuousAt (fun a => a ^ y) x",
"tactic": "by_cases hx : x = ⊤"... | [
513,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
9
] |
Mathlib/Topology/ContinuousOn.lean | mem_nhdsWithin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.4968\nγ : Type ?u.4971\nδ : Type ?u.4974\ninst✝ : TopologicalSpace α\nt : Set α\na : α\ns : Set α\n⊢ t ∈ 𝓝[s] a ↔ ∃ u, IsOpen u ∧ a ∈ u ∧ u ∩ s ⊆ t",
"tactic": "simpa only [and_assoc, and_left_comm] using (nhdsWithin_basis_open a s... | [
96,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.biInf_sets_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.97618\nι : Sort x\nf✝ g : Filter α\ns✝ t✝ : Set α\nf : β → Filter α\ns : Set β\nh : DirectedOn (f ⁻¹'o fun x x_1 => x ≥ x_1) s\nne : Set.Nonempty s\nt : Set α\n⊢ t ∈ (⨅ (i : β) (_ : i ∈ s), f i).sets ↔ t ∈ ⋃ (i : β... | [
833,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
831,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.natCast_nat | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nn : ℕ\n⊢ ↑(Nat.rawCast n) = Nat.rawCast n",
"tactic": "simp"
}
] | [
448,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.mem_boundary | [] | [
73,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.unique_diff_at_image | [] | [
337,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Std/Data/Int/DivMod.lean | Int.add_emod_self_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ (a + b) % a = b % a",
"tactic": "rw [Int.add_comm, Int.add_emod_self]"
}
] | [
418,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
417,
9
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_mono_ae | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.21095160\n𝕜 : Type ?u.21095163\nE : Type ?u.21095166\nF : Type ?u.21095169\nA : Type ?u.21095172\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → ℝ\na b : ℝ\nμ : MeasureTheory.Measure ℝ\nhab : a ≤ b\nhf : ... | [
1390,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1389,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_one_cons | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : Semiring α\nh : ℕ\nL : List ℕ\n⊢ ofDigits 1 (h :: L) = ↑h + ofDigits 1 L",
"tactic": "simp [ofDigits]"
}
] | [
196,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_iff_dvd_of_dvd_add | [
{
"state_after": "a b c : Int\nH : a ∣ b - -c\n⊢ a ∣ b ↔ a ∣ c",
"state_before": "a b c : Int\nH : a ∣ b + c\n⊢ a ∣ b ↔ a ∣ c",
"tactic": "rw [← Int.sub_neg] at H"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nH : a ∣ b - -c\n⊢ a ∣ b ↔ a ∣ c",
"tactic": "rw [Int.dvd_iff_d... | [
632,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
631,
11
] |
Mathlib/Algebra/Lie/DirectSum.lean | DirectSum.lie_of_of_ne | [
{
"state_after": "R : Type u\nι : Type v\ninst✝³ : CommRing R\nL : ι → Type w\ninst✝² : (i : ι) → LieRing (L i)\ninst✝¹ : (i : ι) → LieAlgebra R (L i)\ninst✝ : DecidableEq ι\ni j : ι\nhij : j ≠ i\nx : L i\ny : L j\n⊢ ∀ (i_1 : ι), ↑(lieAlgebraComponent R ι L i_1) ⁅↑(of L i) x, ↑(of L j) y⁆ = ↑(lieAlgebraComponen... | [
171,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Std/Data/List/Lemmas.lean | List.length_filterMap_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → Option β\nl : List α\n⊢ length (filter (fun b => Option.isSome b) (map f l)) ≤ length (map f l)",
"state_before": "α : Type u_1\nβ : Type u_2\nf : α → Option β\nl : List α\n⊢ length (filterMap f l) ≤ length l",
"tactic": "rw [← length_map _ some, map... | [
1224,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1221,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_mul | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : f ≈ 0\nhg : f * g ≈ 0\n⊢ norm (f * g) = norm f * norm g",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhf : f ≈ 0\n⊢ norm (f * g) = norm f * norm g",
"tactic": "have hg : f * g ≈ 0 := mul_equiv_zero' _ hf"
}... | [
298,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | MonotoneOn.intervalIntegrable | [
{
"state_after": "ι : Type ?u.8489962\n𝕜 : Type ?u.8489965\nE : Type u_1\nF : Type ?u.8489971\nA : Type ?u.8489974\ninst✝⁴ : NormedAddCommGroup E\nμ : MeasureTheory.Measure ℝ\ninst✝³ : IsLocallyFiniteMeasure μ\ninst✝² : ConditionallyCompleteLinearOrder E\ninst✝¹ : OrderTopology E\ninst✝ : SecondCountableTopolo... | [
384,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.isWeightedHomogeneous_one | [] | [
233,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.map_ne_one_iff | [] | [
552,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.constantCoeff_eq | [] | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Std/Logic.lean | Decidable.not_and' | [] | [
603,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
602,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.mul_eq_zero | [
{
"state_after": "n✝ m✝ : Nat\nh✝ : n✝ * m✝ = 0\nn m : Nat\nh : n * m + m = 0\n⊢ n + 1 = 0 ∨ m = 0",
"state_before": "n✝ m✝ : Nat\nh✝ : n✝ * m✝ = 0\nn m : Nat\nh : (n + 1) * m = 0\n⊢ n + 1 = 0 ∨ m = 0",
"tactic": "rw [succ_mul] at h"
},
{
"state_after": "no goals",
"state_before": "n✝ m✝ : N... | [
330,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
326,
1
] |
Mathlib/Topology/MetricSpace/Infsep.lean | Set.le_edist_of_le_infsep | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.59969\ninst✝ : PseudoMetricSpace α\nx✝ y✝ z : α\ns t : Set α\nd : ℝ\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ s\nhxy : x ≠ y\nhd : d ≤ infsep s\nhs : Set.Nontrivial s\n⊢ d ≤ dist x y\n\ncase neg\nα : Type u_1\nβ : Type ?u.59969\ninst✝ : PseudoMetricSpace α\nx✝ y✝ ... | [
422,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Lattice.lean | le_inf_sup | [] | [
708,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
src/lean/Init/Data/Nat/Div.lean | Nat.mod_eq_of_lt | [] | [
115,
27
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
111,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.emptySum_apply_inr | [] | [
413,
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412,
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Mathlib/Data/List/Basic.lean | List.concat_eq_append' | [] | [
553,
23
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Mathlib/Data/Real/Basic.lean | Real.mk_neg | [
{
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_transpose_add_self | [] | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_empty | [] | [
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Mathlib/Order/Filter/Cofinite.lean | Set.Finite.compl_mem_cofinite | [] | [
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Mathlib/Order/Atoms.lean | IsAtom.of_isAtom_coe_Iic | [] | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_lt_iff_inv_lt | [
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Mathlib/Topology/PathConnected.lean | Filter.Tendsto.path_extend | [] | [
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Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_matrix' | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.mem_support_iff | [] | [
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Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean | Matrix.GeneralLinearGroup.ext | [] | [
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Mathlib/RingTheory/FractionalIdeal.lean | IsFractional.inf_right | [
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinearMapRight'_mul_apply | [] | [
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Mathlib/Data/Real/Sqrt.lean | NNReal.sqrt_mul_self | [
{
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Mathlib/Data/Stream/Init.lean | Stream'.nth_tail | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.inv_rpow | [
{
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Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_l_u_eq_u | [] | [
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Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.isLUB_sSup | [] | [
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Mathlib/Algebra/Quaternion.lean | Quaternion.sub_self_re | [] | [
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_eq_sum_range' | [
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_mulHom_id | [] | [
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.norm_toLp | [
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Mathlib/Order/CompleteLattice.lean | le_iInf_comp | [] | [
991,
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990,
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Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.mem_zpowers | [] | [
36,
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Mathlib/Topology/MetricSpace/Basic.lean | ULift.nndist_eq | [] | [
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Mathlib/Data/Finite/Defs.lean | Finite.of_equiv | [
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Mathlib/Data/Int/Log.lean | Int.clog_of_right_le_one | [
{
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Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_inter' | [] | [
310,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_pos_iff_abs_toReal_lt_pi_div_two | [
{
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755,
96
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Mathlib/Algebra/Ring/Commute.lean | mul_self_sub_one | [
{
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156,
65
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Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.isubtree_cons | [
{
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95
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_c_ne_zero' | [] | [
428,
36
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427,
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Mathlib/Data/Set/Lattice.lean | Set.sInter_eq_biInter | [
{
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Mathlib/Order/Filter/Prod.lean | Filter.prod_pure_pure | [
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Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.dcongr_arg | [
{
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301,
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_inter | [] | [
513,
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511,
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Std/Data/Rat/Lemmas.lean | Rat.ofNat_num | [] | [
165,
77
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165,
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Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_le_restrict_iff | [] | [
877,
52
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872,
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Mathlib/Data/Real/NNReal.lean | Real.toNNReal_of_nonneg | [
{
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42
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Mathlib/Order/OmegaCompletePartialOrder.lean | Pi.OmegaCompletePartialOrder.flip₂_continuous' | [
{
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.succAbove_cases_eq_insertNth | [] | [
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Mathlib/Algebra/Order/Sub/Defs.lean | tsub_add_eq_tsub_tsub | [] | [
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25
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269,
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Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lieIdeal_oper_eq_linear_span | [
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.to_affine_map_contLinear | [
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Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin_symm_of_one | [] | [
40,
41
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_cofinite_iff | [
{
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Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.mkPiAlgebraFin_apply | [] | [
1028,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Connected.lean | IsConnected.closure | [] | [
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60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictDerivAt.to_local_left_inverse | [] | [
721,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Disjoint.subset_left_of_subset_union | [] | [
2977,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2976,
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Mathlib/AlgebraicTopology/DoldKan/Decomposition.lean | AlgebraicTopology.DoldKan.MorphComponents.preComp_φ | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX X' : SimplicialObject C\nn : ℕ\nZ Z' : C\nf : MorphComponents X n Z\ng : X' ⟶ X\nh : Z ⟶ Z'\n⊢ HomologicalComplex.Hom.f PInfty (n + 1) ≫ { a := g.app [n + 1].op ≫ f.a, b := fun i => g.app [n].op ≫ b f i }.a +\n ∑ i : Fin (n + 1),... | [
155,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.algebraMap_eq_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\nA₁ : Type v\nA₂ : Type w\nA₃ : Type u₁\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A₁\ninst✝⁴ : Semiring A₂\ninst✝³ : Semiring A₃\ninst✝² : Algebra R A₁\ninst✝¹ : Algebra R A₂\ninst✝ : Algebra R A₃\ne✝ e : A₁ ≃ₐ[R] A₂\ny : R\nx : A₁\nh : ↑(algebraMap... | [
746,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.norm_lt_iff_of_nonempty_compact | [
{
"state_after": "F : Type ?u.1009057\nα : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : SeminormedAddCommGroup β\nf✝ g : α →ᵇ β\nx : α\nC : ℝ\ninst✝¹ : Nonempty α\ninst✝ : CompactSpace α\nf : α →ᵇ β\nM : ℝ\n⊢ dist f 0 < M ↔ ∀ (x : α), dist (↑f x) 0 < M",
"state_before": "F : Type ?u... | [
859,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.toFun_eq_coe | [] | [
257,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le | [
{
"state_after": "G : Type u_2\nH : Type ?u.17508\nα : Type u_1\nβ : Type ?u.17514\nE : Type ?u.17517\ninst✝⁸ : Group G\ninst✝⁷ : Group H\ninst✝⁶ : MulAction G α\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : MulAction H β\ninst✝³ : MeasurableSpace β\ninst✝² : NormedAddCommGroup E\ns t : Set α\nμ : Measure α\ninst✝¹ : I... | [
131,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.toFinset_setOf | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns t : Set α\na : α\nhs : Set.Finite s\nht : Set.Finite t\ninst✝¹ : Fintype α\np : α → Prop\ninst✝ : DecidablePred p\nh : Set.Finite {x | p x}\na✝ : α\n⊢ a✝ ∈ Finite.toFinset h ↔ a✝ ∈ Finset.filter p Finset.univ",
"state_before": "α : ... | [
230,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_union | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.113978\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns✝ t✝ : Set α\nx : α\nδ : ℝ\ns t : Set α\n⊢ thickening δ (s ∪ t) = thickening δ s ∪ thickening δ t",
"tactic": "simp_rw [thickening, infEdist_union, inf_eq_min, min_lt_iff, s... | [
1180,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1178,
1
] |
Mathlib/Data/Set/Countable.lean | Finset.countable_toSet | [] | [
294,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Tactic/NormNum/NatFib.lean | Mathlib.Meta.NormNum.isFibAux_zero | [] | [
25,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
24,
1
] |
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