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/Data/Finset/Image.lean | Finset.image_toFinset | [
{
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"tactic": "simp o... | [
404,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
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Mathlib/Order/Hom/Lattice.lean | SupBotHom.coe_toSupHom | [] | [
733,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
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Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.compl₂_id | [
{
"state_after": "case h.h\nR : Type u_4\ninst✝²³ : CommSemiring R\nR₂ : Type u_6\ninst✝²² : CommSemiring R₂\nR₃ : Type u_5\ninst✝²¹ : CommSemiring R₃\nR₄ : Type ?u.460205\ninst✝²⁰ : CommSemiring R₄\nM : Type u_1\nN : Type u_2\nP : Type u_3\nQ : Type ?u.460220\nMₗ : Type ?u.460223\nNₗ : Type ?u.460226\nPₗ : Typ... | [
340,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.zero_right | [] | [
61,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Algebra/Field/ULift.lean | ULift.up_ratCast | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/SetLike/Basic.lean | SetLike.exists | [] | [
129,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Std/Data/Array/Lemmas.lean | Array.swapAt_def | [] | [
127,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
126,
9
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src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.evalList_mergeIdem | [
{
"state_after": "α : Sort u_1\nctx : Context α\nh✝ : ContextInformation.isIdem ctx = true\ne : List Nat\nh : IsIdempotent ctx.op\n⊢ evalList α ctx (mergeIdem e) = evalList α ctx e",
"state_before": "α : Sort u_1\nctx : Context α\nh : ContextInformation.isIdem ctx = true\ne : List Nat\n⊢ evalList α ctx (mer... | [
158,
19
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
130,
1
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Mathlib/Data/Finset/Lattice.lean | Finset.set_biInter_inter | [] | [
2044,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2042,
1
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Mathlib/Data/Set/Basic.lean | Set.ite_inter_of_inter_eq | [
{
"state_after": "no goals",
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"tactic": "rw [← ite_inter, ← h, ite_same]"
}
] | [
2319,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2318,
1
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Mathlib/Algebra/Star/Module.lean | selfAdjointPart_comp_subtype_skewAdjoint | [
{
"state_after": "no goals",
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166,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
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Mathlib/Algebra/GroupPower/Order.lean | pow_lt_pow_iff' | [] | [
277,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.join_cons | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : Seq α\nS : Seq (Seq1 α)\n⊢ IsBisimulation fun s1 s2 => s1 = s2 ∨ ∃ a s S, s1 = join (cons (a, s) S) ∧ s2 = cons a (append s (join S))",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\ns : Seq α\nS : Seq (Seq1 α)\n⊢ join (cons (a, s... | [
786,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
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Mathlib/Topology/SubsetProperties.lean | IsOpen.locallyCompactSpace | [] | [
1215,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.abs_re_le_norm | [
{
"state_after": "K : Type u_1\nE : Type ?u.6600797\ninst✝ : IsROrC K\nz : K\n⊢ ↑re z * ↑re z ≤ ↑normSq z",
"state_before": "K : Type u_1\nE : Type ?u.6600797\ninst✝ : IsROrC K\nz : K\n⊢ abs (↑re z) ≤ ‖z‖",
"tactic": "rw [mul_self_le_mul_self_iff (abs_nonneg _) (norm_nonneg _), abs_mul_abs_self, mul_sel... | [
716,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
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Std/Data/Rat/Lemmas.lean | Rat.normalize_self | [] | [
34,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
34,
1
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Mathlib/Data/Finset/PiInduction.lean | Finset.induction_on_pi_max | [] | [
101,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | Homeomorph.contDiff_symm | [] | [
1840,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1836,
1
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Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.left_of_comp | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3348\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\ng : α → α\nhco : Commute f g\nhfg : IsFixedPt (f^[n] ∘ g^[n]) x\nhg : IsPeriodicPt g n x\n⊢ IsPeriodicPt f n x",
"state_before": "α : Type u_1\nβ : Type ?u.3348\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\ng : α → ... | [
157,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_eq_nat | [
{
"state_after": "no goals",
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"tactic": "simp only [le_antisymm_iff, card_le_nat, nat_le_card]"
}
] | [
1582,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1581,
1
] |
Mathlib/Data/Set/Sups.lean | Set.infs_subset_left | [] | [
245,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
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Mathlib/Data/Set/Pointwise/SMul.lean | Set.subsingleton_zero_smul_set | [] | [
819,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_of_neg | [] | [
776,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.isLocallyFiniteMeasure_of_le | [] | [
4161,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4158,
1
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Formula.equivSentence_not | [] | [
1050,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
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Mathlib/Topology/Connected.lean | Sigma.isPreconnected_iff | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\nι : Type u_1\nπ : ι → Type u_2\ninst✝¹ : TopologicalSpace α\ns✝ t u v : Set α\nhι : Nonempty ι\ninst✝ : (i : ι) → TopologicalSpace (π i)\ns : Set ((i : ι) × π i)\nhs : IsPreconnected s\n⊢ ∃ i t, IsPreconnected t ∧ s = mk i '' t\n\ncase refine'_2\nα : Typ... | [
535,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | exists_prime_orderOf_dvd_card | [
{
"state_after": "α : Type ?u.562614\ninst✝³ : Fintype α\nG✝ : Type ?u.562620\ninst✝² : Group G✝\nn : ℕ\nG : Type u_1\ninst✝¹ : Group G\ninst✝ : Fintype G\np : ℕ\nhp : Fact (Nat.Prime p)\nhdvd : p ∣ Fintype.card G\nhp' : p - 1 ≠ 0\n⊢ ∃ x, orderOf x = p",
"state_before": "α : Type ?u.562614\ninst✝³ : Fintype... | [
486,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
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] |
Mathlib/RingTheory/PolynomialAlgebra.lean | support_subset_support_matPolyEquiv | [
{
"state_after": "R : Type u_1\nA : Type ?u.640013\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\nn : Type w\ninst✝¹ : DecidableEq n\ninst✝ : Fintype n\nm : Matrix n n R[X]\ni j : n\nk : ℕ\n⊢ k ∈ support (m i j) → k ∈ support (↑matPolyEquiv m)",
"state_before": "R : Type u_1\nA : Type ... | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Polynomial.eq_of_degrees_lt_of_eval_finset_eq | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : R[X]\ns : Finset R\ndegree_f_lt : f ∈ degreeLT R (Finset.card s)\ndegree_g_lt : g ∈ degreeLT R (Finset.card s)\neval_fg : ∀ (x : R), x ∈ s → eval x f = eval x g\n⊢ f = g",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝... | [
70,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.sum_tensor | [
{
"state_after": "C : Type u_3\ninst✝³ : Category C\ninst✝² : Preadditive C\ninst✝¹ : MonoidalCategory C\ninst✝ : MonoidalPreadditive C\nP Q R S : C\nJ : Type u_1\ns : Finset J\nf : P ⟶ Q\ng : J → (R ⟶ S)\n⊢ ((∑ j in s, g j) ⊗ 𝟙 P) ≫ (𝟙 S ⊗ f) = ∑ j in s, g j ⊗ f",
"state_before": "C : Type u_3\ninst✝³ : ... | [
115,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.blocksFun_congr | [
{
"state_after": "case refl\nn : ℕ\nc : Composition n\nn₁ : ℕ\nc₁ : Composition n₁\ni₁ : Fin (length c₁)\nc₂ : Composition n₁\ni₂ : Fin (length c₂)\nhc : c₁.blocks = c₂.blocks\nhi : ↑i₁ = ↑i₂\n⊢ blocksFun c₁ i₁ = blocksFun c₂ i₂",
"state_before": "n : ℕ\nc : Composition n\nn₁ n₂ : ℕ\nc₁ : Composition n₁\nc₂... | [
469,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.zero_quot | [
{
"state_after": "no goals",
"state_before": "R : Type u₁\ninst✝³ : Semiring R\nS : Type u₂\ninst✝² : CommSemiring S\nA : Type u₃\ninst✝¹ : Semiring A\ninst✝ : Algebra S A\nr : R → R → Prop\n⊢ { toQuot := Quot.mk (Rel r) 0 } = RingQuot.zero r",
"tactic": "rw [zero_def]"
}
] | [
229,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.srange_eq_map | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝⁴ : NonUnitalNonAssocSemiring R\nM : Subsemigroup R\ninst✝³ : NonUnitalNonAssocSemiring S\ninst✝² : NonUnitalNonAssocSemiring T\nF : Type u_1\nG : Type ?u.178504\ninst✝¹ : NonUnitalRingHomClass F R S\ninst✝ : NonUnitalRingHomClass G S T\nf : F\n... | [
370,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/BinaryProducts.lean | hasBinaryProducts_of_hasTerminal_and_pullbacks | [] | [
102,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.inv_sqrt_one_add_tan_sq | [
{
"state_after": "no goals",
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"tactic": "rw [← sqrt_sq hx.le, ← sqrt_inv, inv_one_add_tan_sq hx.ne']"
}
] | [
1324,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycle_iff_exists_isCycleOn | [
{
"state_after": "case refine'_1\nι : Type ?u.1652168\nα : Type u_1\nβ : Type ?u.1652174\nf g : Perm α\ns t : Set α\na b x y : α\nhf : IsCycle f\n⊢ Set.Nontrivial {x | ↑f x ≠ x}\n\ncase refine'_2\nι : Type ?u.1652168\nα : Type u_1\nβ : Type ?u.1652174\nf g : Perm α\ns t : Set α\na b x y : α\n⊢ (∃ s, Set.Nontriv... | [
825,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | not_differentiableAt_of_local_left_inverse_hasDerivAt_zero | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf✝ f₀ f₁ g✝ : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nf g : 𝕜 → 𝕜\na : 𝕜... | [
133,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
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] |
Mathlib/Data/List/OfFn.lean | List.ofFn_const | [
{
"state_after": "α : Type u\nn : ℕ\nc : α\n⊢ (ofFn fun x => c) = c :: ofFn fun x => c",
"state_before": "α : Type u\nn : ℕ\nc : α\n⊢ (ofFn fun x => c) = replicate (n + 1) c",
"tactic": "rw [replicate, ← ofFn_const n]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\nc : α... | [
216,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_symm | [
{
"state_after": "no goals",
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477,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.coe_inv | [] | [
131,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_eq_neg_pi_div_two | [] | [
260,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.comap_le_comap_of_le_range | [] | [
3039,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3037,
1
] |
Mathlib/Data/List/Basic.lean | List.foldl_hom₂ | [
{
"state_after": "ι : Type u_1\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nl : List ι\nf : α → β → γ\nop₁ : α → ι → α\nop₂ : β → ι → β\nop₃ : γ → ι → γ\nh : ∀ (a : α) (b : β) (i : ι), f (op₁ a i) (op₂ b i) = op₃ (f a b) i\n⊢ ∀ (a : α) (b : β), f (foldl op₁ a l) (foldl op₂ b l) = foldl op₃ (... | [
2497,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2492,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.sinh | [] | [
1140,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1138,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | div_zpow | [
{
"state_after": "no goals",
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"tactic": "simp only [div_eq_mul_inv, mul_zpow, inv_zpow]"
}
] | [
399,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
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src/lean/Init/Core.lean | Iff.refl | [] | [
661,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
660,
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Mathlib/Analysis/Complex/Liouville.lean | Complex.norm_deriv_le_of_forall_mem_sphere_norm_le | [
{
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90,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Data/Finmap.lean | Finmap.keys_union | [
{
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}
] | [
582,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
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Mathlib/Data/Set/Basic.lean | Set.insert_subset_insert | [] | [
1159,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_proj_pos | [
{
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"tactic": "by_cases pp : p.Prime"
},
{
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"state_before":... | [
385,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.IsSheafFor.isSeparatedFor | [] | [
606,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_eq_zero | [
{
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250,
62
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241,
1
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Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.inf | [] | [
528,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
11
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Mathlib/Order/SuccPred/IntervalSucc.lean | Antitone.pairwise_disjoint_on_Ioc_pred | [] | [
128,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.mem_filterMap | [] | [
2175,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2173,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_inj | [] | [
499,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.aeval_root_derivative_of_splits | [
{
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459,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
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Mathlib/Data/List/Basic.lean | List.foldrM_eq_foldr | [
{
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"tactic": "indu... | [
2810,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2809,
1
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.add_apply | [] | [
678,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.pow_mem_pow | [
{
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949,
44
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943,
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Mathlib/Algebra/Star/SelfAdjoint.lean | isSelfAdjoint_zero | [] | [
110,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Algebra/Group/Pi.lean | Set.piecewise_div | [] | [
679,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
676,
1
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | CommGroupCat.mono_iff_injective | [] | [
429,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Data/Nat/Interval.lean | Nat.card_fintypeIco | [
{
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}
] | [
133,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Data/Finset/Card.lean | Finset.card_eq_succ | [
{
"state_after": "no goals",
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}
] | [
602,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.div_rpow | [
{
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"tactic": "simp only [div_eq_mul_inv, mul_rpow hx (inv_nonneg.2 hy), inv_rpow hy]"
}
] | [
401,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inr_comp_pushoutSymmetry_inv | [
{
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}
] | [
1587,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
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Mathlib/Analysis/Seminorm.lean | Seminorm.uniform_continuous' | [] | [
1159,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
11
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Mathlib/Algebra/Quaternion.lean | Quaternion.add_imK | [] | [
896,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
9
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_univ_prod_of_one_le' | [] | [
179,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.nat_coe_dvd_iff | [
{
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"state_before": "a b : Cardinal\nn m : ℕ\n⊢ ↑n ∣ ↑m ↔ n ∣ m",
"tactic": "refine' ⟨_, fun ⟨h, ht⟩ => ⟨h, by exact_mod_cast ht⟩⟩"
},
{
"state_after": "case intro\na b : Cardinal\nn m : ℕ\nk : Cardinal\nhk : ↑m = ↑n * k\n⊢ n ∣ m",
"... | [
110,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
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Mathlib/Algebra/Free.lean | FreeSemigroup.lift_comp_of' | [] | [
550,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.hasFiniteIntegral_smul_iff | [
{
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414,
33
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408,
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Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.of_iso | [
{
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102,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finite_factors | [
{
"state_after": "R : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : IsDomain R\ninst✝³ : IsDedekindDomain R\nK : Type ?u.2605\ninst✝² : Field K\ninst✝¹ : Algebra R K\ninst✝ : IsFractionRing R K\nv : HeightOneSpectrum R\nI : Ideal R\nhI : I ≠ 0\n⊢ Finite { x // x.asIdeal ∣ I }",
"state_before": "R : Type u_1\ninst... | [
55,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Order/WellFoundedSet.lean | Set.isWf_insert | [
{
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"tactic": "simp only [← singleton_union, isWf_union, isWf_singleton, true_and_iff]"
}
] | [
479,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.iSup_edist_ne_top_aux | [
{
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326,
22
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320,
1
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isBigO_one_exp_comp | [
{
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"tactic": "simp only [← exp_zero, isBigO_exp_comp_exp_comp, Pi.sub_def, zero_sub, isBoundedUnder_le_neg]"
}
] | [
401,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.const_one | [] | [
473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.destruct_eq_cons | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\na : α\ns' : Seq α\n⊢ Option.map (fun a' => (a', tail s)) (get? s 0) = some (a, s') → s = cons a s'",
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"tactic":... | [
234,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
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Mathlib/GroupTheory/Congruence.lean | Con.sInf_def | [
{
"state_after": "case h.h.a\nM : Type u_1\nN : Type ?u.20259\nP : Type ?u.20262\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nc : Con M\nS : Set (Con M)\nx✝¹ x✝ : M\n⊢ ↑(sInf S) x✝¹ x✝ ↔ sInf (FunLike.coe '' S) x✝¹ x✝",
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457,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.sub_seq | [] | [
289,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/LinearAlgebra/Dimension.lean | LinearMap.rank_comp_le | [
{
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1362,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1360,
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Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.list_prod_ofFn_of_eq_dProd | [
{
"state_after": "no goals",
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307,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_closedBall | [
{
"state_after": "no goals",
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412,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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src/lean/Init/Data/List/Basic.lean | List.length_concat | [
{
"state_after": "no goals",
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"tactic": "induction as with\n| nil => rfl\n| cons _ xs ih => simp [concat, ih]"
},
{
"state_after": "no goals",
"state_before": "case nil\nα : Type ... | [
773,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
770,
9
] |
Mathlib/Dynamics/Ergodic/Conservative.lean | MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem | [
{
"state_after": "ι : Type ?u.75187\nα : Type u_1\ninst✝ : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nhf : Conservative f μ\nhs : MeasurableSet s\nk : ℕ\n⊢ ∀ᵐ (a : α) ∂μ, (f^[k]) a ∈ s → ∃ᶠ (n : ℕ) in atTop, (f^[n]) a ∈ s",
"state_before": "ι : Type ?u.75187\nα : Type u_1\ninst✝ : MeasurableSpa... | [
162,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_neg | [
{
"state_after": "x✝ y x : ℝ\n⊢ -x + sqrt (1 + (-x) ^ 2) = (x + sqrt (1 + x ^ 2))⁻¹",
"state_before": "x✝ y x : ℝ\n⊢ arsinh (-x) = -arsinh x",
"tactic": "rw [← exp_eq_exp, exp_arsinh, exp_neg, exp_arsinh]"
},
{
"state_after": "case h\nx✝ y x : ℝ\n⊢ (-x + sqrt (1 + (-x) ^ 2)) * (x + sqrt (1 + x ^... | [
76,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Part.lean | Part.some_sdiff_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.103033\nγ : Type ?u.103036\ninst✝ : SDiff α\na b : α\n⊢ some a \\ some b = some (a \\ b)",
"tactic": "simp [sdiff_def]"
}
] | [
878,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.iSup_dualAnnihilator_le_iInf | [
{
"state_after": "R : Type u\nM : Type v\ninst✝² : CommSemiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nW : Submodule R M\nι : Type u_1\nU : ι → Submodule R M\n⊢ (⨅ (i : ι), U i) ≤ ⨅ (i : ι), dualCoannihilator (dualAnnihilator (U i))",
"state_before": "R : Type u\nM : Type v\ninst✝² : CommSemiring ... | [
933,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Data/MvPolynomial/Cardinal.lean | MvPolynomial.cardinal_lift_mk_le_max | [
{
"state_after": "case inl\nσ✝ : Type u\nR✝ : Type v\ninst✝¹ : CommSemiring R✝\nσ : Type u\nR : Type v\ninst✝ : CommSemiring R\nh✝ : Subsingleton R\n⊢ (#MvPolynomial σ R) ≤ max (max (lift (#R)) (lift (#σ))) ℵ₀\n\ncase inr\nσ✝ : Type u\nR✝ : Type v\ninst✝¹ : CommSemiring R✝\nσ : Type u\nR : Type v\ninst✝ : CommS... | [
54,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.neg_subst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Ring α\nn e t : α\nh1 : n * e = t\n⊢ n * -e = -t",
"tactic": "simp [*]"
}
] | [
61,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.of_comp | [
{
"state_after": "case inl\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁶ : Ring k\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module k V\ninst✝³ : AffineSpace V P\nι : Type u_6\nV₂ : Type u_4\nP₂ : Type u_5\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module k V₂\ninst✝ : AffineSpace V₂ P₂\np : ι → P\nf : P →ᵃ[k] P₂\nhai : A... | [
374,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_apply | [] | [
73,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Int/GCD.lean | Int.ne_zero_of_gcd | [
{
"state_after": "x y : ℤ\nhc : x = 0 ∧ y = 0\n⊢ gcd x y = 0",
"state_before": "x y : ℤ\nhc : gcd x y ≠ 0\n⊢ x ≠ 0 ∨ y ≠ 0",
"tactic": "contrapose! hc"
},
{
"state_after": "no goals",
"state_before": "x y : ℤ\nhc : x = 0 ∧ y = 0\n⊢ gcd x y = 0",
"tactic": "rw [hc.left, hc.right, gcd_zero... | [
370,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_add' | [] | [
1177,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1175,
1
] |
Mathlib/Data/Int/Basic.lean | Int.neg_pred | [
{
"state_after": "no goals",
"state_before": "a : ℤ\n⊢ -pred a = succ (-a)",
"tactic": "rw [neg_eq_iff_eq_neg.mp (neg_succ (-a)), neg_neg]"
}
] | [
165,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.ext | [] | [
141,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_eq_left | [] | [
362,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.integral_eq_setToL1S | [] | [
533,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
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