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/List/Basic.lean | List.zipRight'_nil_cons | [] | [
4085,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4083,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.ext_iff | [] | [
150,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_true_of_mem | [] | [
2698,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2697,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | MulAction.surjective_smul | [] | [
162,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Computability/Primrec.lean | PrimrecPred.of_eq | [] | [
512,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Order/Max.lean | NoTopOrder.to_noMaxOrder | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.5028\nβ : Type ?u.5031\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : NoTopOrder α\na : α\n⊢ ∃ b, a < b",
"tactic": "simpa [not_le] using exists_not_le a"
}
] | [
150,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | aemeasurable_congr | [] | [
708,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.orderOf | [] | [
456,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
11
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.k_mul_j | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.27887\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq : Basis A c₁ c₂\n⊢ q.k * q.j = c₂ • q.i",
"tactic": "rw [← i_mul_j, mul_assoc, j_mul_j, mul_smul_com... | [
99,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_one | [] | [
871,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
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Mathlib/Order/Hom/Lattice.lean | SupHom.coe_comp | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
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Mathlib/Algebra/Order/SMul.lean | BddBelow.smul_of_nonneg | [] | [
156,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/Algebra/GeomSum.lean | geom_sum_eq_zero_iff_neg_one | [
{
"state_after": "α : Type u\nβ : Type ?u.252702\nn : ℕ\nx : α\ninst✝ : LinearOrderedRing α\nhn : n ≠ 0\nh : ∑ i in range n, x ^ i = 0\n⊢ x = -1 ∧ Even n",
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... | [
566,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | lt_of_abs_lt | [] | [
208,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Std/Classes/Order.lean | Std.TransCmp.cmp_congr_left | [] | [
83,
17
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
76,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.pi | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nδ : Type u_1\ninst✝ : Finite δ\nκ : δ → Type u_2\nt : (d : δ) → Set (κ d)\nht : ∀ (d : δ), Set.Finite (t d)\nval✝ : Fintype δ\n⊢ Set.Finite (Set.pi univ t)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nδ : Typ... | [
1010,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_iff_mod_eq_zero | [] | [
685,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
684,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv | [] | [
1440,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1438,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.singleton_inj | [
{
"state_after": "α : Type u_1\nβ : Type ?u.25432\nγ : Type ?u.25435\na b : α\n⊢ a ::ₘ 0 = b ::ₘ 0 ↔ a = b",
"state_before": "α : Type u_1\nβ : Type ?u.25432\nγ : Type ?u.25435\na b : α\n⊢ {a} = {b} ↔ a = b",
"tactic": "simp_rw [← cons_zero]"
},
{
"state_after": "no goals",
"state_before": "... | [
350,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.mem_Icc_of_Ico | [] | [
667,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Data/List/Basic.lean | List.length_erase_add_one | [
{
"state_after": "no goals",
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"tactic": "rw [erase_eq_eraseP, length_eraseP_add_one h (decide_eq_true rfl)]"... | [
3729,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3727,
9
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Mathlib/Data/Set/Ncard.lean | Set.exists_intermediate_Set | [
{
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588,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_inf | [] | [
656,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
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src/lean/Init/Control/Lawful.lean | map_eq_pure_bind | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα β : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → β\nx : m α\n⊢ f <$> x = do\n let a ← x\n pure (f a)",
"tactic": "rw [← bind_pure_comp]"
}
] | [
63,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
62,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.perm_inv_mapsTo_iff_mapsTo | [] | [
86,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | dvd_lcm_left | [] | [
716,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_injective | [
{
"state_after": "case a\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ x y : MvPolynomial σ R\nh : Coe.coe x = Coe.coe y\nm✝ : σ →₀ ℕ\n⊢ coeff m✝ x = coeff m✝ y",
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... | [
1139,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Std/Data/List/Basic.lean | List.zipWithLeft_eq_zipWithLeftTR | [
{
"state_after": "case h.h.h.h.h.h\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nf : α → Option β → γ\nas : List α\nbs : List β\n⊢ zipWithLeft f as bs = zipWithLeftTR f as bs",
"state_before": "⊢ @zipWithLeft = @zipWithLeftTR",
"tactic": "funext α β γ f as bs"
},
{
"state_after": "case h.h.h.h.h.h\... | [
1374,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1368,
10
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_sum | [
{
"state_after": "case refine'_1\nR : Type u\nS : Type v\nσ : Type u_2\nτ : Type ?u.34158\nr : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\nι : Type u_1\ninst✝ : DecidableEq σ\ns : Finset ι\nf : ι → MvPolynomial σ R\n⊢ degrees (∑ i in ∅, f i) ≤ Finset.sup ∅ fun i => degrees (... | [
159,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Inner.lean | MeasureTheory.StronglyMeasurable.inner | [] | [
32,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
11
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | GenLoop.Homotopic.trans | [] | [
185,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
8
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_range_eq_iUnion | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.180962\nι : Sort u_3\nι' : Sort ?u.180968\nι₂ : Sort ?u.180971\nκ : ι → Sort ?u.180976\nκ₁ : ι → Sort ?u.180981\nκ₂ : ι → Sort ?u.180986\nκ' : ι' → Sort ?u.180991\nC : ι → Set α\nf : (x : ι) → β → ↑(C x)\nhf : ∀ (x : ι), Surjective (f x)\nx : α\n... | [
1394,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1387,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | not_summable_of_ratio_test_tendsto_gt_one | [
{
"state_after": "α✝ : Type ?u.1387057\nβ : Type ?u.1387060\nι : Type ?u.1387063\nα : Type u_1\ninst✝ : SeminormedAddCommGroup α\nf : ℕ → α\nl : ℝ\nhl : 1 < l\nh : Tendsto (fun n => ‖f (n + 1)‖ / ‖f n‖) atTop (𝓝 l)\nkey : ∀ᶠ (n : ℕ) in atTop, ‖f n‖ ≠ 0\n⊢ ¬Summable f",
"state_before": "α✝ : Type ?u.1387057... | [
569,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
1
] |
Mathlib/Data/Rat/Cast.lean | RingHom.ext_rat | [] | [
487,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.subset_hom | [
{
"state_after": "case intro\nV : Type u\nG : SimpleGraph V\nK L L' M : Set V\nh : K ⊆ L\nc : V\ncL : ¬c ∈ L\n⊢ c ∈ ↑(hom h (componentComplMk G cL))",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\nh : K ⊆ L\n⊢ ↑C ⊆ ↑(hom h C)",
"tactic": "rintro c ⟨cL, rfl⟩"
... | [
183,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.smul_bot' | [] | [
237,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedTotalDegree_coe | [
{
"state_after": "R : Type u_2\nM : Type u_3\ninst✝³ : CommSemiring R\nσ : Type u_1\ninst✝² : AddCommMonoid M\ninst✝¹ : SemilatticeSup M\ninst✝ : OrderBot M\nw : σ → M\np : MvPolynomial σ R\nhp : ∃ a, ↑a = weightedTotalDegree' w p\n⊢ weightedTotalDegree' w p = ↑(weightedTotalDegree w p)",
"state_before": "R... | [
116,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.tendsto_log_nhdsWithin_zero | [
{
"state_after": "x y : ℝ\n⊢ Tendsto (fun x => log (abs x)) (𝓝[{0}ᶜ] 0) atBot",
"state_before": "x y : ℝ\n⊢ Tendsto log (𝓝[{0}ᶜ] 0) atBot",
"tactic": "rw [← show _ = log from funext log_abs]"
},
{
"state_after": "x y : ℝ\n⊢ Tendsto log (𝓝[Ioi 0] 0) atBot",
"state_before": "x y : ℝ\n⊢ Tend... | [
301,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_spec_mk | [] | [
273,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | derivWithin_inv' | [] | [
170,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_injective | [] | [
485,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_addMonoidHom_injective | [] | [
211,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRelAux.ret_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nC : Computation α → Computation β → Prop\nb : β\nca : Computation α\n⊢ LiftRelAux R C (destruct ca) (Sum.inl b) ↔ ∃ a, a ∈ ca ∧ R a b",
"tactic": "rw [← LiftRelAux.swap, LiftRelAux.ret_left]"
}
] | [
1282,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1280,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_atBot | [] | [
1281,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1279,
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] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_map_degree_eq_one | [
{
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"st... | [
91,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat_self | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ Part.get (multiplicity p p) (_ : multiplicity.Finite p p) = 1",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ padicValNat p p = 1",
"tactic": "rw [padicValNat_def (@Fact.out p.Prime).pos]"
},
{
"state_after": "no goals",
"state_b... | [
236,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.congr_strictAntiOn | [] | [
287,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.periodicOrbit_eq_nil_of_not_periodic_pt | [] | [
514,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.tan_add' | [] | [
43,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_comp | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nx✝ : R\ninst✝ : CommSemiring S\nf : R →+* S\nx : S\n⊢ eval₂ f x (eval₂ C q (∑ i in range (natDegree p + 1), ↑(monomial i) (coeff p i))) =\n eval₂ f (eval₂ f x q) (∑ i in range (natDegree p + 1... | [
1034,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1033,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | IsLUB.biUnion_Iic_eq_Iio | [] | [
223,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalRingHom.srangeRestrict_surjective | [] | [
885,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.add_tmul | [] | [
143,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.eqv_classes_of_disjoint_union | [
{
"state_after": "α : Type u_1\nc : Set (Set α)\nhu : ⋃₀ c = Set.univ\nH : Set.PairwiseDisjoint c id\na : α\n⊢ a ∈ Set.univ",
"state_before": "α : Type u_1\nc : Set (Set α)\nhu : ⋃₀ c = Set.univ\nH : Set.PairwiseDisjoint c id\na : α\n⊢ a ∈ ⋃₀ c",
"tactic": "rw [hu]"
},
{
"state_after": "no goals... | [
181,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/AddTorsor.lean | Prod.fst_vadd | [] | [
306,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | natCast_mem | [
{
"state_after": "no goals",
"state_before": "S : Type u_1\nR : Type u_2\ninst✝² : AddMonoidWithOne R\ninst✝¹ : SetLike S R\ns : S\ninst✝ : AddSubmonoidWithOneClass S R\nn : ℕ\n⊢ ↑n ∈ s",
"tactic": "induction n <;> simp [zero_mem, add_mem, one_mem, *]"
}
] | [
44,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_support | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.187796\nι : Type ?u.187799\nM : Type u_3\nM' : Type ?u.187805\nN : Type ?u.187808\nP : Type ?u.187811\nG : Type ?u.187814\nH : Type ?u.187817\nR : Type ?u.187820\nS : Type ?u.187823\ninst✝¹ : AddCommMonoid M\nv v₁ v₂ : α →... | [
543,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.map_zero₂ | [] | [
159,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/Multiset/Antidiagonal.lean | Multiset.antidiagonal_coe' | [] | [
41,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_eq' | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\ns : Finset (Perm α)\nh1 : ∀ (f : Perm α), f ∈ s → IsCycle f\nh2 : Set.Pairwise (↑s) Disjoint\nh0 : Finset.noncommProd s id (_ : Set.Pairwise ↑s fun a b => Commute (id a) (id b)) = σ\n⊢ map (Finset.card ∘ support) (cycleFactor... | [
66,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/Cover.lean | Wcovby.trans_antisymm_rel | [] | [
92,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/List/Basic.lean | List.get?_injective | [
{
"state_after": "no goals",
"state_before": "case nil\nι : Type ?u.83779\nα✝ : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : Type u\ni j : ℕ\nh₀ : i < length []\nh₁ : Nodup []\nh₂ : get? [] i = get? [] j\n⊢ i = j",
"tactic": "cases h₀"
},
{
"state_after": "case cons.zero.zero... | [
1286,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Icc_add_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ (⋃ (n : ℤ), Icc (a + ↑n) (a + ↑n + 1)) = univ",
"tactic": "simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using\n iUnion_Icc_add_zsmul zero_lt_one a"
}
] | [
1104,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_disjoint_ball | [] | [
532,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_mul_single | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCancelAddCommMonoid Γ\ninst✝ : NonUnitalNonAssocSemiring R\na b : Γ\nr s : R\nx : Γ\n⊢ coeff (↑(single a) r * ↑(single b) s) x = coeff (↑(single (a + b)) (r * s)) x",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : OrderedCanc... | [
945,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.symm_apply_apply | [] | [
383,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.prod | [] | [
540,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.chain_map | [
{
"state_after": "case nil\nα : Type u_2\nβ : Type u_1\nr : α → α → Prop\nf : β → α\ns : Cycle β\n⊢ Chain r (map f (Quotient.mk'' [])) ↔ Chain (fun a b => r (f a) (f b)) (Quotient.mk'' [])\n\ncase cons\nα : Type u_2\nβ : Type u_1\nr : α → α → Prop\nf : β → α\ns : Cycle β\na : β\nl : List β\n⊢ Chain r (map f (Qu... | [
964,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.card_image₂_singleton_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.51463\nβ : Type u_3\nβ' : Type ?u.51469\nγ : Type u_2\nγ' : Type ?u.51475\nδ : Type ?u.51478\nδ' : Type ?u.51481\nε : Type ?u.51484\nε' : Type ?u.51487\nζ : Type ?u.51490\nζ' : Type ?u.51493\nν : Type ?u.51496\ninst✝⁷ : DecidableEq α'\... | [
262,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | discreteTopology_iff_open_singleton_one | [] | [
164,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mk_surjective | [] | [
767,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/CategoryTheory/Limits/FullSubcategory.lean | CategoryTheory.Limits.ClosedUnderLimitsOfShape.limit | [] | [
51,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.covby_iff_succ_eq | [] | [
80,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
11
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.copy_eq | [] | [
486,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/Order/Concept.lean | Concept.swap_swap | [] | [
384,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | Equiv.divLeft_eq_inv_trans_mulLeft | [] | [
204,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.extend_apply | [] | [
377,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/List/Basic.lean | List.map₂Right'_cons_cons | [] | [
4027,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4023,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousWithinAt_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.321718\nδ : Type ?u.321721\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ns t : Set α\nx : α\nh : t ∈ 𝓝 x\n⊢ ContinuousWithinAt f (s ∩ t) x ↔... | [
713,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/Algebra/Order/SMul.lean | smul_lt_smul_of_pos | [] | [
93,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
11
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.CliqueFree.mono | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\nm n : ℕ\ns✝ : Finset α\nh : m ≤ n\nhG : CliqueFree G m\ns : Finset α\nhs : IsNClique G n s\n⊢ False",
"state_before": "α : Type u_1\nG H : SimpleGraph α\nm n : ℕ\ns : Finset α\nh : m ≤ n\n⊢ CliqueFree G m → CliqueFree G n",
"tactic": "intro hG s hs"
... | [
219,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Algebra/DirectLimit.lean | Ring.DirectLimit.of_f | [] | [
410,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.rangeS_le | [] | [
112,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_const_smul | [] | [
364,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Logic/Basic.lean | or_congr_left' | [] | [
390,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | closedEmbedding_of_spaced_out | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : UniformSpace α✝\ninst✝³ : UniformSpace β\ninst✝² : UniformSpace γ\nα : Type u_1\ninst✝¹ : SeparatedSpace β\nf : α → β\ns : Set (β × β)\nhs : s ∈ 𝓤 β\nhf : Pairwise fun x y => ¬(f x, f y) ∈ s\ninst✝ : DiscreteTopology α\n⊢ ClosedEmbedding f",
"... | [
243,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_zero' | [
{
"state_after": "no goals",
"state_before": "h : Decidable 0.Dom\n⊢ toWithTop 0 = 0",
"tactic": "convert toWithTop_zero"
}
] | [
570,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.dart_edge_eq_iff | [
{
"state_after": "case mk.mk\nι : Sort ?u.97949\n𝕜 : Type ?u.97952\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\np : V × V\nhp : Adj G p.fst p.snd\nq : V × V\nhq : Adj G q.fst q.snd\n⊢ Dart.edge { toProd := p, is_adj := hp } = Dart.edge { toProd := q, ... | [
776,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | le_one_div | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.79768\nα : Type u_1\nβ : Type ?u.79774\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\nhb : 0 < b\n⊢ a ≤ 1 / b ↔ b ≤ 1 / a",
"tactic": "simpa using le_inv ha hb"
}
] | [
442,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | Basis.ext_linearIsometry | [] | [
1196,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/RingTheory/OreLocalization/OreSet.lean | OreLocalization.ore_left_cancel | [] | [
51,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.monomial_zero_left | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.hasDerivAt | [] | [
61,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/Data/Real/EReal.lean | EReal.abs_def | [] | [
1062,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.eqOn | [] | [
128,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
11
] |
Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_card_fiber_le_of_card_le_mul | [] | [
310,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.ext_iff | [] | [
165,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_ofPNatMultiset | [
{
"state_after": "v : Multiset ℕ+\nh : ∀ (p : ℕ+), p ∈ v → PNat.Prime p\n⊢ Multiset.prod (toPNatMultiset (ofPNatMultiset v h)) = Multiset.prod v",
"state_before": "v : Multiset ℕ+\nh : ∀ (p : ℕ+), p ∈ v → PNat.Prime p\n⊢ prod (ofPNatMultiset v h) = Multiset.prod v",
"tactic": "dsimp [prod]"
},
{
... | [
189,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | ENNReal.coe_essSup | [
{
"state_after": "α : Type u_1\nβ : Type ?u.5738175\nm : MeasurableSpace α\nμ ν : MeasureTheory.Measure α\nf✝ : α → ℝ≥0∞\nf : α → ℝ≥0\nhf : IsBoundedUnder (fun x x_1 => x ≤ x_1) (Measure.ae μ) f\nr : ℝ≥0∞\n⊢ (∀ (i : ℝ≥0), (i ∈ fun x => sets (map f (Measure.ae μ)) {x_1 | x_1 ≤ x}) → r ≤ ↑i) ↔\n ∀ (r_1 : ℝ≥0),... | [
341,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/CategoryTheory/Limits/ExactFunctor.lean | CategoryTheory.RightExactFunctor.forget_obj | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
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