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/Vector/Basic.lean | Vector.cons_val | [] | [
58,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.mem_of_mem | [] | [
296,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_eq_self | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ ∃ z, b = b + z • p",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ toIocMod hp a b = b ↔ b ∈ Set.Io... | [
726,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Logic/Denumerable.lean | Denumerable.encode_ofNat | [
{
"state_after": "case intro.intro\nα : Type u_1\nβ : Type ?u.516\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\nn : ℕ\na : ?m.551\nh : a ∈ decode n\ne : encode a = n\n⊢ encode (ofNat α n) = n",
"state_before": "α : Type u_1\nβ : Type ?u.516\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\nn : ℕ\n⊢ encode (... | [
70,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Logic/Nontrivial.lean | subsingleton_or_nontrivial | [
{
"state_after": "α✝ : Type ?u.3498\nβ : Type ?u.3501\nα : Type u_1\n⊢ Nontrivial α ∨ ¬Nontrivial α",
"state_before": "α✝ : Type ?u.3498\nβ : Type ?u.3501\nα : Type u_1\n⊢ Subsingleton α ∨ Nontrivial α",
"tactic": "rw [← not_nontrivial_iff_subsingleton, or_comm]"
},
{
"state_after": "no goals",
... | [
133,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | sInf_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝³ : CompleteLattice α\ninst✝² : Group α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ns t : Set α\n⊢ sInf (s / t) = sInf s / sSup t",
... | [
97,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.preimage_coe_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Ico ↑a ↑b = Ico a b",
"tactic": "simp [← Ici_inter_Iio]"
}
] | [
172,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.llift_symm_apply | [] | [
434,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.or | [] | [
724,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
11
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_right_cancel₀ | [] | [
86,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.neBot | [] | [
2932,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2930,
1
] |
Mathlib/MeasureTheory/Group/Action.lean | MeasureTheory.measure_smul | [] | [
186,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDeriv_succ_eq_comp_left | [] | [
1542,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_quadratic_lt_degree_C_mul_X_cb | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1327898\nha : a ≠ 0\n⊢ degree (↑C b * X ^ 2 + ↑C c * X + ↑C d) < degree (↑C a * X ^ 3)",
"tactic": "simpa only [degree_C_mul_X_pow 3 ha] using degree_quadratic_lt"
}
... | [
1222,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Std/Data/List/Lemmas.lean | List.range'_sublist_right | [
{
"state_after": "no goals",
"state_before": "step s m n : Nat\nh : range' s m step <+ range' s n step\n⊢ m ≤ n",
"tactic": "simpa only [length_range'] using h.length_le"
},
{
"state_after": "step s m n : Nat\nh : m ≤ n\n⊢ range' s m step <+ range' s m step ++ range' (s + step * m) (n - m) step"... | [
1859,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1857,
1
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Mathlib/Data/Stream/Init.lean | Stream'.tail_map | [] | [
156,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Part.lean | Part.some_dom | [] | [
143,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.rename_comp_expand | [
{
"state_after": "case hf\nσ : Type u_1\nτ : Type u_2\nR : Type u_3\nS : Type ?u.347378\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : σ → τ\np : ℕ\nφ : σ\n⊢ ↑(AlgHom.comp (rename f) (expand p)) (X φ) = ↑(AlgHom.comp (expand p) (rename f)) (X φ)",
"state_before": "σ : Type u_1\nτ : Type u_2\nR : Type... | [
97,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_nat_cast | [] | [
392,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_of_mul_lt_mul_left | [] | [
172,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/List/Indexes.lean | List.mapIdx_nil | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.lt_rpow_iff_log_lt | [
{
"state_after": "no goals",
"state_before": "x y z : ℝ\nhx : 0 < x\nhy : 0 < y\n⊢ x < y ^ z ↔ log x < z * log y",
"tactic": "rw [← Real.log_lt_log_iff hx (Real.rpow_pos_of_pos hy z), Real.log_rpow hy]"
}
] | [
603,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/FieldTheory/Adjoin.lean | PowerBasis.equivAdjoinSimple_aeval | [] | [
1288,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero | [
{
"state_after": "𝕜 : Type ?u.3112345\nE : Type ?u.3112348\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nx y : F\n⊢ 2 = 0 ∨ ↑re (inner x y) = 0 ↔ inner x y = 0",
"state_... | [
1493,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
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Mathlib/GroupTheory/PGroup.lean | IsPGroup.nontrivial_iff_card | [
{
"state_after": "p : ℕ\nG : Type u_1\ninst✝¹ : Group G\nhG : IsPGroup p G\nhp : Fact (Nat.Prime p)\ninst✝ : Fintype G\nhGnt : Nontrivial G\nk : ℕ\nhk : card G = 1\nhk0 : k = 0\n⊢ False",
"state_before": "p : ℕ\nG : Type u_1\ninst✝¹ : Group G\nhG : IsPGroup p G\nhp : Fact (Nat.Prime p)\ninst✝ : Fintype G\nh... | [
168,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.coe_rTensorHom | [] | [
1033,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_eq_single | [
{
"state_after": "G : Type ?u.34693\nM : Type u_2\nN : Type ?u.34699\nα : Sort u_1\nβ : Sort ?u.34705\nι : Sort ?u.34708\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf : α → M\na : α\nha : ∀ (x : α), x ≠ a → f x = 1\nthis : mulSupport (f ∘ PLift.down) ⊆ ↑{{ down := a }}\n⊢ (∏ᶠ (x : α), f x) = f a",
"state_... | [
224,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Order/Disjointed.lean | preimage_find_eq_disjointed | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.14611\ns : ℕ → Set α\nH : ∀ (x : α), ∃ n, x ∈ s n\ninst✝ : (x : α) → (n : ℕ) → Decidable (x ∈ s n)\nn : ℕ\nx : α\n⊢ x ∈ (fun x => Nat.find (_ : ∃ n, x ∈ s n)) ⁻¹' {n} ↔ x ∈ disjointed s n",
"state_before": "α : Type u_1\nβ : Type ?u.14611\ns : ℕ → Set α\nH... | [
181,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/List/Pairwise.lean | List.Pairwise.of_map | [] | [
191,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.supp_eq_of_isUniform | [
{
"state_after": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\nh : IsUniform\nα : TypeVec n\na : (P F).A\nf : MvPFunctor.B (P F) a ⟹ α\ni✝ : Fin2 n\n⊢ supp (abs { fst := a, snd := f }) i✝ = f i✝ '' univ",
"state_before": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF ... | [
236,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.pi_div_two_pos | [] | [
174,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
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Mathlib/Order/Grade.lean | grade_self | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.exact_iff_image_eq_kernel | [
{
"state_after": "case mp\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ Exact f g → imageSubobject f = kernelSubobject g\n\ncase mpr\nC : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\n⊢ imageSubobject f = kernelSubobject g → Exact f ... | [
66,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.coprod_apply | [] | [
688,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node3L | [] | [
1133,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/Order/Interval.lean | Interval.dual_top | [] | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.productMap_left | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nA : Type u_1\nB : Type u_4\nS : Type u_2\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Semiring B\ninst✝³ : CommSemiring S\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ninst✝ : Algebra R S\nf : A →ₐ[R] S\ng : B →ₐ[R] S\n⊢ ∀ (x : A), ↑(AlgH... | [
975,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | id_eq_sum_orthogonalProjection_self_orthogonalComplement | [
{
"state_after": "case h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.968584\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace { x // x ∈ K }\nw : E\... | [
1046,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.modByMonic_eq_sub_mul_div | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q✝ p q : R[X]\nhq : Monic q\nh : degree q ≤ degree p ∧ p ≠ 0\n_wf : degree (p - ↑C (leadingCoeff p) * X ^ (natDegree p - natDegree q) * q) < degree p\n⊢ p %ₘ q = p - q * (p /ₘ q)",
"state_before": "R : T... | [
249,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.isBoundedLinearMap_comp_right | [] | [
464,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Mathlib/RingTheory/WittVector/Basic.lean | WittVector.mapFun.one | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nR : Type u_2\nS : Type u_1\nT : Type ?u.54735\nhp : Fact (Nat.Prime p)\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : CommRing T\nα : Type ?u.54750\nβ : Type ?u.54753\nf : R →+* S\nx y : 𝕎 R\n⊢ mapFun (↑f) 1 = 1",
"tactic": "map_fun_tac"
}
] | [
112,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.prod_X_sub_C_coeff_card_pred | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type w\ns✝ : Finset ι\ninst✝ : CommRing R\ns : Finset ι\nf : ι → R\nhs : 0 < Finset.card s\n⊢ coeff (∏ i in s, (X - ↑C (f i))) (Finset.card s - 1) = -∑ i in s, f i",
"tactic": "simpa using multiset_prod_X_sub_C_coeff_card_pred (s.1.map f) (by... | [
283,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.eq_bot_iff_forall | [
{
"state_after": "no goals",
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1364,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
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] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.mk_coe | [] | [
176,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.tendsto_zero_of_tendsto | [
{
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2018,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2013,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isPwo_of_finite | [] | [
447,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
9
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.le_of_exists | [] | [
797,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_mono | [] | [
1319,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1319,
1
] |
Mathlib/Data/List/Lex.lean | List.Lex.to_ne | [] | [
153,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Finset/Functor.lean | Finset.map_comp_coe | [] | [
213,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.fuzzy_irrefl | [] | [
916,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
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Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.mem_carrier_iff | [] | [
67,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/Data/Sum/Basic.lean | Sum.map_surjective | [
{
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614,
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603,
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Mathlib/Algebra/Hom/Units.lean | IsUnit.div | [
{
"state_after": "F : Type ?u.56333\nG : Type ?u.56336\nα : Type u_1\nM : Type ?u.56342\nN : Type ?u.56345\ninst✝ : DivisionMonoid α\na b c : α\nha : IsUnit a\nhb : IsUnit b\n⊢ IsUnit (a * b⁻¹)",
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399,
22
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397,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.const_mul | [] | [
104,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Order/Bounds/Basic.lean | bddAbove_singleton | [] | [
633,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_add_cancel_iff_le | [
{
"state_after": "α : Type u_1\ninst✝² : CanonicallyOrderedAddMonoid α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\n⊢ a + (b - a) = b ↔ a ≤ b",
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323,
31
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321,
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.exists_T_pow | [
{
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403,
25
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393,
1
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Mathlib/Algebra/Quandle.lean | Rack.PreEnvelGroupRel.trans | [] | [
658,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
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Mathlib/Algebra/GroupWithZero/Basic.lean | one_div_ne_zero | [
{
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"state_before": "α : Type ?u.27916\nM₀ : Type ?u.27919\nG₀ : Type u_1\nM₀' : Type ?u.27925\nG₀' : Type ?u.27928\nF : Type ?u.27931\nF' : Type ?u.27934\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\nh : a ≠ 0\n⊢ 1 / a ≠ 0",
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}
... | [
395,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.prod_div_prod_filter | [] | [
962,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
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Mathlib/Data/Nat/Totient.lean | Nat.filter_coprime_Ico_eq_totient | [
{
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"state_before": "a n : ℕ\n⊢ card (filter (coprime a) (Ico n (n + a))) = φ a",
"tactic": "rw [totient, filter_Ico_card_eq_of_periodic, count_eq_card_filter_range]"
},
{
"state_after": "no goals",
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82,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.apply_symm_apply | [] | [
1264,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.sum | [] | [
261,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Std/Data/Array/Lemmas.lean | getElem?_neg | [] | [
27,
90
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26,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sub_nonempty | [] | [
534,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
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Mathlib/Logic/Function/Basic.lean | Function.Surjective.forall₂ | [] | [
200,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
11
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Mathlib/Order/Filter/Basic.lean | Filter.biInter_mem | [
{
"state_after": "no goals",
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nf... | [
187,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Mathlib/Order/Filter/AtTopBot.lean | Filter.atTop_basis | [] | [
133,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLinearMapRight'_one | [
{
"state_after": "case h.h.h\nR : Type u_1\ninst✝² : Semiring R\nl : Type ?u.170495\nm : Type u_2\nn : Type ?u.170501\ninst✝¹ : Fintype m\ninst✝ : DecidableEq m\ni✝ x✝ : m\n⊢ ↑(comp (↑toLinearMapRight' 1) (single i✝)) 1 x✝ = ↑(comp LinearMap.id (single i✝)) 1 x✝",
"state_before": "R : Type u_1\ninst✝² : Sem... | [
169,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
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Mathlib/MeasureTheory/MeasurableSpace.lean | exists_measurable_piecewise_nat | [
{
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825,
39
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821,
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Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_zero | [] | [
3143,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3142,
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Mathlib/Analysis/Normed/Group/Pointwise.lean | ball_mul_singleton | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ ball x δ * {y} = ball (x * y) δ",
"tactic": "rw [mul_comm, singleton_mul_ball, mul_comm y]"
}
] | [
118,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/MeasureTheory/Measure/Haar/Quotient.lean | MeasureTheory.IsFundamentalDomain.map_restrict_quotient | [
{
"state_after": "G : Type u_1\ninst✝¹² : Group G\ninst✝¹¹ : MeasurableSpace G\ninst✝¹⁰ : TopologicalSpace G\ninst✝⁹ : TopologicalGroup G\ninst✝⁸ : BorelSpace G\nμ : Measure G\nΓ : Subgroup G\n𝓕 : Set G\nh𝓕 : IsFundamentalDomain { x // x ∈ ↑Subgroup.opposite Γ } 𝓕\ninst✝⁷ : Countable { x // x ∈ Γ }\ninst✝⁶ :... | [
142,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
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Mathlib/Topology/UniformSpace/Compact.lean | nhdsSet_diagonal_eq_uniformity | [
{
"state_after": "α : Type u_1\nβ : Type ?u.20\nγ : Type ?u.23\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : CompactSpace α\n⊢ 𝓤 α ≤ 𝓝ˢ (diagonal α)",
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62,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.CommSq.left_adjoint | [
{
"state_after": "C : Type u_4\nD : Type u_1\ninst✝¹ : Category C\ninst✝ : Category D\nG : C ⥤ D\nF : D ⥤ C\nA B : C\nX Y : D\ni : A ⟶ B\np : X ⟶ Y\nu : A ⟶ F.obj X\nv : B ⟶ F.obj Y\nsq : CommSq u i (F.map p) v\nadj : G ⊣ F\n⊢ G.map u ≫ adj.counit.app X ≫ p = G.map (u ≫ F.map p) ≫ adj.counit.app Y",
"state_... | [
92,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/Monoidal/Limits.lean | CategoryTheory.Limits.limLax_obj | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/CategoryTheory/Idempotents/HomologicalComplex.lean | CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f | [] | [
53,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\nh : angle x y = π\n⊢ inner x y = -(‖x‖ * ‖y‖)",
"tactic": "simp [← cos_angle_mul_norm_mul_norm, h]"
}
] | [
242,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.fderivWithin | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.38206\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.38301\ni... | [
98,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
11
] |
Mathlib/Topology/Algebra/Monoid.lean | Submonoid.isClosed_topologicalClosure | [] | [
451,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | tendsto_const_uniformity | [] | [
506,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.vector_head | [] | [
1301,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1300,
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] |
Mathlib/Data/W/Cardinal.lean | WType.cardinal_mk_eq_sum | [
{
"state_after": "α : Type u\nβ : α → Type u\n⊢ (#WType β) = (#(i : α) × (β i → WType β))",
"state_before": "α : Type u\nβ : α → Type u\n⊢ (#WType β) = sum fun a => (#WType β) ^ (#β a)",
"tactic": "simp only [Cardinal.power_def, ← Cardinal.mk_sigma]"
},
{
"state_after": "no goals",
"state_be... | [
46,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/FieldTheory/Normal.lean | Normal.of_isSplittingField | [
{
"state_after": "case inl\nF : Type u_1\nK : Type ?u.87123\ninst✝¹¹ : Field F\ninst✝¹⁰ : Field K\ninst✝⁹ : Algebra F K\nE : Type u_2\ninst✝⁸ : Field E\ninst✝⁷ : Algebra F E\ninst✝⁶ : Algebra K E\ninst✝⁵ : IsScalarTower F K E\nE' : Type ?u.87603\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\ninst✝¹ ... | [
245,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | bit0_mul | [
{
"state_after": "α : Type ?u.268299\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝ : NonUnitalNonAssocRing R\nn r : R\n⊢ (n + n) * r = 2 • (n * r)",
"state_before": "α : Type ?u.268299\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB :... | [
562,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivWithinAt.cos | [] | [
809,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.binomial_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : a ≠ b\n⊢ multinomial {a, b} f = (f a + f b)! / ((f a)! * (f b)!)",
"tactic": "simp [multinomial, Finset.sum_pair h, Finset.prod_pair h]"
}
] | [
108,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
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Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.finite_product_eq_finset_inf | [
{
"state_after": "α : Type u\nJ : Type w\ninst✝⁴ : SmallCategory J\ninst✝³ : FinCategory J\ninst✝² : SemilatticeInf α\ninst✝¹ : OrderTop α\nι : Type u\ninst✝ : Fintype ι\nf : ι → α\n⊢ (∏ f) = ?m.26818\n\nα : Type u\nJ : Type w\ninst✝⁴ : SmallCategory J\ninst✝³ : FinCategory J\ninst✝² : SemilatticeInf α\ninst✝¹ ... | [
97,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.congr_arg | [] | [
137,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
8
] |
Mathlib/Algebra/PUnitInstances.lean | PUnit.gcd_eq | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.LHom.sumElim_inl_inr | [] | [
193,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/Constructions.lean | isOpenMap_fst | [] | [
709,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
708,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_sdiff | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.86958\n𝕜 : Type ?u.86961\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\ns✝ s t : Set (Sym2 V)\nv w : V\n⊢ Adj (fromEdgeSet s \\ fromEdgeSet t) v w ↔ Adj (fromEdgeSet (s \\ t)) v w",
"state_before": "ι ... | [
667,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_of_add_lt_add_right | [
{
"state_after": "no goals",
"state_before": "a b c : Nat\nh : a + b < c + b\n⊢ b + a < b + c",
"tactic": "rwa [Nat.add_comm b a, Nat.add_comm b c]"
}
] | [
78,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
77,
11
] |
Mathlib/Analysis/Normed/MulAction.lean | lipschitzWith_smul | [] | [
50,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.card_Ico | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝² : PartialOrder α\ninst✝¹ : Zero α\ninst✝ : LocallyFiniteOrder α\nf g : ι →₀ α\n⊢ card (Ico f g) = ∏ i in f.support ∪ g.support, card (Icc (↑f i) (↑g i)) - 1",
"tactic": "rw [card_Ico_eq_card_Icc_sub_one, card_Icc]"
}
] | [
116,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.cg_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nM : Type u_3\ninst✝ : Structure L M\n⊢ CG L M ↔ ∃ S, Set.Countable S ∧ LowerAdjoint.toFun (closure L) S = ⊤",
"tactic": "rw [cg_def, Substructure.cg_def]"
}
] | [
235,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_sUnion | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.2906\nπ : ι → Type ?u.2911\ninst✝ : TopologicalSpace α\ns t u v : Set α\nx : α\nc : Set (Set α)\nH1 : ∀ (s : Set α), s ∈ c → x ∈ s\nH2 : ∀ (s : Set α), s ∈ c → IsPreconnected s\n⊢ ∀ (y : α), y ∈ ⋃₀ c → ∃ t, t ⊆ ⋃₀ c ∧ x ∈ t ∧ y ∈ t ∧ IsPreconnected t",
"... | [
134,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.const_smul' | [] | [
472,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
11
] |
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