file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sub' | [
{
"state_after": "x✝ y✝ z✝ x : ℝ\nhx : 0 ≤ x\ny z : ℝ\nh : y + -z ≠ 0\n⊢ x ^ (y + -z) = x ^ y / x ^ z",
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"tactic": "simp only [sub_eq_add_neg] at h⊢"
},
{
"state_after": "no goals",
"state_bef... | [
234,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_filter_of_ne | [] | [
358,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
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Mathlib/Analysis/Calculus/Deriv/Mul.lean | HasDerivAt.clm_comp | [
{
"state_after": "𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : 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\nG : Type u_1\ninst✝¹ :... | [
368,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.smul_zero' | [
{
"state_after": "case H\nR : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ndata : R × { x // x ∈ S }\n⊢ Localization.mk data.fst data.snd • 0 = 0",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCo... | [
367,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
9
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_inl | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Algebra/Order/Field/Canonical/Basic.lean | tsub_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CanonicallyLinearOrderedSemifield α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c : α\n⊢ (a - b) / c = a / c - b / c",
"tactic": "simp_rw [div_eq_mul_inv, tsub_mul]"
}
] | [
25,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
25,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.Measure.FiniteAtFilter.integrableAtFilter_of_tendsto_ae | [] | [
456,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_inj_iff | [] | [
87,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.subtype_mk | [] | [
214,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/CategoryTheory/ConcreteCategory/Basic.lean | CategoryTheory.congr_hom | [] | [
128,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Topology/Separation.lean | nhds_injective | [] | [
218,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.const_apply | [] | [
183,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.PullbackCone.unop_inl | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nJ : Type u₂\ninst✝ : Category J\nX✝ : Type v₂\nX Y Z : Cᵒᵖ\nf : X ⟶ Z\ng : Y ⟶ Z\nc : PullbackCone f g\n⊢ PushoutCocone.inl (unop c) = (fst c).unop",
"tactic": "aesop_cat"
}
] | [
524,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Data/Int/Basic.lean | Int.toNat_coe_nat_add_one | [] | [
298,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
9
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_erase_eq_ite | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.109096\nγ : Type ?u.109099\ninst✝ : DecidableEq α\ns✝ t : Multiset α\na✝ b a : α\ns : Multiset α\nh : a ∈ s\n⊢ ↑card (erase s a) = if a ∈ s then pred (↑card s) else ↑card s\n\ncase neg\nα : Type u_1\nβ : Type ?u.109096\nγ : Type ?u.109099\ninst✝ : DecidableE... | [
1126,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1122,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_add_cancel_right | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a + -b + b = a",
"tactic": "rw [Int.add_assoc, Int.add_left_neg, Int.add_zero]"
}
] | [
327,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
326,
11
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_comap_iff_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.226876\nι : Sort x\nf : α → β\nl : Filter β\np : α → Prop\ns : Set α\n⊢ s ∈ comap f l ↔ (f '' sᶜ)ᶜ ∈ l",
"tactic": "simp only [mem_comap', compl_def, mem_image, mem_setOf_eq, not_exists, not_and', not_not]"
}... | [
1925,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1924,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_sup | [] | [
1477,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1475,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | strictMono_vecCons | [] | [
34,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.add_emod_eq_add_mod_right | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nn✝ : ℕ\nm n k i : ℤ\nH : m % n = k % n\n⊢ (m + i) % n = (k + i) % n",
"tactic": "rw [← emod_add_emod, ← emod_add_emod k, H]"
}
] | [
257,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_left | [
{
"state_after": "α : Type u_1\nα' : Type ?u.39933\nβ : Type u_2\nβ' : Type ?u.39939\nγ : Type u_3\nγ' : Type ?u.39945\nδ : Type ?u.39948\nδ' : Type ?u.39951\nε : Type ?u.39954\nε' : Type ?u.39957\nζ : Type ?u.39960\nζ' : Type ?u.39963\nν : Type ?u.39966\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
202,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithBot.coe_sInf' | [] | [
154,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_compl | [
{
"state_after": "α : Type u_1\nβ : Type ?u.30071\nγ : Type ?u.30074\nδ : Type ?u.30077\nι : Type ?u.30080\nR : Type ?u.30083\nR' : Type ?u.30086\nm : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\nh₁ : MeasurableSet s\nh_fin : ↑↑μ s ≠ ⊤\n⊢ ↑↑μ (univ \\ s) = ↑↑μ univ - ↑↑μ s",
"state_before": "α... | [
293,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.coe_continuous_linearProjOfClosedCompl | [] | [
119,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_exponent_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.909486\nF : Type u_2\nG : Type ?u.909492\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\n⊢ snorm' f 0 μ = 1",
"tacti... | [
175,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.coeff_reverse | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ f : R[X]\nn : ℕ\n⊢ coeff (reverse f) n = coeff f (↑(revAt (natDegree f)) n)",
"tactic": "rw [reverse, coeff_reflect]"
}
] | [
254,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.inter | [] | [
483,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isRat_ratCast | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : DivisionRing R\ninst✝ : CharZero R\nnum✝ : ℤ\ndenom✝ : ℕ\nqi : ℚ\ninvOf_mul_self✝ : qi * ↑denom✝ = 1\nmul_invOf_self✝ : ↑denom✝ * qi = 1\n⊢ ↑qi * ↑denom✝ = 1",
"tactic": "norm_cast"
},
{
"state_after": "no goals",
"state_be... | [
114,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_induction | [] | [
923,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
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] |
Mathlib/Analysis/Complex/Schwarz.lean | Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nR R₁ R₂ : ℝ\nf : ℂ → E\nc z z₀ : ℂ\ninst✝¹ : CompleteSpace E\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (ball (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\ng : ℂ → E := dslope f... | [
131,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_sup_self' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.3131\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ y \\ x ⊔ x = y \\ x ⊔ (x ⊔ x ⊓ y)",
"tactic": "rw [sup_inf_self]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.3131\nw x y z : α\ninst✝ ... | [
149,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
9
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousSubmodule_mul | [
{
"state_after": "R : Type u_1\nM : Type u_3\ninst✝¹ : CommSemiring R\nσ : Type u_2\ninst✝ : AddCommMonoid M\nw : σ → M\nm n : M\n⊢ ∀ (m_1 : MvPolynomial σ R),\n m_1 ∈ weightedHomogeneousSubmodule R w m →\n ∀ (n_1 : MvPolynomial σ R),\n n_1 ∈ weightedHomogeneousSubmodule R w n → m_1 * n_1 ∈ weigh... | [
190,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.zero_pow | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nb✝ b : ℕ\nx✝ : 0 < b + 1\n⊢ 0 ^ (b + 1) = 0",
"tactic": "simp [pow_succ]"
}
] | [
763,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Logic/Relation.lean | Symmetric.iff | [] | [
81,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
11
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.norm_rat | [
{
"state_after": "E : Type ?u.188465\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nr : ℚ\n⊢ ‖↑↑r‖ = Abs.abs ↑r",
"state_before": "E : Type ?u.188465\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nr : ℚ\n⊢ ‖↑r‖ = Abs.abs ↑r",
"tactic": "rw [← ofReal_rat_cast]"
},
{
"state_aft... | [
158,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Computability/Ackermann.lean | ack_succ_succ | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ack (m + 1) (n + 1) = ack m (ack (m + 1) n)",
"tactic": "rw [ack]"
}
] | [
80,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_diff_singleton | [] | [
2078,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2077,
1
] |
Mathlib/Data/Matrix/PEquiv.lean | PEquiv.toMatrix_trans | [
{
"state_after": "case a.h\nk : Type ?u.18057\nl : Type u_3\nm : Type u_1\nn : Type u_2\nα : Type v\ninst✝³ : Fintype m\ninst✝² : DecidableEq m\ninst✝¹ : DecidableEq n\ninst✝ : Semiring α\nf : l ≃. m\ng : m ≃. n\ni : l\nj : n\n⊢ toMatrix (PEquiv.trans f g) i j = (toMatrix f ⬝ toMatrix g) i j",
"state_before... | [
123,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.coeFn_zero | [] | [
403,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.bot_toSubalgebra | [
{
"state_after": "case h\nF : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nx✝ : E\n⊢ x✝ ∈ ⊥.toSubalgebra ↔ x✝ ∈ ⊥",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\n⊢ ⊥.toSubalgebra = ⊥",
"tactic": "ext"
},
{
... | [
99,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | PiLp.equiv_symm_single | [] | [
266,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_type_le | [] | [
171,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleFactorsFinset_eq_singleton_iff | [
{
"state_after": "ι : Type ?u.2753358\nα : Type u_1\nβ : Type ?u.2753364\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ f g : Perm α\n⊢ f = g → (IsCycle g ↔ IsCycle f)",
"state_before": "ι : Type ?u.2753358\nα : Type u_1\nβ : Type ?u.2753364\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ f g : Perm α\n⊢ cyc... | [
1467,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1461,
1
] |
Mathlib/Data/Set/Function.lean | Set.InjOn.bijOn_image | [] | [
958,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
957,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_add_aux | [
{
"state_after": "no goals",
"state_before": "x y a b c d : ℂ\n⊢ (a + b) * (c + d) + (a - b) * (c - d) = 2 * (a * c + b * d)",
"tactic": "ring"
}
] | [
627,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
9
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.sq_eq_normSq | [
{
"state_after": "R : Type u_1\ninst✝ : LinearOrderedCommRing R\na : ℍ[R]\n⊢ star a = a ∨ a = 0 ↔ star a = a",
"state_before": "R : Type u_1\ninst✝ : LinearOrderedCommRing R\na : ℍ[R]\n⊢ a ^ 2 = ↑(↑normSq a) ↔ a = ↑a.re",
"tactic": "rw [← star_eq_self, ← star_mul_self, sq, mul_eq_mul_right_iff, eq_comm]... | [
1299,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.coe_div | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Std/Data/String/Lemmas.lean | String.get!_eq_get | [] | [
232,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
232,
9
] |
Mathlib/Order/SymmDiff.lean | symmDiff_eq | [] | [
714,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictMono.dual | [] | [
240,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_neg_one | [
{
"state_after": "no goals",
"state_before": "⊢ sin (-(π / 2)) = -1",
"tactic": "rw [sin_neg, sin_pi_div_two]"
}
] | [
130,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | le_of_le_mul_of_le_one_right | [] | [
1110,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Prime.dvd_iff_one_le_factorization | [
{
"state_after": "no goals",
"state_before": "p n : ℕ\npp : Prime p\nhn : n ≠ 0\n⊢ p ∣ n ↔ p ^ 1 ∣ n",
"tactic": "simp"
}
] | [
502,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Algebra/Homology/Single.lean | CochainComplex.single₀_obj_x_dFrom | [
{
"state_after": "V : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZeroObject V\nX : V\nj : ℕ\n⊢ d ((single₀ V).obj X) j (j + 1) ≫ (xNextIso ((single₀ V).obj X) (_ : j + 1 = j + 1)).inv = 0",
"state_before": "V : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZe... | [
365,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Data/Real/Basic.lean | Real.is_glb_sInf | [
{
"state_after": "x y : ℝ\nS : Set ℝ\nh₁ : Set.Nonempty S\nh₂ : BddBelow S\n⊢ IsLUB (-S) (sSup (-S))",
"state_before": "x y : ℝ\nS : Set ℝ\nh₁ : Set.Nonempty S\nh₂ : BddBelow S\n⊢ IsGLB S (sInf S)",
"tactic": "rw [sInf_def, ← isLUB_neg', neg_neg]"
},
{
"state_after": "no goals",
"state_befor... | [
757,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
11
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.sInf_coe | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\nS : Set (LieSubmodule R L M)\n⊢ (⋂ (p : Submod... | [
430,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/GroupTheory/GroupAction/Units.lean | Units.smul_inv | [] | [
120,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.single_eq_zero | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ i : ι\nxi : β i\n⊢ i = i ∧ HEq xi 0 ∨ xi = 0 ∧ 0 = 0 ↔ xi = 0",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ ... | [
695,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Algebra/GroupWithZero/Semiconj.lean | SemiconjBy.inv_right₀ | [
{
"state_after": "case pos\nα : Type ?u.1223\nM₀ : Type ?u.1226\nG₀ : Type u_1\nM₀' : Type ?u.1232\nG₀' : Type ?u.1235\nF : Type ?u.1238\nF' : Type ?u.1241\ninst✝ : GroupWithZero G₀\na x y x' y' : G₀\nh : SemiconjBy a x y\nha : a = 0\n⊢ SemiconjBy a x⁻¹ y⁻¹\n\ncase neg\nα : Type ?u.1223\nM₀ : Type ?u.1226\nG₀ :... | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLE_refl | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝ : Category D\nB : C\nX : Subobject B\n⊢ ofLE X X (_ : X ≤ X) ≫ arrow X = 𝟙 (underlying.obj X) ≫ arrow X",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX✝ Y Z : C\nD : Type u₂\ninst✝ : Category D\nB : C\nX : Subobject B... | [
455,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Algebra/AddTorsor.lean | vadd_right_cancel_iff | [] | [
108,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.modByMonic_eq_of_dvd_sub | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : Semiring S\nhq : Monic q\np₁ p₂ : R[X]\nh : q ∣ p₁ - p₂\n✝ : Nontrivial R\n⊢ p₁ %ₘ q = p₂ %ₘ q",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]... | [
73,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_neg_atBot | [] | [
830,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | aemeasurable_iInf | [] | [
1277,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1275,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.of_eq | [
{
"state_after": "u : Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nb : R\n⊢ b = b",
"state_before": "u : Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na c b : R\nx✝¹ : a = c\nx✝ : b = c\n⊢ a = b",
"tactic": "subst_vars"
... | [
1084,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_limit | [] | [
527,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Std/Data/List/Lemmas.lean | List.elem_iff | [] | [
91,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
90,
9
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_preimage_singleton | [] | [
794,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_lt_nat | [] | [
900,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isTrail_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' v' : V\np : Walk G u' v'\n⊢ IsTrail (Walk.copy p (_ : u' = u') (_ : v' = v')) ↔ IsTrail p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V... | [
876,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.continuous_map | [] | [
199,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_single_same | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx✝ : (i : ↑↑s) → β ↑i\ni✝ i : ι\nx : β i\n⊢ erase i (single i x) = 0",
"tactic": "rw [erase_single, if_pos rfl]"
}
... | [
800,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_target' | [] | [
731,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/LinearAlgebra/Charpoly/Basic.lean | LinearMap.isIntegral | [] | [
79,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/CategoryTheory/PUnit.lean | CategoryTheory.equiv_pUnit_iff_unique | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\n⊢ Nonempty (C ≌ Discrete PUnit) → Nonempty C ∧ ∀ (x y : C), Nonempty (Unique (x ⟶ y))\n\ncase mpr\nC : Type u\ninst✝ : Category C\n⊢ (Nonempty C ∧ ∀ (x y : C), Nonempty (Unique (x ⟶ y))) → Nonempty (C ≌ Discrete PUnit)",
"state_before": "C : Type u\... | [
105,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_const | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/RingTheory/Artinian.lean | IsArtinianRing.isNilpotent_jacobson_bot | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsArtinianRing R\nJac : Ideal R := Ideal.jacobson ⊥\n⊢ IsNilpotent (Ideal.jacobson ⊥)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsArtinianRing R\n⊢ IsNilpotent (Ideal.jacobson ⊥)",
"tactic": "let Jac := Ideal.jacobson (⊥ : ... | [
421,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | ApproximatesLinearOn.toLocalHomeomorph_target | [] | [
515,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.op | [] | [
856,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.toLex_update_le_self_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nβ : ι → Type u_2\nr : ι → ι → Prop\ns : {i : ι} → β i → β i → Prop\ninst✝² : LinearOrder ι\ninst✝¹ : IsWellOrder ι fun x x_1 => x < x_1\ninst✝ : (i : ι) → PartialOrder (β i)\nx y : (i : ι) → β i\ni : ι\na : β i\n⊢ ↑toLex (update x i a) ≤ ↑toLex x ↔... | [
174,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/Order/Chebyshev.lean | MonovaryOn.sum_mul_sum_le_card_mul_sum | [
{
"state_after": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.17209\ninst✝ : LinearOrderedRing α\ns : Finset ι\nσ : Perm ι\nf g : ι → α\nhfg : MonovaryOn f g ↑s\n⊢ (∑ i in s, f i) * ∑ i in s, g i ≤ card s • ∑ i in s, f i * g i",
"state_before": "ι : Type u_1\nα : Type u_2\nβ : Type ?u.17209\ninst✝ : LinearOrder... | [
115,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | strictAnti_iff_map_pos | [] | [
277,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearEquiv.rank_eq | [] | [
201,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_assoc | [] | [
140,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
138,
11
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_comp_lmapDomain | [
{
"state_after": "case h.h\nα : Type u_1\nM : Type ?u.346247\nN : Type ?u.346250\nP : Type ?u.346253\nR : Type u_2\nS : Type ?u.346259\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Mo... | [
632,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.const_top | [] | [
703,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycle_swap_mul_aux₁ | [
{
"state_after": "ι : Type ?u.610936\nα✝ : Type ?u.610939\nβ : Type ?u.610942\nf g : Perm α✝\nx y : α✝\ninst✝² : DecidableEq α✝\ninst✝¹ : Fintype α✝\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\n⊢ ∀ {b x : α} {f : Perm α},\n ↑(swap x (↑f x) * f) b ≠ b → ↑(f ^ n) (↑f x) = b → ∃ i, ↑((swap x (↑f x) * f) ^ i) (↑... | [
464,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_of_emod_eq_zero | [] | [
676,
52
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
675,
1
] |
Mathlib/Algebra/Parity.lean | odd_iff_exists_bit1 | [
{
"state_after": "F : Type ?u.75707\nα : Type u_1\nβ : Type ?u.75713\nR : Type ?u.75716\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n a b : α\n⊢ a = b + b + 1 ↔ a = bit1 b",
"state_before": "F : Type ?u.75707\nα : Type u_1\nβ : Type ?u.75713\nR : Type ?u.75716\ninst✝¹ : Semiring α\ninst✝ : Semiring β\nm n a... | [
312,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.neg_domain | [] | [
447,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.conjAe_coe | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.div | [] | [
453,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
11
] |
Mathlib/Order/Filter/Extr.lean | isMaxFilter_const | [] | [
185,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lt_aleph0_iff_subtype_finite | [] | [
1491,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1490,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.mem_inf | [] | [
839,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Analysis/Normed/Group/BallSphere.lean | coe_neg_sphere | [] | [
33,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_id' | [] | [
1048,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/OpensLeCover.lean | TopCat.Presheaf.isSheaf_iff_isSheafOpensLeCover | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : TopCat\nF : Presheaf C X\nι : Type w\nU : ι → Opens ↑X\nY : Opens ↑X\nhY : Y = iSup U\n⊢ (∀ ⦃X_1 : Opens ↑X⦄ (S : Sieve X_1),\n S ∈ GrothendieckTopology.sieves (Opens.grothendieckTopology ↑X) X_1 →\n Nonempty (IsLimit (F.mapCone (Cocone.op (Presi... | [
251,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_eq_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα✝ : Type u_2\nf : α → α✝\nx : Option α\n⊢ Option.map f x = Option.bind x (some ∘ f)",
"tactic": "cases x <;> simp [Option.bind]"
}
] | [
137,
33
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
136,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.abs_prod | [] | [
278,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
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