file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/RingTheory/DedekindDomain/Factorization.lean | Ideal.finite_mulSupport_coe | [
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Mathlib/Data/Set/Basic.lean | Set.inter_eq_inter_iff_right | [] | [
997,
23
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996,
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Std/Data/Nat/Lemmas.lean | Nat.mul_div_right | [
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571,
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570,
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Mathlib/Data/Multiset/Basic.lean | Multiset.eq_replicate | [] | [
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47
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932,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.zero_update | [
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577,
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Mathlib/Order/Basic.lean | eq_or_gt_of_le | [] | [
402,
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Mathlib/LinearAlgebra/FreeModule/Finite/Rank.lean | FiniteDimensional.finrank_tensorProduct | [
{
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173,
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171,
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Mathlib/Algebra/BigOperators/Finsupp.lean | MonoidHom.map_finsupp_prod | [] | [
241,
25
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Mathlib/RingTheory/PrincipalIdealDomain.lean | Irreducible.coprime_or_dvd | [] | [
457,
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456,
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Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.limsup_measure_le_of_le_liminf_measure_compl | [] | [
165,
94
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161,
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_inf | [] | [
976,
10
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Mathlib/Data/Fin/Basic.lean | Fin.le_castSucc_iff | [
{
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}
] | [
1228,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | subset_interior_iff_isOpen | [
{
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"tactic": "simp only [interior_eq_iff_isOpen.symm, Subset.antisymm_iff, interior_subset, true_and]"
}
] | [
310,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_coeIdeal | [
{
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758,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.div_zero | [
{
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}
] | [
1363,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
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Mathlib/Order/Heyting/Hom.lean | CoheytingHom.cancel_left | [
{
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488,
94
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487,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycle.orderOf | [
{
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443,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
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Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_coeff_zero | [
{
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}
] | [
92,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.cone_nonempty | [
{
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"tactic": "... | [
715,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
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Mathlib/Data/Complex/Exponential.lean | Real.one_sub_div_pow_le_exp_neg | [
{
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"state_before": "n : ℕ\nt : ℝ\nht' : t ≤ ↑n\n⊢ (1 - t / ↑n) ^ n ≤ exp (-t)",
"tactic": "rcases eq_or_ne n 0 with (rfl | hn)"
},
{
"s... | [
2004,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1993,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.iSup_mul | [
{
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656,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_prod | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommSemiring R\ns✝ : Multiset ι\nf : ι → R[X]\ni : ι\ns : Multiset ι\nh :\n ↑derivative (Multiset.prod (Multiset.map f s)) =\n Multiset.sum (Multiset.map (fun i => Multiset.prod (Multiset.map f (Multiset.er... | [
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15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.epi_of_epi_left | [] | [
221,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_thickening_iff_exists_edist_lt | [] | [
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18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
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Mathlib/Data/Finset/Basic.lean | Finset.mem_inter | [] | [
1571,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1570,
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.mono | [
{
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529,
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.integrableOn_compact_subset | [] | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Countable.lean | Set.countable_setOf_finite_subset | [
{
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... | [
264,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Std/Data/Int/Lemmas.lean | Int.le_of_lt | [] | [
634,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
633,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sub_nat | [
{
"state_after": "no goals",
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"tactic": "simpa using rpow_sub_int hx y n"
}
] | [
342,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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Mathlib/Data/Set/NAry.lean | Set.image_image2_right_anticomm | [] | [
429,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
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Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_lt_one_left | [
{
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"tactic": "simpa only [one_mul] using mul_lt_mul_of_pos_right h hb"
}
] | [
686,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
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Mathlib/Data/List/Perm.lean | List.Perm.rec_heq | [
{
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540,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PushoutCocone.mk_ι_app_right | [] | [
845,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.existsUnique | [] | [
244,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/GroupTheory/Subsemigroup/Membership.lean | Subsemigroup.mem_sup_left | [
{
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83,
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Mathlib/Data/Finset/Basic.lean | Finset.sdiff_erase | [
{
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"tactic": "rw [← sdiff_singleton_eq_erase, sdiff_sdiff_eq_sdiff_union (singleton_subset_iff.2 h), inse... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Function.lean | StrictConvexOn.comp_strictConcaveOn | [] | [
175,
26
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172,
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Mathlib/Algebra/Star/Module.lean | selfAdjointPart_comp_subtype_selfAdjoint | [] | [
152,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_neg | [] | [
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46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Computability/Reduce.lean | OneOneEquiv.to_many_one | [] | [
206,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_C_zero | [] | [
727,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
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Mathlib/Order/Basic.lean | LE.le.not_lt_iff_eq | [] | [
268,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lmapDomain_apply | [] | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Subsingleton.einfsep | [
{
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102,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mul_le_right | [] | [
482,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
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Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.isTransitive_iff_mem_trans | [] | [
56,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_eq_one | [
{
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"tactic": "apply Iff.intro <;> intro"
},
{
"state_after": "case mp\nm n : ℕ\na✝ : n ! = 1\n⊢ ¬1 < 1",
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131,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_iInf' | [
{
"state_after": "α : Type u_3\nβ : Type ?u.31201\nγ : Type ?u.31204\nι✝ : Sort ?u.31207\nι'✝ : Sort ?u.31210\nl✝ l' : Filter α\np✝ : ι✝ → Prop\ns✝ : ι✝ → Set α\nt✝ : Set α\ni : ι✝\np' : ι'✝ → Prop\ns' : ι'✝ → Set α\ni' : ι'✝\nι : Type u_1\nι' : ι → Type u_2\nl : ι → Filter α\np : (i : ι) → ι' i → Prop\ns : (i ... | [
512,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.eq_one_of_pos_of_logb_eq_zero_of_base_lt_one | [] | [
335,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Separation.lean | nhdsSet_inj_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns t : Set α\n⊢ 𝓝ˢ s ≤ 𝓝ˢ t ∧ 𝓝ˢ t ≤ 𝓝ˢ s ↔ s ≤ t ∧ t ≤ s",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns t : Set α\n⊢ 𝓝ˢ s = 𝓝ˢ t ↔ s = t",
"tactic": "simp_rw [le_... | [
693,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.range_dualMap_eq_dualAnnihilator_ker_of_surjective | [
{
"state_after": "R : Type u_1\nM : Type u_2\nM' : Type u_3\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nhf : Function.Surjective ↑f\n⊢ range (dualMap f) = range (dualMap (mkQ (ker f)))",
"state_before": "R : Type u_1\nM :... | [
1310,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
src/lean/Init/Data/Nat/Div.lean | Nat.div_le_self | [
{
"state_after": "no goals",
"state_before": "n k : Nat\n⊢ n / k ≤ n",
"tactic": "induction n using Nat.strongInductionOn with\n| ind n ih =>\n rw [div_eq]\n cases (inferInstance : Decidable (0 < k ∧ k ≤ n)) with\n | isFalse h => simp [h]\n | isTrue h =>\n suffices (n - k) / k + 1 ≤ n by simp [h,... | [
54,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
42,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Matrix.lean | AffineBasis.toMatrix_inv_vecMul_toMatrix | [
{
"state_after": "ι : Type u₁\nk : Type u₂\nV : Type u₃\nP : Type u₄\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : AffineSpace V P\ninst✝³ : CommRing k\ninst✝² : Module k V\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nb b₂ : AffineBasis ι k P\nx : P\nhu : IsUnit (toMatrix b ↑b₂)\n⊢ vecMul (↑(coords b) x) (toMatrix b ↑b₂)⁻¹... | [
166,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.iSup_range_stdBasis_le_iInf_ker_proj | [
{
"state_after": "R : Type u_3\nι : Type u_1\ninst✝³ : Semiring R\nφ : ι → Type u_2\ninst✝² : (i : ι) → AddCommMonoid (φ i)\ninst✝¹ : (i : ι) → Module R (φ i)\ninst✝ : DecidableEq ι\nI J : Set ι\nh : Disjoint I J\ni : ι\nhi : i ∈ I\n⊢ comap (stdBasis R φ i) (⨅ (i : ι) (_ : i ∈ J), ker (proj i)) = ⊤",
"state... | [
108,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/Heyting/Basic.lean | Codisjoint.himp_le_of_right_le | [] | [
455,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.rel_symm_apply | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.82847\nδ : Type ?u.82850\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nu : δ → δ → Prop\ne : r ≃r s\nx : α\ny : β\n⊢ r x (↑(RelIso.symm e) y) ↔ s (↑e x) y",
"tactic": "rw [← e.map_rel_iff, e.apply_symm_apply]"... | [
795,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Data/Nat/Hyperoperation.lean | hyperoperation_ge_four_zero | [
{
"state_after": "case zero\nn : ℕ\n⊢ hyperoperation (n + 4) 0 Nat.zero = if Even Nat.zero then 1 else 0\n\ncase succ\nn kk : ℕ\nkih : hyperoperation (n + 4) 0 kk = if Even kk then 1 else 0\n⊢ hyperoperation (n + 4) 0 (Nat.succ kk) = if Even (Nat.succ kk) then 1 else 0",
"state_before": "n k : ℕ\n⊢ hyperope... | [
131,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.unit_rightAdjointUniq_hom_app | [
{
"state_after": "case a\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG G' : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F ⊣ G'\nx : C\n⊢ (adj1.unit.app x ≫ (rightAdjointUniq adj1 adj2).hom.app (F.obj x)).op = (adj2.unit.app x).op",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Ty... | [
252,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.coe_mkOfOrthogonalEqBot | [] | [
573,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
11
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_natCast | [] | [
282,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Set/Accumulate.lean | Set.accumulate_def | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/MvPolynomial/Expand.lean | MvPolynomial.map_expand | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type ?u.204198\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nf : R →+* S\np : ℕ\nφ : MvPolynomial σ R\n⊢ ↑(map f) (↑(expand p) φ) = ↑(expand p) (↑(map f) φ)",
"tactic": "simp [expand, map_bind₁]"
}
] | [
83,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.LiftRel.refl | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α → Prop\nH : Reflexive R\ns✝ s t : WSeq α\nh : s = t\n⊢ Computation.LiftRel (LiftRelO R fun x x_1 => x = x_1) (destruct s) (destruct s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → α → Prop\nH : Reflexive R\ns✝ s t : WSeq α\nh ... | [
545,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
536,
1
] |
Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.min_def | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nφ : Ultrafilter α\nK : LinearOrder β\nx y : Germ (↑φ) β\na b : α → β\nh : ↑a ≤ ↑b\n⊢ min ↑a ↑b = map₂ min ↑a ↑b\n\ncase inr\nα : Type u\nβ : Type v\nφ : Ultrafilter α\nK : LinearOrder β\nx y : Germ (↑φ) β\na b : α → β\nh : ↑b ≤ ↑a\n⊢ min ↑a ↑b = map₂ min ↑a ↑b... | [
233,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.integrable_iff_finMeasSupp | [] | [
378,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_embedding | [] | [
1355,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_add | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.decode₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.140489\nγ : Type ?u.140492\nδ : Type ?u.140495\nσ : Type ?u.140498\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\n⊢ Primrec₂ fun p a => encode a",
"tactic": "e... | [
770,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
11
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom | [
{
"state_after": "C : Type u_2\ninst✝³ : Category C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ pushout.inl ≫\n (colimit.isoColimitCocone\n { cocone := PushoutCocone.mk coprod.inl coprod.inr (_ : 0 ≫ coprod.inl = 0 ≫ coprod.inr),\n ... | [
213,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | sameRay_iff_norm_add | [] | [
211,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.sin_surjective | [
{
"state_after": "x : ℂ\n⊢ ∃ a, sin a = x",
"state_before": "⊢ Function.Surjective sin",
"tactic": "intro x"
},
{
"state_after": "case intro\nz : ℂ\n⊢ ∃ a, sin a = cos z",
"state_before": "x : ℂ\n⊢ ∃ a, sin a = x",
"tactic": "rcases cos_surjective x with ⟨z, rfl⟩"
},
{
"state_aft... | [
198,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Int.norm_cast_real | [] | [
1787,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1786,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.comp_contDiffWithinAt | [] | [
717,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.map_map | [] | [
434,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/RingTheory/PolynomialAlgebra.lean | PolyEquivTensor.toFunLinear_algebraMap_tmul_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝² : CommSemiring R\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nr : R\n⊢ ↑(toFunLinear R A) (↑(algebraMap R A) r ⊗ₜ[R] 1) = ↑(algebraMap R A[X]) r",
"tactic": "rw [toFunLinear_tmul_apply, toFunBilinear_apply_apply, Polynomial.a... | [
117,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | Valuation.map_neg | [] | [
292,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.bit1_mod_bit0 | [
{
"state_after": "m n : ℕ\nh₁ : bit1 (m * (n / m) + n % m) = bit1 n\n⊢ bit1 n % bit0 m = bit1 (n % m)",
"state_before": "m n : ℕ\n⊢ bit1 n % bit0 m = bit1 (n % m)",
"tactic": "have h₁ := congr_arg bit1 (Nat.div_add_mod n m)"
},
{
"state_after": "m n : ℕ\nh₁ : bit0 m * (n / m) + bit1 (n % m) = bi... | [
275,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.rel_head | [] | [
268,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.sub_zmodRepr_mem | [] | [
212,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_eq_self_iff | [
{
"state_after": "case refine'_1\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np : P\nv : V\nhp : secondInter s p v = p\n⊢ inner v (p -ᵥ s.center) = 0\n\ncase refine'_2\nV : Type u_2\nP : Type u_1\ni... | [
81,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | Antitone.tendsto_set_integral | [
{
"state_after": "α : Type u_1\nβ : Type ?u.314392\nE : Type u_2\nF : Type ?u.314398\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\ns : ℕ → Set α\nf : α → E\nhsm : ∀ (i : ℕ), MeasurableSet (s i)\nh_anti : Antitone s\nhfi : Integrable... | [
853,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Topology/Homotopy/Equiv.lean | Homeomorph.symm_toHomotopyEquiv | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae | [
{
"state_after": "ι : Type ?u.1646574\n𝕜 : Type ?u.1646577\nE : Type u_1\nF : Type ?u.1646583\nA : Type ?u.1646586\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : CompleteSpace E\ninst✝² : NormedSpace ℝ E\nf : ℝ → E\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\na b z : ℝ\nu v ua ub va vb : ι → ℝ\ninst✝¹... | [
619,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Topology/SubsetProperties.lean | isClopen_range_inr | [] | [
1648,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1647,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.mem_uIcc | [] | [
504,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Differentiable.ccosh | [] | [
472,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_mul_X_pow' | [
{
"state_after": "case inl\nR : Type u_1\ninst✝ : Semiring R\np : PowerSeries R\nn d : ℕ\nh : n ≤ d\n⊢ ↑(coeff R d) (p * X ^ n) = ↑(coeff R (d - n)) p\n\ncase inr\nR : Type u_1\ninst✝ : Semiring R\np : PowerSeries R\nn d : ℕ\nh : ¬n ≤ d\n⊢ ↑(coeff R d) (p * X ^ n) = 0",
"state_before": "R : Type u_1\ninst✝ ... | [
1621,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1615,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | skewAdjoint.bit0_mem | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type ?u.107570\ninst✝¹ : AddCommGroup R\ninst✝ : StarAddMonoid R\nx : R\nhx : x ∈ skewAdjoint R\n⊢ bit0 x ∈ skewAdjoint R",
"tactic": "rw [mem_iff, star_bit0, mem_iff.mp hx, bit0, bit0, neg_add]"
}
] | [
481,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Data/List/Basic.lean | List.drop_one | [] | [
2136,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2135,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_toAddMonoidHom | [] | [
148,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_mem_Ioc | [] | [
95,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate | [] | [
234,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_of_isUnit | [] | [
141,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.zero_smul_nonneg | [] | [
1360,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1357,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_eq_empty_iff_mem_false | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\np q : α → Prop\nx : α\n⊢ {x | x ∈ s ∧ p x} = ∅ ↔ ∀ (x : α), x ∈ s → ¬p x",
"tactic": "simp_rw [ext_iff, mem_sep_iff, mem_empty_iff_false, iff_false_iff, not_and]"
}
] | [
1439,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1438,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.94256\ns✝ t : Set α\ninst✝² : DecidableEq β\nf : α → β\ns : Set α\ninst✝¹ : Fintype ↑s\ninst✝ : Fintype ↑(f '' s)\n⊢ ↑(toFinset (f '' s)) = ↑(Finset.image f (toFinset s))",
"tactic": "simp"
}
] | [
771,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.ceil_logb_nat_cast | [
{
"state_after": "case inl\nb✝ x y : ℝ\nb : ℕ\nhb : 1 < b\nhr : 0 ≤ 0\n⊢ ⌈logb (↑b) 0⌉ = Int.clog b 0\n\ncase inr\nb✝ x y : ℝ\nb : ℕ\nr : ℝ\nhb : 1 < b\nhr✝ : 0 ≤ r\nhr : 0 < r\n⊢ ⌈logb (↑b) r⌉ = Int.clog b r",
"state_before": "b✝ x y : ℝ\nb : ℕ\nr : ℝ\nhb : 1 < b\nhr : 0 ≤ r\n⊢ ⌈logb (↑b) r⌉ = Int.clog b r... | [
379,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.iff_op | [] | [
73,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.hasStrictDerivAt_arctan | [
{
"state_after": "x : ℝ\nA : cos (arctan x) ≠ 0\n⊢ HasStrictDerivAt arctan (↑1 / (↑1 + x ^ 2)) x",
"state_before": "x : ℝ\n⊢ HasStrictDerivAt arctan (↑1 / (↑1 + x ^ 2)) x",
"tactic": "have A : cos (arctan x) ≠ 0 := (cos_arctan_pos x).ne'"
},
{
"state_after": "no goals",
"state_before": "x : ... | [
90,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
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