file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | UniqueDiffWithinAt.eq | [] | [
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51
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282,
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Mathlib/CategoryTheory/Yoneda.lean | CategoryTheory.yonedaSectionsSmall_inv_app_apply | [] | [
423,
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420,
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Mathlib/Algebra/Hom/Group.lean | MulHom.ext | [] | [
650,
20
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649,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableAt.cos | [] | [
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38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
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Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.prod | [
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104,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_quadratic | [
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1207,
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Mathlib/LinearAlgebra/Orientation.lean | Basis.orientation_unitsSMul | [
{
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168,
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Mathlib/Data/Fin/Interval.lean | Fin.card_fintypeIic | [
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216,
39
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Mathlib/Analysis/NormedSpace/Star/Exponential.lean | Commute.expUnitary_add | [
{
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92
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Mathlib/GroupTheory/Index.lean | Subgroup.inf_relindex_right | [
{
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] | [
137,
48
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Mathlib/Init/Logic.lean | let_value_heq | [
{
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_le_of_nonempty | [] | [
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Mathlib/RingTheory/Ideal/Basic.lean | Ideal.bot_isMaximal | [
{
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{
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63
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Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAtFilter.comp_hasFDerivAtFilter | [
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Mathlib/Logic/Basic.lean | ball_of_forall | [] | [
1062,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/WithBot.lean | WithBot.lt_iff_exists_coe | [
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... | [
285,
69
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283,
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Mathlib/NumberTheory/Padics/Hensel.lean | ncs_tendsto_lim | [] | [
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Mathlib/GroupTheory/Solvable.lean | isSolvable_of_top_eq_bot | [] | [
131,
11
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130,
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Mathlib/Order/CompleteBooleanAlgebra.lean | sSup_inf_sSup | [
{
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] | [
129,
44
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.mul | [] | [
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26
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Mathlib/Data/Set/Image.lean | Set.bex_image_iff | [
{
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}
] | [
239,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittSub_vars | [] | [
404,
30
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403,
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Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_X_sub_C | [] | [
145,
51
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144,
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Mathlib/Data/PFunctor/Multivariate/W.lean | MvPFunctor.wMk_eq | [] | [
248,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
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Mathlib/Analysis/Calculus/Dslope.lean | differentiableWithinAt_dslope_of_ne | [
{
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.map_smul | [] | [
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Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.of_zsmul | [
{
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}
] | [
152,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Basic.lean | List.splitOnP_cons | [
{
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Std/Data/Array/Lemmas.lean | Array.data_swap | [
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src/lean/Init/Prelude.lean | Nat.lt_of_le_of_lt | [] | [
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.dual_ordConnected_iff | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.9938\ninst✝¹ ... | [
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218,
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Mathlib/CategoryTheory/Subobject/WellPowered.lean | CategoryTheory.wellPowered_of_essentiallySmall_monoOver | [] | [
66,
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64,
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Mathlib/Data/Nat/Order/Basic.lean | Nat.find_pos | [
{
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}
] | [
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575,
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Path.ordered_iff | [
{
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.coeFn_comp₂ | [
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.map_extend_symm_nhdsWithin_range | [
{
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Mathlib/Algebra/Order/Floor.lean | Int.fract_div_mul_self_add_zsmul_eq | [
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Mathlib/Order/Filter/NAry.lean | Filter.map₂_sup_left | [
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.weightedSMul_add_measure | [
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Mathlib/Analysis/Normed/Group/Basic.lean | Real.nnnorm_two | [
{
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Mathlib/Logic/Encodable/Basic.lean | Encodable.skolem | [] | [
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Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.inf_mem_closed_subalgebra | [
{
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.induction_on₃ | [] | [
415,
54
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Mathlib/Order/Disjoint.lean | Codisjoint.sup_right' | [] | [
351,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/RingTheory/Ideal/Over.lean | Ideal.IsIntegralClosure.isMaximal_of_isMaximal_comap | [] | [
321,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxFilter.comp_mono | [] | [
318,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/RingTheory/TensorProduct.lean | TensorProduct.AlgebraTensorModule.restrictScalars_curry | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.not_mem_Icc_of_gt | [] | [
721,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/Data/Quot.lean | Quotient.out_equiv_out | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort ?u.34616\ns : Setoid α\nx y : Quotient s\n⊢ out x ≈ out y ↔ x = y",
"tactic": "rw [← Quotient.eq_mk_iff_out, Quotient.out_eq]"
}
] | [
397,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_right | [] | [
1356,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1356,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_X | [] | [
150,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_sum_subset | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.192546\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np q : MvPolynomial σ R\nι : Type u_2\nt : Finset ι\nφ : ι → MvPolynomial σ R\ninst✝ : DecidableEq σ\n⊢ vars (∑ i in t, φ i) ⊆ Finset.biUnion t f... | [
427,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/Topology/Connected.lean | QuotientMap.image_connectedComponent | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.111703\nπ : ι → Type ?u.111708\ninst✝¹ : TopologicalSpace α\ns t u v : Set α\ninst✝ : TopologicalSpace β\nf : α → β\nhf : QuotientMap f\nh_fibers : ∀ (y : β), IsConnected (f ⁻¹' {y})\na : α\n⊢ f '' connectedComponent a = conne... | [
1098,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.induce_self_verts | [
{
"state_after": "case verts.h\nι : Sort ?u.260819\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' G'' : Subgraph G\ns s' : Set V\nx✝ : V\n⊢ x✝ ∈ (induce G' G'.verts).verts ↔ x✝ ∈ G'.verts\n\ncase Adj.h.h.a\nι : Sort ?u.260819\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' G'' : Subgraph G\ns s' : Set V\nx✝¹ x✝ ... | [
1179,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.homEquiv_apply_eq | [] | [
170,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.id_pre | [
{
"state_after": "no goals",
"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\ninst✝² : Category K\nC : Type u\ninst✝¹ : Category C\nF✝ : J ⥤ C\ninst✝ : HasLimitsOfShape J C\nG : J ⥤ C\nα : F✝ ⟶ G\nF : J ⥤ C\n⊢ pre F (𝟭 J) = lim.map (leftUnitor F).inv",
"tactic": "aesop_cat"
}
] | [
556,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | OrthonormalBasis.coe_ofRepr | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.767988\n𝕜 : Type u_2\ninst✝¹⁰ : IsROrC 𝕜\nE : Type u_3\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.768017\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type ?u.768035\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ ... | [
379,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.surjective_iff_hasRightInverse | [] | [
507,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.lt_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\nf : α → β\nhf : LeftOrdContinuous f\nh : Injective f\nx y : α\n⊢ f x < f y ↔ x < y",
"tactic": "simp only [lt_iff_le_not_le, hf.le_iff h]"
}
] | [
106,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieSubmodule.trivial_lie_oper_zero | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\ninst✝⁷ : CommRing R\ninst✝⁶ : LieRing L\ninst✝⁵ : LieAlgebra R L\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : LieRingModule L M\ninst✝¹ : LieModule R L M\nN N' : LieSubmodule R L M\nI J : LieIdeal R L\ninst✝ : LieModule.IsTrivial L M\nthis : ⁅I, N... | [
305,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_or | [] | [
762,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iff_isCompact_in_subtype | [] | [
911,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_quotient_le | [] | [
242,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_prod | [] | [
2250,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2248,
1
] |
Mathlib/Data/Polynomial/UnitTrinomial.lean | Polynomial.trinomial_middle_coeff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nk m n : ℕ\nu v w : R\nhkm : k < m\nhmn : m < n\n⊢ coeff (trinomial k m n u v w) m = v",
"tactic": "rw [trinomial_def, coeff_add, coeff_add, coeff_C_mul_X_pow, coeff_C_mul_X_pow, coeff_C_mul_X_pow,\n if_neg hkm.ne', if_pos r... | [
61,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Std/Data/List/Lemmas.lean | List.contains_eq_any_beq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : BEq α\nl : List α\na : α\n⊢ contains l a = any l fun x => a == x",
"tactic": "induction l with simp | cons b l => cases a == b <;> simp [*]"
},
{
"state_after": "no goals",
"state_before": "case cons\nα : Type u_1\ninst✝ : B... | [
877,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
876,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_snd | [] | [
797,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | edist_mul_mul_le | [
{
"state_after": "𝓕 : Type ?u.1099733\n𝕜 : Type ?u.1099736\nα : Type ?u.1099739\nι : Type ?u.1099742\nκ : Type ?u.1099745\nE : Type u_1\nF : Type ?u.1099751\nG : Type ?u.1099754\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na a₁✝ a₂✝ b b₁✝ b₂✝ : E\nr r₁ r₂ : ℝ\na₁ a₂ b₁ b₂ : E\n⊢ ↑(nndist (a... | [
1673,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1669,
1
] |
Mathlib/Data/Int/Units.lean | Int.eq_one_or_neg_one_of_mul_eq_one' | [
{
"state_after": "z w : ℤ\nh : z * w = 1\nh' : w * z = 1\n⊢ z = 1 ∧ w = 1 ∨ z = -1 ∧ w = -1",
"state_before": "z w : ℤ\nh : z * w = 1\n⊢ z = 1 ∧ w = 1 ∨ z = -1 ∧ w = -1",
"tactic": "have h' : w * z = 1 := mul_comm z w ▸ h"
},
{
"state_after": "no goals",
"state_before": "z w : ℤ\nh : z * w =... | [
61,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.cast_rfl | [] | [
474,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coe_reindex | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_toSubalgebra | [] | [
98,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Zoomed.toRootOrdered | [] | [
256,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
252,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_refl | [] | [
423,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.xor_not_right | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (a : Bool), (xor a !a) = true",
"tactic": "decide"
}
] | [
278,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearMap.proj_apply | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_lt_im | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | a < z.im} = {z | z.im = a}",
"tactic": "simpa only [frontier_Ioi] using frontier_preimage_im (Ioi a)"
}
] | [
173,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnion_congr_of_le | [] | [
340,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\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✝ : DivisionMonoid α\na : α\nm n : ℤ\n⊢ a ^ (m * n) = (a ^ n) ^ m",
"tactic": "rw [mul_comm, zpow_mul]"
}
] | [
159,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_injective | [] | [
207,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Topology/Basic.lean | closure_eq_cluster_pts | [] | [
1329,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Algebra/Category/ModuleCat/Biproducts.lean | ModuleCat.biprodIsoProd_inv_comp_snd | [] | [
92,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.trans_eq | [] | [
1672,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1671,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.IsMaximal.ne_top | [] | [
300,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_def | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.125486\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np✝ q : MvPolynomial σ R\ninst✝ : DecidableEq σ\np : MvPolynomial σ R\n⊢ Multiset.toFinset (degrees p) = Multiset.toFinset (degrees p)",
"state_before": "R : Type u\nS : Typ... | [
283,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.univ_mul_of_one_mem | [] | [
990,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuousWithinAt | [] | [
68,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/Analysis/SpecialFunctions/Bernstein.lean | bernstein.variance | [
{
"state_after": "n : ℕ\nh : 0 < ↑n\nx : ↑I\nh' : ↑n ≠ 0\n⊢ ∑ k : Fin (n + 1), (↑x - ↑(k/ₙ)) ^ 2 * ↑(bernstein n ↑k) x = ↑x * (1 - ↑x) / ↑n",
"state_before": "n : ℕ\nh : 0 < ↑n\nx : ↑I\n⊢ ∑ k : Fin (n + 1), (↑x - ↑(k/ₙ)) ^ 2 * ↑(bernstein n ↑k) x = ↑x * (1 - ↑x) / ↑n",
"tactic": "have h' : (n : ℝ) ≠ 0 :... | [
139,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBy_isInternal | [
{
"state_after": "R : Type u_2\nM : Type u_3\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nι : Type u_1\ninst✝ : DecidableEq ι\nS : Finset ι\nq : ι → R\nhq : Set.Pairwise (↑S) (IsCoprime on q)\nhM : Module.IsTorsionBySet R M ↑(⨅ (a : ι) (_ : a ∈ S), Ideal.span {q a})\n⊢ DirectSum.IsInterna... | [
508,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_ge_iff_bounded_gt | [] | [
139,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.cantorFunctionAux_true | [
{
"state_after": "no goals",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\nh : f n = true\n⊢ cantorFunctionAux c f n = c ^ n",
"tactic": "simp [cantorFunctionAux, h]"
}
] | [
68,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Logic/Basic.lean | not_or_of_imp | [] | [
361,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | UniformEquicontinuous.equicontinuous | [] | [
148,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.natCast_lt_top | [
{
"state_after": "x : ℕ\nh : ↑x = ⊤\n⊢ ¬True = ⊤.Dom",
"state_before": "x : ℕ\nh : ↑x = ⊤\n⊢ ¬(↑x).Dom = ⊤.Dom",
"tactic": "simp only [dom_natCast]"
},
{
"state_after": "no goals",
"state_before": "x : ℕ\nh : ↑x = ⊤\n⊢ ¬True = ⊤.Dom",
"tactic": "exact true_ne_false"
}
] | [
353,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Topology/SubsetProperties.lean | ClosedEmbedding.locallyCompactSpace | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.149230\nπ : ι → Type ?u.149235\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns t : Set α\ninst✝ : LocallyCompactSpace β\nf : α → β\nhf : ClosedEmbedding f\nx : α\n⊢ HasBasis (𝓝 x) (fun s => s ∈ 𝓝 (f x) ∧ IsCompact s) fun s => f ⁻¹' s",
"st... | [
1192,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1186,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/StrictInitial.lean | CategoryTheory.Limits.initial.subsingleton_to | [] | [
129,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cases_succ | [
{
"state_after": "case mk\nn✝ m n : ℕ\nC : Fin (n + 1) → Sort u_1\nH0 : C 0\nHs : (i : Fin n) → C (succ i)\nval✝ : ℕ\nisLt✝ : val✝ < n\n⊢ cases H0 Hs (succ { val := val✝, isLt := isLt✝ }) = Hs { val := val✝, isLt := isLt✝ }",
"state_before": "n✝ m n : ℕ\nC : Fin (n + 1) → Sort u_1\nH0 : C 0\nHs : (i : Fin n... | [
1742,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_iff_not_mem_span | [
{
"state_after": "ι : Type u'\nι' : Type ?u.1204971\nR : Type ?u.1204974\nK : Type u_1\nM : Type ?u.1204980\nM' : Type ?u.1204983\nM'' : Type ?u.1204986\nV : Type u\nV' : Type ?u.1204991\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : AddCommGroup V'\ninst✝¹ : Module K V\ninst✝ : Module K V'\nv : ι ... | [
1172,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.ext | [] | [
104,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Combinatorics/SimpleGraph/Hasse.lean | SimpleGraph.hasse_preconnected_of_pred | [
{
"state_after": "α : Type u_1\nβ : Type ?u.6930\ninst✝² : LinearOrder α\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\na b : α\n⊢ ReflTransGen (Function.swap (hasse α).Adj) b a",
"state_before": "α : Type u_1\nβ : Type ?u.6930\ninst✝² : LinearOrder α\ninst✝¹ : PredOrder α\ninst✝ : IsPredArchimedean α\... | [
99,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
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