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/Algebra/Order/Monoid/WithTop.lean | WithTop.coe_add | [] | [
126,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_coeHom | [] | [
240,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/CategoryTheory/Adjunction/Reflective.lean | CategoryTheory.unit_obj_eq_map_unit | [
{
"state_after": "C : Type u₁\nD : Type u₂\nE : Type u₃\ninst✝³ : Category C\ninst✝² : Category D\ninst✝¹ : Category E\ni : D ⥤ C\ninst✝ : Reflective i\nX : C\n⊢ (ofRightAdjoint i).unit.app (i.obj ((leftAdjoint i).obj X)) ≫\n i.map ((ofRightAdjoint i).counit.app ((leftAdjoint i).obj X)) =\n i.map ((left... | [
53,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.coe_copy | [] | [
128,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | CommGroup.is_simple_iff_isCyclic_and_prime_card | [
{
"state_after": "case mp\nα : Type u\na : α\ninst✝¹ : Fintype α\ninst✝ : CommGroup α\n⊢ IsSimpleGroup α → IsCyclic α ∧ Nat.Prime (Fintype.card α)\n\ncase mpr\nα : Type u\na : α\ninst✝¹ : Fintype α\ninst✝ : CommGroup α\n⊢ IsCyclic α ∧ Nat.Prime (Fintype.card α) → IsSimpleGroup α",
"state_before": "α : Type ... | [
555,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
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Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.isometryOfOrthonormal_symm_apply | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1342675\nι' : Type ?u.1342678\n𝕜 : Type ?u.1342681\ninst✝⁹ : IsROrC 𝕜\nE : Type ?u.1342687\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nE' : Type ?u.1342707\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : InnerProductSpace 𝕜 E'\nF : ... | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.mem_submoduleImage_of_le | [
{
"state_after": "case refine'_1\nR : Type u_2\nR₁ : Type ?u.1592131\nR₂ : Type ?u.1592134\nR₃ : Type ?u.1592137\nR₄ : Type ?u.1592140\nS : Type ?u.1592143\nK : Type ?u.1592146\nK₂ : Type ?u.1592149\nM : Type u_3\nM'✝ : Type ?u.1592155\nM₁ : Type ?u.1592158\nM₂ : Type ?u.1592161\nM₃ : Type ?u.1592164\nM₄ : Type... | [
1752,
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1745,
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Mathlib/GroupTheory/Archimedean.lean | AddSubgroup.cyclic_of_min | [
{
"state_after": "case intro.intro\nG : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : Archimedean G\nH : AddSubgroup G\na : G\na_min : a ∈ lowerBounds {g | g ∈ H ∧ 0 < g}\na_in : a ∈ H\na_pos : 0 < a\n⊢ H = closure {a}",
"state_before": "G : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : ... | [
56,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
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Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_of_two_le | [
{
"state_after": "case intro\nR : Type u_1\nS : Type ?u.4734\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\nh : 2 ≤ 2 + n\n⊢ T R (2 + n) = 2 * X * T R (2 + n - 1) - T R (2 + n - 2)",
"state_before": "R : Type u_1\nS : Type ?u.4734\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\nh : 2 ≤ n\n⊢ T R n = 2 * X... | [
94,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Std/Data/List/Lemmas.lean | List.get_cons_drop | [] | [
703,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
701,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_fintypeIic | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Fintype.card ↑(Set.Iic b) = b + 1",
"tactic": "rw [Fintype.card_ofFinset, card_Iic]"
}
] | [
151,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.comp_val_c | [] | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.append_right | [] | [
304,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictDerivAt.sinh | [] | [
886,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | aestronglyMeasurable_derivWithin_Ioi | [] | [
830,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_normSq | [
{
"state_after": "no goals",
"state_before": "⊢ Continuous ↑normSq",
"tactic": "simpa [← normSq_eq_norm_mul_self] using\n (continuous_norm.mul continuous_norm : Continuous fun q : ℍ => ‖q‖ * ‖q‖)"
}
] | [
204,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_takeUntil_subset | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w : V\np : Walk G v w\nh : u ∈ support p\nx : V\nhx : x ∈ support (takeUntil p u h)\n⊢ x ∈ support (takeUntil p u h) ∨ x ∈ support (dropUntil p u h)",
"state_bef... | [
1136,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
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src/lean/Init/Data/Nat/Basic.lean | Nat.mul_le_mul_left | [] | [
441,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
437,
1
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.map_apply_div | [
{
"state_after": "case inl\nK : Type u\ninst✝⁴ : CommRing K\ninst✝³ : IsDomain K\nR : Type u_1\nF : Type u_2\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : MonoidWithZeroHomClass F K[X] R[X]\nφ : F\nhφ : K[X]⁰ ≤ Submonoid.comap φ R[X]⁰\np : K[X]\n⊢ ↑(map φ hφ) (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMa... | [
877,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot' | [] | [
1260,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.compCoverLifting | [] | [
92,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.pi_Ioc_ae_eq_pi_Icc | [] | [
526,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Data/Polynomial/Induction.lean | Polynomial.mem_span_C_coeff | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type x\nk : Type y\nA : Type z\na b : R\nm n : ℕ\ninst✝ : Semiring R\np✝ q r f : R[X]\nI : Ideal R[X]\np : Ideal R[X] := Ideal.span {g | ∃ i, g = ↑C (coeff f i)}\n⊢ f ∈ Ideal.span {g | ∃ i, g = ↑C (coeff f i)}",
"state_before": "R : Type u\nS : Type ... | [
97,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
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Mathlib/Order/Hom/Lattice.lean | InfHom.dual_id | [] | [
1416,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1415,
1
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Mathlib/Data/Sym/Basic.lean | SymOptionSuccEquiv.decode_encode | [
{
"state_after": "case pos\nα : Type u_1\nn : ℕ\ninst✝ : DecidableEq α\ns : Sym (Option α) (Nat.succ n)\nh : none ∈ s\n⊢ decode (encode s) = s\n\ncase neg\nα : Type u_1\nn : ℕ\ninst✝ : DecidableEq α\ns : Sym (Option α) (Nat.succ n)\nh : ¬none ∈ s\n⊢ decode (encode s) = s",
"state_before": "α : Type u_1\nn :... | [
650,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.monomial_zero_eq_C | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | HasFDerivAtFilter.iterate | [
{
"state_after": "case zero\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type ?u.135699\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.135794\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' ... | [
224,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
11
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.closure | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.6925\nα : Type ?u.6928\nX : Type u_2\nY : Type ?u.6934\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g : ι → Set X\nhf : LocallyFinite f\nx : X\n⊢ ∃ t, t ∈ 𝓝 x ∧ Set.Finite {i | Set.Nonempty ((fun i => closure (f i)) i ∩ t)}",
"state_before": "ι : ... | [
129,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.mul | [] | [
425,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
11
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.relatively_discrete | [] | [
319,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/Data/Seq/Computation.lean | Computation.orelse_empty | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation α\n⊢ IsBisimulation fun c₁ c₂ => (HOrElse.hOrElse c₂ fun x => empty α) = c₁",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation α\n⊢ (HOrElse.hOrElse c fun x => empty α) = c",
"tactic": "apply eq_of_bisim (fun c₁ c₂... | [
974,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.abs_div_tendsto_atTop_of_degree_gt | [
{
"state_after": "case pos\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhdeg : degree Q < degree P\nhQ : Q ≠ 0\nh : 0 ≤ leadingCoeff P / leadingCoeff Q\n⊢ Tendsto (fun x => abs (eval x P / eval x Q)) atTop atTop\n\ncase neg\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrd... | [
226,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_inter_subset_right | [] | [
350,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | div_div_self | [
{
"state_after": "α : Type ?u.28722\nM₀ : Type ?u.28725\nG₀ : Type u_1\nM₀' : Type ?u.28731\nG₀' : Type ?u.28734\nF : Type ?u.28737\nF' : Type ?u.28740\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\n⊢ a * a / a = a",
"state_before": "α : Type ?u.28722\nM₀ : Type ?u.28725\nG₀ : Type u_1\nM₀' : Type ?u.28731\nG₀' ... | [
412,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_compl_singleton_iff | [] | [
1776,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1775,
1
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Mathlib/Data/Complex/Module.lean | Complex.coe_basisOneI | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.104284\nS : Type ?u.104287\ni j : Fin 2\n⊢ ↑(↑basisOneI.repr (Matrix.vecCons 1 ![I] i)) j = ↑(Finsupp.single i 1) j",
"tactic": "fin_cases i <;> fin_cases j <;>\n simp [coe_basisOneI_repr, Finsupp.single_eq_of_ne, Matrix.cons_val_zero,\n Matr... | [
178,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Deprecated/Ring.lean | IsRingHom.map_neg | [
{
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114,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.castHom_bijective | [
{
"state_after": "n : ℕ\nR : Type u_1\ninst✝² : Ring R\ninst✝¹ : CharP R n\ninst✝ : Fintype R\nh : Fintype.card R = n\nthis : NeZero n\n⊢ Bijective ↑(castHom (_ : n ∣ n) R)",
"state_before": "n : ℕ\nR : Type u_1\ninst✝² : Ring R\ninst✝¹ : CharP R n\ninst✝ : Fintype R\nh : Fintype.card R = n\n⊢ Bijective ↑(c... | [
425,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_smul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1758951\nγ : Type ?u.1758954\nδ : Type ?u.1758957\nm : MeasurableSpace α\nμ ν : Measure α\nr : ℝ≥0∞\nf : α → ℝ≥0∞\nhf : Measurable f\ns : Set α\nhs : MeasurableSet s\n⊢ ↑↑(withDensity μ (r • f)) s = ↑↑(r • withDensity μ f) s",
"state_before": "α : Type u_1\nβ : Ty... | [
1591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
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Mathlib/Data/Part.lean | Part.mod_mem_mod | [
{
"state_after": "α : Type u_1\nβ : Type ?u.67366\nγ : Type ?u.67369\ninst✝ : Mod α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 % a = ma % mb",
"state_before": "α : Type u_1\nβ : Type ?u.67366\nγ : Type ?u.67369\ninst✝ : Mod α\na b : Part α\nma mb : α\nha : ma ∈ a... | [
785,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
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] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.refl_symm | [] | [
631,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.kronecker_add | [] | [
312,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
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] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.exists_mem_factors_of_dvd | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\na p : α\nha0 : a ≠ 0\nhp : Irreducible p\nx✝ : p ∣ a\nb : α\nhb : a = p * b\nhb0 : b = 0\n⊢ False",
"tactic": "simp_all"
},
{
"state_after... | [
500,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_dvd_gcd_of_dvd_left | [] | [
338,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.coe_sup' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.230811\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.230820\nι : Type ?u.230823\nκ : Type ?u.230826\ninst✝ : SemilatticeSup α\ns : Finset β\nH : Finset.Nonempty s\nf : β → α\n⊢ ↑(sup' s H f) = sup s (WithBot.some ∘ f)",
"tactic": "rw [sup', WithBot.co... | [
783,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/Order/Bounds/Basic.lean | upperBounds_Ioc | [] | [
720,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.preimage_sigmaMap_sigma | [] | [
178,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Mathlib/Analysis/Complex/Schwarz.lean | Complex.norm_dslope_le_div_of_mapsTo_ball | [
{
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110,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Algebra/Module/LinearMap.lean | AddMonoidHom.coe_toRatLinearMap | [] | [
793,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_inv | [] | [
297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackAssoc_inv_fst_fst | [
{
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2405,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2398,
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Mathlib/Data/List/Cycle.lean | List.nextOr_cons_of_ne | [
{
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62,
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Mathlib/Data/List/BigOperators/Basic.lean | List.single_le_prod | [
{
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514,
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507,
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_compl_iff | [] | [
879,
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878,
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Mathlib/Geometry/Manifold/ChartedSpace.lean | chart_source_mem_nhds | [] | [
549,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.freeGroupoidFunctor_id | [
{
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205,
25
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202,
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Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inl_isoPushout_hom | [
{
"state_after": "no goals",
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}
] | [
435,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Order/Category/FinPartOrd.lean | FinPartOrd_dual_comp_forget_to_partOrdCat | [] | [
116,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
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Mathlib/Algebra/Algebra/Hom.lean | AlgHom.ofLinearMap_toLinearMap | [
{
"state_after": "case H\nR : Type u\nA : Type v\nB : Type w\nC : Type u₁\nD : Type v₁\ninst✝⁸ : CommSemiring R\ninst✝⁷ : Semiring A\ninst✝⁶ : Semiring B\ninst✝⁵ : Semiring C\ninst✝⁴ : Semiring D\ninst✝³ : Algebra R A\ninst✝² : Algebra R B\ninst✝¹ : Algebra R C\ninst✝ : Algebra R D\nφ : A →ₐ[R] B\nmap_one : ↑(t... | [
405,
6
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402,
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Mathlib/Data/Real/NNReal.lean | NNReal.coe_one | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
11
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Mathlib/Data/Real/ENNReal.lean | ENNReal.zero_div | [] | [
1554,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1554,
19
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Mathlib/Logic/Basic.lean | congr_refl_left | [] | [
530,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
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Mathlib/Analysis/Complex/RealDeriv.lean | conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj | [
{
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188,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
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Mathlib/Data/Multiset/Powerset.lean | Multiset.powersetLenAux_perm | [
{
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227,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | fderivWithin_arctan | [] | [
184,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.eq_bot_iff | [
{
"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\n⊢ N ≤ ⊥ ↔ ∀ (m : M), m ∈ N → m = 0",
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501,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.mul_left_apply_of_ne | [
{
"state_after": "no goals",
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188,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/Data/Complex/Basic.lean | Complex.I_sq | [
{
"state_after": "no goals",
"state_before": "⊢ I ^ 2 = -1",
"tactic": "rw [sq, I_mul_I]"
}
] | [
694,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | ContinuousAt.stronglyMeasurableAtFilter | [] | [
592,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
1
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Mathlib/Data/Pi/Algebra.lean | Sum.elim_one_one | [] | [
449,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_mul | [] | [
749,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_sup_le_or_aux_right | [] | [
930,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
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Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.symm | [] | [
72,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
8
] |
Mathlib/Algebra/Order/Floor.lean | Int.lt_floor_add_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.125097\nα : Type u_1\nβ : Type ?u.125103\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a : α\n⊢ a < ↑⌊a⌋ + 1",
"tactic": "simpa only [Int.succ, Int.cast_add, Int.cast_one] using lt_succ_floor a"
}
] | [
687,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
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Mathlib/RingTheory/Multiplicity.lean | multiplicity.unit_right | [] | [
327,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
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Std/Data/List/Init/Lemmas.lean | List.reverseAux_eq | [] | [
121,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
120,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ioi_iff_exists_Ioc_subset | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : NoMaxOrder α\ninst✝ : DenselyOrdered α\na : α\ns : Set α\n⊢ (∃ u, u ∈ Ioi a ∧ Ioo a u ⊆ s) ↔ ∃ u, u ∈ Ioi a ∧ Ioc a u ⊆ s",
"state_before": "α : Type u\nβ : Type v\nγ... | [
1667,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1659,
1
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Mathlib/Analysis/Convex/Function.lean | strictConvexOn_iff_div | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.771270\nα : Type ?u.771273\nβ : Type u_3\nι : Type ?u.771279\ninst✝⁴ : LinearOrderedField 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : OrderedAddCommMonoid β\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 β\ns : Set E\nf : E → β\nh :\n ∀ ⦃x : E⦄,\n x ∈ s → ∀ ⦃y : E... | [
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54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
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Mathlib/Analysis/NormedSpace/Units.lean | nonunits.subset_compl_ball | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nx : R\nhx : x ∈ nonunits R\nh₁ : x ∈ Metric.ball 1 1\n⊢ ‖1 - x‖ < 1",
"tactic": "rwa [mem_ball_iff_norm'] at h₁"
}
] | [
100,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.frequently_lt_of_limsInf_lt | [] | [
1116,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.inter_mem_inf | [] | [
435,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Algebra/Star/Basic.lean | starRingEnd_apply | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_eq_bot_iff_compl_range | [] | [
2356,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2355,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.range_snd | [
{
"state_after": "no goals",
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601,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
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Mathlib/Analysis/NormedSpace/Basic.lean | rescale_to_shell_semi_normed | [] | [
297,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/Computability/EpsilonNFA.lean | εNFA.pumping_lemma | [] | [
171,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.im_star | [] | [
636,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.kerLift_mk | [] | [
1032,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | Right.one_le_pow_of_le | [
{
"state_after": "β : Type ?u.56986\nA : Type ?u.56989\nG : Type ?u.56992\nM : Type u_1\nR : Type ?u.56998\ninst✝² : Monoid M\ninst✝¹ : Preorder M\ninst✝ : CovariantClass M M (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\nx : M\nhx : 1 ≤ x\nn : ℕ\n⊢ 1 ≤ x * x ^ n",
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143,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
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Mathlib/Topology/Order/Basic.lean | isClosed_le_prod | [] | [
126,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.eraseNone_insertNone | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.18177\ns : Finset α\na✝ : α\n⊢ a✝ ∈ ↑eraseNone (↑insertNone s) ↔ a✝ ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.18177\ns : Finset α\n⊢ ↑eraseNone (↑insertNone s) = s",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "ca... | [
164,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.coe_eq_toEquiv | [] | [
325,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
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Mathlib/Topology/Separation.lean | Function.LeftInverse.closed_range | [] | [
1232,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictMono_of_le_iff_le | [] | [
543,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
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Mathlib/Data/Set/Basic.lean | Set.eq_univ_of_forall | [] | [
694,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Set.toFinset_smul | [] | [
2226,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2224,
1
] |
Mathlib/Topology/ContinuousOn.lean | nhdsWithin_restrict' | [] | [
193,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Computability/Partrec.lean | Computable.map_decode_iff | [
{
"state_after": "case h.e'_1.h.e'_7.h.h\nα : Type u_1\nβ : Type u_3\nγ : Type ?u.160634\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → β → σ\nx✝¹ : α\nx✝ : ℕ\n⊢ Option.map (f x✝¹) (decode x✝) = Option.bind (decode x✝) (Option.some ∘ f x✝¹)"... | [
664,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
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] |
Mathlib/Topology/PathConnected.lean | Path.extend_zero | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\nY : Type ?u.149853\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx y z : X\nι : Type ?u.149868\nγ : Path x y\n⊢ extend γ 0 = x",
"tactic": "simp"
}
] | [
271,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.invOf_submatrix_equiv_eq | [
{
"state_after": "l : Type ?u.381588\nm : Type u\nn : Type u'\nα : Type v\ninst✝⁶ : Fintype n\ninst✝⁵ : DecidableEq n\ninst✝⁴ : CommRing α\nA✝ B : Matrix n n α\ninst✝³ : Fintype m\ninst✝² : DecidableEq m\nA : Matrix m m α\ne₁ e₂ : n ≃ m\ninst✝¹ : Invertible A\ninst✝ : Invertible (submatrix A ↑e₁ ↑e₂)\nthis : In... | [
655,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
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