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/FieldTheory/Separable.lean | Polynomial.Separable.of_mul_right | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\nf g : R[X]\nh : Separable (g * f)\n⊢ Separable g",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\nf g : R[X]\nh : Separable (f * g)\n⊢ Separable g",
"tactic": "rw [mul_co... | [
92,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.transferTransversal_apply' | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝ : Group G\nH : Subgroup G\ng : G\nq : orbitRel.Quotient { x // x ∈ zpowers g } (G ⧸ H)\nk : ZMod (minimalPeriod ((fun x x_1 => x • x_1) g) (Quotient.out' q))\n⊢ ↑(↑(toEquiv (_ : ↑(transferTransversal H g) ∈ leftTransversals ↑H)) (g ^ ↑k • Quoti... | [
638,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.not_lt | [] | [
221,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/DualNumber.lean | DualNumber.lift_apply_eps | [
{
"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\ne : { e // e * e = 0 }\n⊢ ↑(↑lift e) ε = ↑e",
"tactic": "simp only [lift_apply_apply, fst_eps, map_zero, snd_eps, one_smul, zero_add]"
}
] | [
120,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
src/lean/Init/Prelude.lean | Nat.not_lt_zero | [] | [
1576,
21
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1575,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_denumerable | [] | [
1628,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.convergents'Aux_succ_some | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn✝ : ℕ\ninst✝ : DivisionRing K\ns : Stream'.Seq (Pair K)\np : Pair K\nh : Stream'.Seq.head s = some p\nn : ℕ\n⊢ convergents'Aux s (n + 1) = p.a / (p.b + convergents'Aux (Stream'.Seq.tail s) n)",
"tactic": "si... | [
187,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.finsuppTotal_apply_eq_of_fintype | [
{
"state_after": "case h\nι : Type u_1\nM : Type u_3\ninst✝³ : AddCommGroup M\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nv : ι → M\nhv : Submodule.span R (Set.range v) = ⊤\ninst✝ : Fintype ι\nf : ι →₀ { x // x ∈ I }\n⊢ ∀ (i : ι), ↑0 • v i = 0",
"state_before": "ι : Type u_1\nM : T... | [
1909,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1906,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.refl | [
{
"state_after": "case H\nε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // ¬p a }\nx : ε\n⊢ ↑(subtypeCongr (Equiv.refl { a // p a }) (Equiv.refl { a // ¬p a })) x = ↑(Equiv.refl ε) x",
"state_before": "ε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\n... | [
588,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.funInvIdAssoc_hom_app | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ne : C ≌ D\nF : C ⥤ E\nX : C\n⊢ 𝟙 (F.obj (e.inverse.obj (e.functor.obj X))) ≫ F.map (e.unitIso.inv.app X) ≫ 𝟙 (F.obj X) = F.map ((unitInv e).app X)",
"state_before": "C : Type u₁\ninst✝² :... | [
328,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanCompIso_app_zero | [] | [
352,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_inv_cancel | [
{
"state_after": "case intro\nα : Type ?u.226273\nβ : Type ?u.226276\nb c d : ℝ≥0∞\nr p q a : ℝ≥0\nh0 : ↑a ≠ 0\n⊢ ↑a * (↑a)⁻¹ = 1",
"state_before": "α : Type ?u.226273\nβ : Type ?u.226276\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh0 : a ≠ 0\nht : a ≠ ⊤\n⊢ a * a⁻¹ = 1",
"tactic": "lift a to ℝ≥0 using ht"
},
{
... | [
1384,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
11
] |
Mathlib/Data/List/Func.lean | List.Func.length_add | [] | [
332,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.FinMeasSupp.map₂ | [] | [
1233,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
11
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsAlt.self_eq_zero | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_div_base | [
{
"state_after": "case inl\nb n : ℕ\nhb : b ≤ 1\n⊢ log b (n / b) = log b n - 1\n\ncase inr\nb n : ℕ\nhb : 1 < b\n⊢ log b (n / b) = log b n - 1",
"state_before": "b n : ℕ\n⊢ log b (n / b) = log b n - 1",
"tactic": "cases' le_or_lt b 1 with hb hb"
},
{
"state_after": "case inr.inl\nb n : ℕ\nhb : 1... | [
216,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Analysis/NormedSpace/MStructure.lean | IsLprojection.coe_sup | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/Lattice.lean | le_sup_of_le_left | [] | [
153,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_eq_of_dvd_sub | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.46050\ninst✝² : CommRing α\ninst✝¹ : IsDomain α\ninst✝ : NormalizedGCDMonoid α\ns : Finset β\nf g : β → α\na : α\n⊢ (∀ (x : β), x ∈ s → a ∣ f x - g x) → GCDMonoid.gcd a (gcd s f) = GCDMonoid.gcd a (gcd s g)",
"state_before": "α : Type u_2\nβ : Type u... | [
307,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₂_monomial_one | [
{
"state_after": "no goals",
"state_before": "σ : Type u_3\nτ : Type ?u.1299781\nR : Type u_1\nS : Type u_2\nT : Type ?u.1299790\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* MvPolynomial σ S\nd : σ →₀ ℕ\n⊢ ↑(bind₂ f) (↑(monomial d) 1) = ↑(mo... | [
355,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.algebraMap_eq_inl_comp | [] | [
587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.toHomeomorph_injective | [] | [
663,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_list_prod | [] | [
315,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_const_div_atTop_nhds_0_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.533\nβ : Type ?u.536\nι : Type ?u.539\nC : ℝ\n⊢ Tendsto (fun n => C / ↑n) atTop (𝓝 0)",
"tactic": "simpa only [MulZeroClass.mul_zero] using tendsto_const_nhds.mul tendsto_inverse_atTop_nhds_0_nat"
}
] | [
39,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.le_trans | [
{
"state_after": "a✝ b✝ c✝ a b c : ℚ\nhab : Rat.Nonneg (b - a)\nhbc : Rat.Nonneg (c - b)\n⊢ a ≤ c",
"state_before": "a✝ b✝ c✝ a b c : ℚ\nhab : a ≤ b\nhbc : b ≤ c\n⊢ a ≤ c",
"tactic": "rw [Rat.le_iff_Nonneg] at hab hbc"
},
{
"state_after": "a✝ b✝ c✝ a b c : ℚ\nhab : Rat.Nonneg (b - a)\nhbc : Rat.... | [
189,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
11
] |
Mathlib/Deprecated/Subgroup.lean | Additive.isAddSubgroup_iff | [
{
"state_after": "case mk.mk\nG : Type u_1\nH : Type ?u.2672\nA : Type ?u.2675\na a₁ a₂ b c : G\ninst✝¹ : Group G\ninst✝ : AddGroup A\ns : Set G\nh₃ : ∀ {a : Additive G}, a ∈ s → -a ∈ s\nh₁ : 0 ∈ s\nh₂ : ∀ {a b : Additive G}, a ∈ s → b ∈ s → a + b ∈ s\n⊢ IsSubgroup s",
"state_before": "G : Type u_1\nH : Typ... | [
71,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/DualQuaternion.lean | Quaternion.re_fst_dualNumberEquiv | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_C_mul_of_mul_leadingCoeff_eq_one | [
{
"state_after": "R : Type u\nS : Type v\na b✝ : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nb : R\nhp : b * leadingCoeff p = 1\n⊢ leadingCoeff (↑C b * p) = 1",
"state_before": "R : Type u\nS : Type v\na b✝ : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\nb : R\nhp : b * leadingCoef... | [
83,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.not_fuzzy_of_le | [] | [
944,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoUniformlyOn.congr_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng✝ : ι → α\ng : α → β\nhf : TendstoUniformlyOn F f p s\nhfg : EqOn f g s\nu : Set (β × β)\nhu : u ∈ 𝓤 β\n⊢ ∀ᶠ (n ... | [
226,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_sInf | [] | [
1489,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1488,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.toReal_le_toReal | [] | [
386,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconvexOn.dual | [] | [
73,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.tendsto | [] | [
192,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Topology/Separation.lean | Filter.Tendsto.limUnder_eq | [] | [
1057,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/Topology/Separation.lean | exists_open_nhds_disjoint_closure | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T25Space α\nx y : α\nh : x ≠ y\n⊢ ∃ u, x ∈ u ∧ IsOpen u ∧ ∃ v, y ∈ v ∧ IsOpen v ∧ Disjoint (closure u) (closure v)",
"tactic": "simpa only [exists_prop, and_assoc] using\n ((nhds_basis_opens x).li... | [
1015,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1010,
1
] |
Mathlib/Topology/Constructions.lean | continuous_isLeft | [] | [
876,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_inj | [
{
"state_after": "σ : Type u_2\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\ns t : σ\nh : X s = X t\n⊢ s = t",
"state_before": "σ : Type u_2\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Nontrivial R\ns t : σ\n⊢ X s = X t → s = t",
"tactic": "intro h"
},
{
"state_after": "σ : Type u_2\... | [
554,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/GroupTheory/Coset.lean | QuotientGroup.induction_on' | [] | [
489,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.mul_apply | [] | [
390,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.algHom_subsingleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS✝ : Type v\nK : Type w\ninst✝⁴ : CommRing R\nf✝ : R[X]\ninst✝³ : CommRing S✝\ni : R →+* S✝\na : S✝\nh : eval₂ i a f✝ = 0\ninst✝² : Algebra R S✝\nhfx : ↑(aeval a) f✝ = 0\nS : Type u_1\ninst✝¹ : CommRing S\ninst✝ : Algebra R S\nr : R\nf g : AdjoinRoot... | [
364,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.invUnitsSub_mul_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.167170\ninst✝¹ : Ring R\ninst✝ : Ring S\nu : Rˣ\n⊢ invUnitsSub u * (↑(C R) ↑u - X) = 1",
"tactic": "simp [mul_sub, sub_sub_cancel]"
}
] | [
59,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Finmap.lean | Finmap.erase_erase | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na a' : α\ns✝ : Finmap β\ns : AList β\n⊢ (erase a (erase a' ⟦s⟧)).entries = (erase a' (erase a ⟦s⟧)).entries",
"tactic": "simp only [AList.erase_erase, erase_toFinmap]"
}
] | [
459,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.neg_imK | [] | [
916,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
9
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_map | [] | [
332,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Algebra/Lie/Abelian.lean | LieModule.coe_maxTrivLinearMapEquivLieModuleHom | [
{
"state_after": "case h\nR : Type u\nL : Type v\nM : Type w\nN : Type w₁\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : LieRingModule L... | [
231,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_c_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.592326\nF : Type ?u.592329\nK : Type ?u.592332\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝ : Semiring R\nha : P.a = 0\nhb : P.b = 0\nhc : P.c = 0\n⊢ natDegree (toPoly P) = 0",
"tactic": "rw [of_c_eq_zero ha hb hc, natDegree_C]"
... | [
434,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.Measure.ae_eq_pi | [] | [
465,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.trans_le | [] | [
573,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Iio_ae_eq_Iic' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.595108\nγ : Type ?u.595111\nδ : Type ?u.595114\nι : Type ?u.595117\nR : Type ?u.595120\nR' : Type ?u.595123\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set... | [
2968,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2967,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.eq_of_le_of_finrank_eq | [] | [
855,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.hasBasis_iInf | [
{
"state_after": "case refine'_1\nα : Type u_3\nβ : Type ?u.33284\nγ : Type ?u.33287\nι✝ : Sort ?u.33290\nι'✝ : Sort ?u.33293\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... | [
526,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.p_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf : Hom P Q\n⊢ P.p ≫ f.f = f.f",
"tactic": "rw [f.comm, ← assoc, P.idem]"
}
] | [
88,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Init/Logic.lean | or_comm' | [] | [
166,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
23
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.limit_ext_iff | [] | [
176,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.66086\nι : Sort x\nf✝ g : Filter α\ns t x : Set α\nf : ι → Filter α\n⊢ x ∈ iSup f ↔ ∀ (i : ι), x ∈ f i",
"tactic": "simp only [← Filter.mem_sets, iSup_sets_eq, iff_self_iff, mem_iInter]"
}
] | [
573,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
1
] |
Mathlib/Topology/Separation.lean | Filter.Tendsto.eventually_ne | [] | [
746,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Topology/DenseEmbedding.lean | Dense.denseEmbedding_val | [] | [
307,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_comp_eq | [] | [
256,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_succ | [] | [
351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/RingTheory/Localization/Submodule.lean | IsLocalization.mem_span_iff | [
{
"state_after": "case mp\nR : Type u_2\ninst✝¹¹ : CommRing R\nM : Submonoid R\nS : Type u_3\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nP : Type ?u.169815\ninst✝⁸ : CommRing P\ng : R →+* P\nT : Submonoid P\nhy : M ≤ Submonoid.comap g T\nQ : Type ?u.170647\ninst✝⁷ : CommRing Q\ninst✝⁶ : Algebra P Q\ninst✝⁵ : I... | [
166,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/Calculus/LagrangeMultipliers.lean | IsLocalExtrOn.exists_multipliers_of_hasStrictFDerivAt_1d | [
{
"state_after": "case intro.intro.intro\nE : Type u_1\nF : Type ?u.62036\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nf✝ : E → F\nφ : E → ℝ\nx₀ : E\nf'✝ : E →L[ℝ] F\nφ' : E →L[ℝ] ℝ\nf : E → ... | [
99,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_bot | [] | [
278,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.comp_id | [] | [
251,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | RingHom.unop_map_list_prod | [] | [
247,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Topology/Maps.lean | Inducing.mapClusterPt_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.3026\nδ : Type ?u.3029\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : Inducing f\na : α\nl : Filter α\n⊢ NeBot (𝓝 (f a) ⊓ map f l) ↔ NeBot (𝓝 a ⊓ l)",
"state_befor... | [
117,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | tendsto_pow_div_pow_atTop_zero | [
{
"state_after": "𝕜 : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\np q : ℕ\nhpq : p < q\n⊢ Tendsto (fun x => x ^ (↑p - ↑q)) atTop (𝓝 0)",
"state_before": "𝕜 : Type u_1\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology... | [
76,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.exists_subset_or_subset_of_two_mul_lt_ncard | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.137499\ns t : Set α\na b x y : α\nf : α → β\nn : ℕ\nhst : 2 * n < ncard (s ∪ t)\n⊢ ∃ r, n < ncard r ∧ (r ⊆ s ∨ r ⊆ t)",
"tactic": "classical\nhave hu := Finite_of_ncard_ne_zero ((Nat.zero_le _).trans_lt hst).ne.symm\nrw [ncard_eq_to... | [
631,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Data/PFun.lean | PFun.bind_defined | [] | [
244,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.mul_X_injective | [] | [
307,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Real.cos_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : ℝ\n⊢ cos θ = 0 ↔ ∃ k, θ = (2 * ↑k + 1) * π / 2",
"tactic": "exact_mod_cast @Complex.cos_eq_zero_iff θ"
}
] | [
213,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Sign.lean | SignType.neg_iff | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ a < 0 ↔ a = -1",
"tactic": "cases a <;> decide"
}
] | [
187,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.disjoint | [] | [
2886,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2884,
11
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_sUnion | [
{
"state_after": "case h\nx x✝ : ZFSet\n⊢ x✝ ∈ toSet (⋃₀ x) ↔ x✝ ∈ ⋃₀ (toSet '' toSet x)",
"state_before": "x : ZFSet\n⊢ toSet (⋃₀ x) = ⋃₀ (toSet '' toSet x)",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h\nx x✝ : ZFSet\n⊢ x✝ ∈ toSet (⋃₀ x) ↔ x✝ ∈ ⋃₀ (toSet '' toSet... | [
1104,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_add_left | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1072971\nG : Type ?u.1072974\n𝕜 : Type ?u.1072977\np : ℝ≥0∞\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace ℝ E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedAddCommGroup F'\ninst✝⁵ : NormedSpace ℝ F'\nins... | [
1094,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.cauchy_induction' | [
{
"state_after": "a b c : ℕ\nP : ℕ → Prop\nh : ∀ (n : ℕ), P (n + 1) → P n\nseed : ℕ\nhs : P seed\nhi : ∀ (x : ℕ), seed ≤ x → P x → ∃ y, x < y ∧ P y\nn : ℕ\n⊢ Set.Finite {x | P x} → False",
"state_before": "a b c : ℕ\nP : ℕ → Prop\nh : ∀ (n : ℕ), P (n + 1) → P n\nseed : ℕ\nhs : P seed\nhi : ∀ (x : ℕ), seed ≤... | [
363,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Order/Filter/ModEq.lean | Nat.frequently_modEq | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : n ≠ 0\nd m : ℕ\n⊢ ((fun a => a + d) ∘ fun x => n • id x) m ≡ d [MOD n]",
"tactic": "simp [Nat.modEq_iff_dvd, ← sub_sub]"
}
] | [
28,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_mul_left | [] | [
905,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.ofScientific_true_def | [
{
"state_after": "m e : Nat\n⊢ (if true = true then normalize (↑m) (10 ^ e) else ↑↑(m * 10 ^ e)) = mkRat (↑m) (10 ^ e)",
"state_before": "m e : Nat\n⊢ Rat.ofScientific m true e = mkRat (↑m) (10 ^ e)",
"tactic": "unfold Rat.ofScientific"
},
{
"state_after": "m e : Nat\n⊢ (if true = true then mkRa... | [
307,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
306,
1
] |
Mathlib/Analysis/Convex/StrictConvexSpace.lean | strictConvex_closedBall | [
{
"state_after": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NormedLinearOrderedField 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : StrictConvexSpace 𝕜 E\nx : E\nr : ℝ\nhr : r ≤ 0\n⊢ StrictConvex 𝕜 (closedBall x r)\n\ncase inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝³ : NormedLinearOrd... | [
87,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_le_div | [
{
"state_after": "ι : Type ?u.69452\nα : Type u_1\nβ : Type ?u.69458\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhc : 0 ≤ c\nhac : a ≤ c\nhd : 0 < d\nhbd : d ≤ b\n⊢ a * d ≤ c * b",
"state_before": "ι : Type ?u.69452\nα : Type u_1\nβ : Type ?u.69458\ninst✝ : LinearOrderedSemifield α\na b c d e... | [
392,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.toAddSubgroup_strictMono | [] | [
275,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableAt.const_smul | [] | [
93,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_subset_iff_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nα' : Type ?u.4764\nβ : Type u_3\nβ' : Type ?u.4770\nγ : Type u_1\nγ' : Type ?u.4776\nδ : Type ?u.4779\nδ' : Type ?u.4782\nε : Type ?u.4785\nε' : Type ?u.4788\nζ : Type ?u.4791\nζ' : Type ?u.4794\nν : Type ?u.4797\nf f' : α → β → γ\ng g' : α → β → γ... | [
95,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/SymmDiff.lean | himp_bihimp_left | [] | [
593,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subsingleton_coe | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\n⊢ Subsingleton ↑s → Set.Subsingleton s\n\ncase mpr\nα : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns✝ s₁ s₂ t t₁ t₂ u s : Set α\n⊢ Set.Subsingleton s → Subsingleton ↑s",
"state_before"... | [
2414,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2410,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.lift_mkRingHom_apply | [
{
"state_after": "R : Type u₁\ninst✝⁴ : Semiring R\nS : Type u₂\ninst✝³ : CommSemiring S\nA : Type u₃\ninst✝² : Semiring A\ninst✝¹ : Algebra S A\nr✝ : R → R → Prop\nT : Type u₄\ninst✝ : Semiring T\nf : R →+* T\nr : R → R → Prop\nw : ∀ ⦃x y : R⦄, r x y → ↑f x = ↑f y\nx : R\n⊢ ↑(↑{\n toFun := fun f =... | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_one | [] | [
439,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.natIsoOfCompFullyFaithful_hom | [
{
"state_after": "case w.h\nC : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nE : Type u_2\ninst✝² : Category E\nF G : C ⥤ D\nH : D ⥤ E\ninst✝¹ : Full H\ninst✝ : Faithful H\ni : F ⋙ H ≅ G ⋙ H\nx✝ : C\n⊢ (natIsoOfCompFullyFaithful H i).hom.app x✝ = (natTransOfCompFullyFaithful H i.hom).app x✝",... | [
229,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivWithinAt.comp | [
{
"state_after": "𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace 𝕜 F\nE : Type w\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : 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\n𝕜' : Type u_1\ninst✝³... | [
173,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.dist_right | [] | [
411,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
11
] |
Mathlib/SetTheory/Lists.lean | Lists.isList_of_mem | [] | [
297,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Algebra/Group/ULift.lean | ULift.smul_down | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/PNat/Basic.lean | Nat.succPNat_mono | [] | [
85,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Infix.lean | List.prefix_concat | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.160\nl✝ l₁ l₂ l₃ : List α\na✝ b : α\nm n : ℕ\na : α\nl : List α\n⊢ l <+: concat l a",
"tactic": "simp"
}
] | [
73,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.coprod_unique | [
{
"state_after": "no goals",
"state_before": "A : Type ?u.68969\nB : Type ?u.68972\nG : Type ?u.68975\nH : Type ?u.68978\nM : Type u_2\nN : Type u_1\nP : Type u_3\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : CommMonoid P\nf✝ : M →* P\ng : N →* P\nf : M × N →* P\nx : M × N\n⊢ ↑(coprod (comp f (in... | [
656,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.apply_order_ne_zero' | [] | [
252,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearEquiv.coord_self | [] | [
327,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sq_sin_pi_div_three | [
{
"state_after": "x : ℝ\n⊢ cos (π / 2 - π / 3) ^ 2 = cos (π / 6) ^ 2",
"state_before": "x : ℝ\n⊢ sin (π / 3) ^ 2 = 3 / 4",
"tactic": "rw [← cos_pi_div_two_sub, ← sq_cos_pi_div_six]"
},
{
"state_after": "case e_a.e_x\nx : ℝ\n⊢ π / 2 - π / 3 = π / 6",
"state_before": "x : ℝ\n⊢ cos (π / 2 - π /... | [
901,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf₂_le_of_le | [] | [
813,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.