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/GroupTheory/QuotientGroup.lean | QuotientGroup.congr_mk | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto | [
{
"state_after": "Ω : Type u_2\ninst✝² : MeasurableSpace Ω\ninst✝¹ : TopologicalSpace Ω\ninst✝ : OpensMeasurableSpace Ω\nγ : Type u_1\nF : Filter γ\nμs : γ → ProbabilityMeasure Ω\nμ : ProbabilityMeasure Ω\n⊢ Tendsto (toFiniteMeasure ∘ μs) F (𝓝 (toFiniteMeasure μ)) ↔\n ∀ (f : Ω →ᵇ ℝ), Tendsto (fun i => ∫ (ω ... | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Algebra/Category/MonCat/Basic.lean | MonCat.coe_of | [] | [
123,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Int/Lemmas.lean | Int.natAbs_eq_iff_sq_eq | [
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a = natAbs b ↔ a * a = b * b",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a = natAbs b ↔ a ^ 2 = b ^ 2",
"tactic": "rw [sq, sq]"
},
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a = natAbs b ↔... | [
51,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | hasDerivWithinAt_inv | [] | [
79,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_inter_Ico | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na b c d : α\n⊢ Ico a b ∩ Ico c d = Ico (max a c) (min b d)",
"tactic": "rw [Ico, Ico, Ico, ← Finset.inter_val, Finset.Ico_inter_Ico]"
}
] | [
260,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.sup_smul | [] | [
208,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.apply_swap_eq_self | [
{
"state_after": "case pos\nα : Sort u_2\ninst✝ : DecidableEq α\nβ : Sort u_1\nv : α → β\ni j : α\nhv : v i = v j\nk : α\nhi : k = i\n⊢ v (↑(swap i j) k) = v k\n\ncase neg\nα : Sort u_2\ninst✝ : DecidableEq α\nβ : Sort u_1\nv : α → β\ni j : α\nhv : v i = v j\nk : α\nhi : ¬k = i\n⊢ v (↑(swap i j) k) = v k",
... | [
1638,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1630,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_int_cast | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Ring R\nn : ℤ\n⊢ natDegree ↑n = 0",
"tactic": "rw [← C_eq_int_cast, natDegree_C]"
}
] | [
546,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Order/Monotone/Union.lean | MonotoneOn.Iic_union_Ici | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\na : α\nf : α → β\nh₁ : MonotoneOn f (Iic a)\nh₂ : MonotoneOn f (Ici a)\n⊢ MonotoneOn f (Iic a ∪ Ici a)",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : Preorder β\na : α\nf : α → β\nh₁ : M... | [
113,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
11
] |
Mathlib/Order/Interval.lean | NonemptyInterval.map_map | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
src/lean/Init/SizeOfLemmas.lean | UInt8.sizeOf | [
{
"state_after": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝ } = toNat { val := val✝ } + 2",
"state_before": "a : UInt8\n⊢ SizeOf.sizeOf a = toNat a + 2",
"tactic": "cases a"
},
{
"state_after": "no goals",
"state_before": "case mk\nval✝ : Fin size\n⊢ SizeOf.sizeOf { val := val✝... | [
15,
36
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
14,
9
] |
Mathlib/Data/Polynomial/Inductions.lean | Polynomial.coeff_divX | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff (divX p) n = coeff p (1 + n)",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np q : R[X]\n⊢ coeff (divX p) n = coeff p (n + 1)",
... | [
48,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.coeff_opRingEquiv | [
{
"state_after": "case h\nR : Type u_1\ninst✝ : Semiring R\nn : ℕ\np : R[X]\n⊢ coeff (↑(opRingEquiv R) (op p)) n = op (coeff (unop (op p)) n)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np : R[X]ᵐᵒᵖ\nn : ℕ\n⊢ coeff (↑(opRingEquiv R) p) n = op (coeff (unop p) n)",
"tactic": "induction' p using Mu... | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.im_imJ | [] | [
125,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nA : Type u_2\ninst✝² : Monoid R\ninst✝¹ : NonUnitalNonAssocSemiring A\ninst✝ : DistribMulAction R A\nr₁ r₂ : R\n⊢ 0 = r₁ • 0 + r₂ • 0 + 0 * 0",
"tactic": "simp only [smul_zero, add_zero, MulZeroClass.mul_zero]"
}
] | [
394,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.coe_injective | [] | [
352,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.leRecOn_trans | [
{
"state_after": "case refl\nm✝ n✝ k✝ : ℕ\nC : ℕ → Sort u\nn m k : ℕ\nhnm : n ≤ m\nnext : {k : ℕ} → C k → C (k + 1)\nx : C n\n⊢ leRecOn (_ : n ≤ m) next x = leRecOn (_ : Nat.le m m) next (leRecOn hnm next x)\n\ncase step\nm✝ n✝ k✝¹ : ℕ\nC : ℕ → Sort u\nn m k✝ : ℕ\nhnm : n ≤ m\nnext : {k : ℕ} → C k → C (k + 1)\n... | [
424,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.nonneg_of_normalize_eq_self | [
{
"state_after": "no goals",
"state_before": "z : ℤ\nhz : ↑normalize z = z\n⊢ abs z = z",
"tactic": "rw [abs_eq_normalize, hz]"
}
] | [
124,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/FieldTheory/Finite/Polynomial.lean | MvPolynomial.map_restrict_dom_evalₗ | [
{
"state_after": "case intro\nK : Type u_1\nσ : Type u_2\ninst✝² : Field K\ninst✝¹ : Fintype K\ninst✝ : Finite σ\nval✝ : Fintype σ\n⊢ Submodule.map (evalₗ K σ) (restrictDegree σ K (Fintype.card K - 1)) = ⊤",
"state_before": "K : Type u_1\nσ : Type u_2\ninst✝² : Field K\ninst✝¹ : Fintype K\ninst✝ : Finite σ\... | [
155,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | tsum_mul_tsum_eq_tsum_sum_range | [
{
"state_after": "ι : Type ?u.34737\nκ : Type ?u.34740\nR : Type ?u.34743\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : NonUnitalNonAssocSemiring α\nf g : ℕ → α\ninst✝¹ : T3Space α\ninst✝ : TopologicalSemiring α\nhf : Summable f\nhg : Summable g\nhfg : Summable fun x => f x.fst * g x.snd\n⊢ ((∑' (n : ℕ),... | [
246,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin_symm | [] | [
332,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | FractionRing.mk_eq_div | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.450373\ninst✝⁵ : CommRing R\nM : Submonoid R\nS : Type ?u.450565\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nP : Type ?u.450802\ninst✝² : CommRing P\nA : Type u_1\ninst✝¹ : CommRing A\ninst✝ : IsDomain A\nK : Type ?u.450982\nr : A\ns : { x // x ∈ non... | [
311,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.support_ofFintype | [] | [
215,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Topology/Separation.lean | lift'_nhds_closure | [] | [
1542,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1541,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.intervalIntegrable_deriv_of_nonneg | [
{
"state_after": "case inl\nι : Type ?u.1879888\n𝕜 : Type ?u.1879891\nE : Type ?u.1879894\nF : Type ?u.1879897\nA : Type ?u.1879900\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝ : ℝ → E\ng' g φ : ℝ → ℝ\nf f' : ℝ → E\na b : ℝ\nhcont : ContinuousOn g [[a, b]]\nhderiv : ∀ (... | [
1307,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/MeasureTheory/Group/Arithmetic.lean | AEMeasurable.const_div | [] | [
311,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.id_def | [] | [
587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.map_prod_eq_map₂ | [
{
"state_after": "case a\nα : Type u_1\nα' : Type ?u.3075\nβ : Type u_2\nβ' : Type ?u.3081\nγ : Type u_3\nγ' : Type ?u.3087\nδ : Type ?u.3090\nδ' : Type ?u.3093\nε : Type ?u.3096\nε' : Type ?u.3099\nm✝ : α → β → γ\nf✝ f₁ f₂ : Filter α\ng✝ g₁ g₂ : Filter β\nh h₁ h₂ : Filter γ\ns✝ s₁ s₂ : Set α\nt t₁ t₂ : Set β\n... | [
70,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_def_field | [] | [
42,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_seq_def | [] | [
2613,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2611,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.zero_apply | [] | [
296,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | LinearIsometry.toAffineIsometry_linearIsometry | [
{
"state_after": "case h\n𝕜 : Type u_3\nV : Type u_1\nV₁ : Type ?u.35987\nV₂ : Type u_2\nV₃ : Type ?u.35993\nV₄ : Type ?u.35996\nP₁ : Type ?u.35999\nP : Type ?u.36002\nP₂ : Type ?u.36005\nP₃ : Type ?u.36008\nP₄ : Type ?u.36011\ninst✝²⁰ : NormedField 𝕜\ninst✝¹⁹ : SeminormedAddCommGroup V\ninst✝¹⁸ : SeminormedA... | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.const_add | [] | [
274,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/CategoryTheory/Preadditive/Yoneda/Injective.lean | CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditive_yoneda_obj' | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nJ : C\n⊢ Functor.PreservesEpimorphisms (yoneda.obj J) ↔ Functor.PreservesEpimorphisms (preadditiveYonedaObj J)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\nJ : C\n⊢ Injective J ↔ Functor.PreservesEpimorph... | [
54,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.addHaar_image_eq_zero_of_det_fderivWithin_eq_zero_aux | [
{
"state_after": "case inl\nE : Type u_1\nF : Type ?u.607843\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : FiniteDimensional ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ :... | [
657,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Data/Real/ENatENNReal.lean | ENat.toENNReal_one | [] | [
98,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.max_eq_zero_iff | [] | [
732,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
9
] |
Mathlib/Algebra/BigOperators/Basic.lean | Commute.sum_left | [] | [
1779,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1777,
1
] |
Mathlib/Data/Set/Sups.lean | Set.singleton_infs_singleton | [] | [
312,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixedPoints_submonoid_iSup | [] | [
104,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAt.sub | [] | [
493,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
8
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_abs_abs | [] | [
846,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.norm_rpow | [
{
"state_after": "case h.e'_6\nα : Type u_2\nE : Type u_1\nF : Type ?u.729318\nG : Type ?u.729321\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → E\nhf : Memℒp f p\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ... | [
839,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.toMeasure_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.85068\nγ : Type ?u.85071\ninst✝ : MeasurableSpace α\np : Pmf α\ns✝ t✝ s t : Set α\nhs : MeasurableSet s\nht : MeasurableSet t\nh : s ∩ support p ⊆ t\n⊢ ↑↑(toMeasure p) s ≤ ↑↑(toMeasure p) t",
"tactic": "simpa only [p.toMeasure_apply... | [
286,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | Complex.continuousAt_cpow_const_of_re_pos | [] | [
384,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Topology/Order/Basic.lean | IsCompact.bddAbove | [] | [
818,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | OpenEmbedding.continuousAt_iff | [] | [
1318,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1316,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.nonsing_inv_eq_ring_inverse | [
{
"state_after": "case pos\nl : Type ?u.181457\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nh_det : IsUnit (det A)\n⊢ A⁻¹ = Ring.inverse A\n\ncase neg\nl : Type ?u.181457\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹... | [
289,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/CategoryTheory/Abelian/Homology.lean | homology.map_eq_lift_desc'_right | [
{
"state_after": "A : Type u\ninst✝¹ : Category A\ninst✝ : Abelian A\nX Y Z : A\nf : X ⟶ Y\ng : Y ⟶ Z\nw : f ≫ g = 0\nX' Y' Z' : A\nf' : X' ⟶ Y'\ng' : Y' ⟶ Z'\nw' : f' ≫ g' = 0\nα : Arrow.mk f ⟶ Arrow.mk f'\nβ : Arrow.mk g ⟶ Arrow.mk g'\nh : α.right = β.left\n⊢ f ≫ α.right ≫ cokernel.π f' = 0",
"state_befor... | [
309,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.inv_rev | [] | [
1686,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1684,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.symm_dual_id | [] | [
1580,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1578,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_one | [] | [
1787,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1785,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_sInf | [] | [
507,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.X_mul_monomial | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nr : R\n⊢ X * ↑(monomial n) r = ↑(monomial (n + 1)) r",
"tactic": "rw [X_mul, monomial_mul_X]"
}
] | [
637,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sdiff_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.135885\nα : Type u_1\nβ : Type ?u.135891\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ (a \\ b) \\ a = ⊥",
"tactic": "rw [sdiff_sdiff_comm, sdiff_self, bot_sdiff]"
}
] | [
640,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.testBit_lor' | [] | [
505,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.zero_mem | [] | [
230,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
11
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_mul_cancel_left | [] | [
414,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_smul | [
{
"state_after": "α : Type u_4\nE✝ : Type ?u.693591\nF : Type u_3\nF' : Type ?u.693597\nG : Type ?u.693600\n𝕜 : Type u_2\np : ℝ≥0∞\ninst✝¹² : NormedAddCommGroup E✝\ninst✝¹¹ : NormedSpace ℝ E✝\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedAddCommGroup F'\ninst✝⁷ : NormedSpace ℝ F'\ni... | [
800,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_congr_right | [] | [
989,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_mul_Iio_of_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a c : α\nh : c < 0\n⊢ (fun x x_1 => x * x_1) c ⁻¹' Iio a = Ioi (a / c)",
"tactic": "simpa only [mul_comm] using preimage_mul_const_Iio_of_neg a h"
}
] | [
643,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Algebra/Category/GroupCat/Zero.lean | GroupCat.isZero_of_subsingleton | [
{
"state_after": "case refine'_1\nG : GroupCat\ninst✝ : Subsingleton ↑G\nX : GroupCat\nf : G ⟶ X\n⊢ f = default\n\ncase refine'_2\nG : GroupCat\ninst✝ : Subsingleton ↑G\nX : GroupCat\nf : X ⟶ G\n⊢ f = default",
"state_before": "G : GroupCat\ninst✝ : Subsingleton ↑G\n⊢ IsZero G",
"tactic": "refine' ⟨fun ... | [
37,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.of_to_nat' | [
{
"state_after": "⊢ cond true Num.bit1 Num.bit0 0 = Num.pos 1",
"state_before": "⊢ Num.ofNat' ↑1 = Num.pos 1",
"tactic": "erw [@Num.ofNat'_bit true 0, Num.ofNat'_zero]"
},
{
"state_after": "no goals",
"state_before": "⊢ cond true Num.bit1 Num.bit0 0 = Num.pos 1",
"tactic": "rfl"
},
{... | [
355,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Iio b = Iio (b - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
386,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.zoom_del | [
{
"state_after": "α : Type u_1\ncut : α → Ordering\npath : Path α\nt' : RBNode α\npath' : Path α\nt : RBNode α\n⊢ zoom cut t path = (t', path') →\n del path\n (match t with\n | nil => nil\n | node c a y b =>\n match cut y with\n | Ordering.lt =>\n match isBla... | [
88,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
72,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_abs_integral_norm | [
{
"state_after": "ι : Type ?u.11937590\n𝕜 : Type ?u.11937593\nE : Type u_1\nF : Type ?u.11937599\nA : Type ?u.11937602\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\n⊢ ‖∫ (x : ℝ) in Ι a b, f x ∂μ‖ ≤ ‖∫ (x : ℝ) in Ι a b, ‖f x... | [
551,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Std/Data/Int/DivMod.lean | Int.mod_neg | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ mod a (-b) = mod a b",
"tactic": "rw [mod_def, mod_def, Int.div_neg, Int.neg_mul_neg]"
}
] | [
341,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
340,
9
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.subring_closure_le | [] | [
696,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | ContinuousLinearMap.toSesqForm_apply_norm_le | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3387427\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nE' : Type u_3\ninst✝¹ : NormedAddCommGroup E'\ninst✝ : InnerProductSpace �... | [
1845,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.mapAlgEquiv_symm | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_δ'' | [
{
"state_after": "n : ℕ\ni : Fin (n + 3)\nj : Fin (n + 2)\nH : i ≤ ↑Fin.castSucc j\n⊢ δ j ≫ δ (↑Fin.castSucc (Fin.castLT i (_ : ↑i < n + 2))) = δ j ≫ δ i\n\nn : ℕ\ni : Fin (n + 3)\nj : Fin (n + 2)\nH : i ≤ ↑Fin.castSucc j\n⊢ Fin.castLT i (_ : ↑i < n + 2) ≤ j",
"state_before": "n : ℕ\ni : Fin (n + 3)\nj : Fi... | [
242,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Algebra/Algebra/Pi.lean | Pi.algebraMap_def | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/CategoryTheory/Limits/FunctorCategory.lean | CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\nD : Type u'\ninst✝³ : Category D\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : HasLimitsOfShape J C\ni j : K\nF : J ⥤ K ⥤ C\nf : i ⟶ j\n⊢ (limitObjIsoLimitCompEvaluation F i).inv ≫ (limit F).map f =... | [
249,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Std/Data/List/Lemmas.lean | List.getLast!_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : α\nl : List α\ninst✝ : Inhabited α\n⊢ getLast! (a :: l) = getLastD l a",
"tactic": "simp [getLast!, getLast_eq_getLastD]"
}
] | [
473,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
472,
1
] |
Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.continuous_inr | [] | [
74,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.eq_comp_symm | [] | [
425,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/Homology/Single.lean | ChainComplex.single₀_obj_X_dTo | [
{
"state_after": "V : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZeroObject V\nX : V\nj : ℕ\n⊢ (xPrevIso ((single₀ V).obj X) (_ : j + 1 = j + 1)).hom ≫ d ((single₀ V).obj X) (j + 1) j = 0",
"state_before": "V : Type u\ninst✝² : Category V\ninst✝¹ : HasZeroMorphisms V\ninst✝ : HasZe... | [
168,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isPredLimit_iff | [
{
"state_after": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na b : α\nC : α → Sort ?u.16674\n⊢ ¬IsSuccLimit (↑toDual a) ↔ ∃ b, ¬IsMin b ∧ pred b = a",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na b : α\nC : α → Sort ?u.16674\n⊢ ¬IsPredLimit a ↔ ∃ b, ¬IsMin ... | [
345,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Std/Data/List/Init/Lemmas.lean | List.head_cons | [] | [
28,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
28,
9
] |
Mathlib/Data/List/Chain.lean | List.Chain.iff | [] | [
45,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongMono_comp | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\ninst✝² : StrongMono f\ninst✝¹ : StrongMono g\nX✝ Y✝ : C\nz✝ : X✝ ⟶ Y✝\ninst✝ : Epi z✝\n⊢ HasLiftingProperty z✝ (f ≫ g)",
"state_before": "C : Type u\ninst✝² : Category C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\ninst✝¹ : StrongMono ... | [
114,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.map_neg | [] | [
105,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.lift₂Expand_of | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.FG.map₂ | [] | [
440,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.toEquiv_eq_coe | [] | [
203,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.Prime.prod_divisors | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : CommMonoid α\np : ℕ\nf : ℕ → α\nh : Prime p\n⊢ ∏ x in Nat.divisors p, f x = f p * f 1",
"tactic": "rw [← cons_self_properDivisors h.ne_zero, prod_cons, h.prod_properDivisors]"
}
] | [
389,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.independent_of_dfinsupp_lsum_injective | [
{
"state_after": "ι : Type u_3\nR : Type u_1\nS : Type ?u.488476\nM : ι → Type ?u.488481\nN : Type u_2\ndec_ι : DecidableEq ι\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\np : ι → Submodule R N\nh : Function.Injective ↑(↑(lsum ℕ) fun i => Submodule.subtype (p i))\n⊢ ∀ (i : ι) (x : { x // x... | [
453,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_iff_left_ne_and_right_mem_image_Ioi | [
{
"state_after": "case refine'_1\nR : Type u_1\nV : Type u_2\nV' : Type ?u.490916\nP : Type u_3\nP' : Type ?u.490922\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y z : P\nh : Sbtw R x y z\n⊢ z ∈ ↑(lineMap x y) '' Set.Ioi 1\n\ncase refine'_2\nR : Type u_1... | [
724,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.comp | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
651,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Init/Algebra/Classes.lean | lt_of_lt_of_incomp | [] | [
398,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.smul_mem_pointwise_smul_iff | [] | [
108,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.comap_comap | [] | [
585,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.isBounded_sup | [
{
"state_after": "case inl\n𝕜 : Type u_1\n𝕜₂ : Type u_3\n𝕝 : Type ?u.136429\n𝕝₂ : Type ?u.136432\nE : Type u_2\nF : Type u_4\nG : Type ?u.136441\nι : Type u_5\nι' : Type u_6\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : NormedField 𝕜₂\ninst✝² : AddCommGroup F\ninst✝¹ : M... | [
261,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.intermediate_value_Iii | [] | [
185,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.xgcd_aux_fst | [
{
"state_after": "no goals",
"state_before": "x y : ℕ\n⊢ ∀ (n : ℕ) (s t s' t' : ℤ), (xgcdAux 0 s t n s' t').fst = gcd 0 n",
"tactic": "simp"
},
{
"state_after": "x✝ y✝ x y : ℕ\nh : 0 < x\nIH : ∀ (s t s' t' : ℤ), (xgcdAux (y % x) s t x s' t').fst = gcd (y % x) x\ns t s' t' : ℤ\n⊢ gcd (y % x) x = ... | [
117,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/List/Lattice.lean | List.bagInter_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl✝ l₁ l₂ : List α\np : α → Prop\na : α\ninst✝ : DecidableEq α\nl : List α\n⊢ List.bagInter l [] = []",
"tactic": "cases l <;> rfl"
}
] | [
213,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.sizeOf_get | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : SizeOf α\nas : List α\ni : Fin (length as)\n⊢ sizeOf (get as i) < sizeOf as",
"tactic": "match as, i with\n| a::as, ⟨0, _⟩ => simp_arith [get]\n| a::as, ⟨i+1, h⟩ =>\n have ih := sizeOf_get as ⟨i, Nat.le_of_succ_le_succ h⟩\n apply Nat... | [
166,
15
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
160,
9
] |
Mathlib/ModelTheory/Satisfiability.lean | Cardinal.empty_infinite_Theory_isComplete | [
{
"state_after": "no goals",
"state_before": "L : Language\nκ : Cardinal\nT : Theory L\n⊢ lift (card Language.empty) ≤ lift ℵ₀",
"tactic": "simp"
}
] | [
685,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_pow_left_dvd_pow_gcd | [] | [
585,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.