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/Data/Int/LeastGreatest.lean | Int.exists_greatest_of_bdd | [
{
"state_after": "P : ℤ → Prop\ninst✝ : DecidablePred P\nHbdd : ∃ b, ∀ (z : ℤ), P z → z ≤ b\nHinh : ∃ z, P z\nb : ℤ\nHb : ∀ (z : ℤ), P z → z ≤ b\n⊢ ∃ ub, P ub ∧ ∀ (z : ℤ), P z → z ≤ ub",
"state_before": "P : ℤ → Prop\ninst✝ : DecidablePred P\nHbdd : ∃ b, ∀ (z : ℤ), P z → z ≤ b\nHinh : ∃ z, P z\n⊢ ∃ ub, P ub... | [
106,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/MeasureTheory/Function/AEMeasurableSequence.lean | aeSeq.iSup | [
{
"state_after": "ι : Sort u_2\nα : Type u_3\nβ : Type u_1\nγ : Type ?u.727906\ninst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nf : ι → α → β\nμ : MeasureTheory.Measure α\np : α → (ι → β) → Prop\ninst✝¹ : CompleteLattice β\ninst✝ : Countable ι\nhf : ∀ (i : ι), AEMeasurable (f i)\nhp : ∀ᵐ (x : α) ∂μ, p x... | [
140,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_subset_Ioo | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.16340\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Ioo a₁ b₁ ⊆ Ioo a₂ b₂",
"tactic": "simpa [← coe_subset] using Set.Ioo_subset_Ioo ha hb"
}
] | [
175,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | linearIndependent_le_basis | [
{
"state_after": "case inl\nK : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι✝ : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.369966\nR : Type u\ninst✝³ : Ring R\ninst✝² : StrongRankCondition R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nι : Type u_1\nb : Basis ι R M\nκ :... | [
754,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.inverse_asEquivalence | [
{
"state_after": "case mk'\nC : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nfunctor✝ : C ⥤ D\ninverse✝ : D ⥤ C\nunitIso✝ : 𝟭 C ≅ functor✝ ⋙ inverse✝\ncounitIso✝ : inverse✝ ⋙ functor✝ ≅ 𝟭 D\nfunctor_unitIso_comp✝ :\n ∀ (X : C), functor✝.map (unitIso✝.hom.app X) ≫ counitIso✝.hom.app (functor... | [
594,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Topology/Order.lean | continuous_bot | [] | [
810,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.mrange_mk' | [] | [
881,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/Real/Basic.lean | Real.iSup_le | [] | [
883,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
11
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.church_rosser | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ a b✝ c b : List (α × Bool)\nhab hac : Step a b\n⊢ ReflGen Step b b",
"tactic": "rfl"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ a b✝ c b : List (α × Bool)\nhab hac : Step a b\n⊢ ReflTransG... | [
244,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | SemilinearIsometryClass.antilipschitz | [] | [
106,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
11
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | summable_of_norm_bounded_eventually | [] | [
167,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cosh_three_mul | [
{
"state_after": "x y : ℝ\n⊢ ↑(cosh (3 * x)) = ↑(4 * cosh x ^ 3 - 3 * cosh x)",
"state_before": "x y : ℝ\n⊢ cosh (3 * x) = 4 * cosh x ^ 3 - 3 * cosh x",
"tactic": "rw [← ofReal_inj]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cosh (3 * x)) = ↑(4 * cosh x ^ 3 - 3 * cosh x)"... | [
1453,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1452,
8
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycleOn_empty | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1633030\nα : Type u_1\nβ : Type ?u.1633036\nf g : Perm α\ns t : Set α\na b x y : α\n⊢ IsCycleOn f ∅",
"tactic": "simp [IsCycleOn, Set.bijOn_empty]"
}
] | [
759,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Analysis/ODE/Gronwall.lean | gronwallBound_of_K_ne_0 | [] | [
58,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | Real.pow_arith_mean_le_arith_mean_pow_of_even | [] | [
72,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/List/Sigma.lean | List.nodupKeys_join | [
{
"state_after": "α : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\nL : List (List (Sigma β))\n⊢ (∀ (l : List (Sigma β)), l ∈ L → Pairwise (fun s s' => s.fst ≠ s'.fst) l) ∧\n Pairwise (fun l₁ l₂ => ∀ (x : Sigma β), x ∈ l₁ → ∀ (y : Sigma β), y ∈ l₂ → x.fst ≠ y.fst) L ↔\n (∀ (l : List (Sigma β)), l ∈ ... | [
153,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_pi_const | [] | [
2035,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2033,
1
] |
Mathlib/Algebra/Hom/Units.lean | IsUnit.div_mul_cancel | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.53366\nG : Type ?u.53369\nα : Type u_1\nM : Type ?u.53375\nN : Type ?u.53378\ninst✝ : DivisionMonoid α\na✝ b c : α\nh : IsUnit b\na : α\n⊢ a / b * b = a",
"tactic": "rw [div_eq_mul_inv, h.inv_mul_cancel_right]"
}
] | [
368,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
11
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.of_isZero | [
{
"state_after": "ctx : Context\np : Poly\nh :\n (match p with\n | [] => true\n | x => false) =\n true\n⊢ denote ctx p = 0",
"state_before": "ctx : Context\np : Poly\nh : isZero p = true\n⊢ denote ctx p = 0",
"tactic": "simp [isZero] at h"
},
{
"state_after": "case h_1\nctx : Context\n... | [
628,
18
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
624,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_normalizer_eq_of_bijective | [] | [
3259,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3257,
1
] |
Mathlib/Data/Multiset/Fold.lean | Multiset.fold_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8358\nop : α → α → α\nhc : IsCommutative α op\nha : IsAssociative α op\nb₁ b₂ : α\ns₁ s₂ : Multiset α\n⊢ fold op (op b₁ b₂) (s₁ + 0) = op (fold op b₁ s₁) (fold op b₂ 0)",
"tactic": "rw [add_zero, fold_zero, ← fold_cons'_right, ← fol... | [
83,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_isPrime_of_equiv | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_3\nF : Type ?u.1964564\ninst✝³ : Ring R\ninst✝² : Ring S\nrc : RingHomClass F R S\nF' : Type u_1\ninst✝¹ : RingEquivClass F' R S\nf : F'\nI : Ideal R\ninst✝ : IsPrime I\n⊢ RingHom.ker f ≤ I",
"tactic": "simp only [RingHom.ker_equiv, ... | [
2155,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2153,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivAt.cos | [] | [
804,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.eqOn_const_of_mapsTo | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nι : Type ?u.150118\nπ : ι → Type ?u.150123\ninst✝² : TopologicalSpace α\ns t u v : Set α\ninst✝¹ : TopologicalSpace β\nT : Set β\ninst✝ : DiscreteTopology ↑T\nf : α → β\nhne : Set.Nonempty T\nhS : IsPreconnected ∅\nhc : ContinuousOn f ∅\nhTm : MapsTo f ∅ T\n⊢ ... | [
1623,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1618,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_lt_add_iff_right | [] | [
786,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
11
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | LiouvilleNumber.summable | [] | [
84,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
11
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.mul_left_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : Monic p\nq : R[X]\n⊢ q * p = 0 ↔ q = 0",
"tactic": "by_cases hq : q = 0 <;> simp [h.mul_left_ne_zero, hq]"
}
] | [
471,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Analysis/NormedSpace/Basic.lean | inv_norm_smul_mem_closed_unit_ball | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9079\nβ : Type u_1\nγ : Type ?u.9085\nι : Type ?u.9088\ninst✝² : NormedField α\ninst✝¹ : SeminormedAddCommGroup β\ninst✝ : NormedSpace ℝ β\nx : β\n⊢ ‖x‖⁻¹ • x ∈ closedBall 0 1",
"tactic": "simp only [mem_closedBall_zero_iff, norm_smul, norm_inv, ... | [
80,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.coe_toInfHom | [] | [
1052,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1051,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain.addMonoidHom_comp | [] | [
526,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.mem_comap | [] | [
308,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Continuous.of_bundled | [] | [
266,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_blockDiag' | [] | [
449,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_disjoint_append_right_right | [] | [
1405,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1404,
1
] |
Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.ext | [
{
"state_after": "R : Type u\ninst✝¹⁰ : CommSemiring R\nA : Type v₁\ninst✝⁹ : Semiring A\ninst✝⁸ : Algebra R A\nB : Type v₂\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R B\nS : Type ?u.721832\ninst✝⁵ : CommSemiring S\ninst✝⁴ : Algebra R S\ninst✝³ : Algebra S A\ninst✝² : IsScalarTower R S A\nC : Type v₃\ninst✝¹ : Sem... | [
535,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_lt_sub_left_of_lt_add | [
{
"state_after": "a b c : Int\nh✝ : c < a + b\nh : -a < -c + b\n⊢ -a < b - c",
"state_before": "a b c : Int\nh : c < a + b\n⊢ -a < b - c",
"tactic": "have h := Int.lt_neg_add_of_add_lt (Int.sub_left_lt_of_lt_add h)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : c < a + b... | [
1108,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1106,
11
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBot | [] | [
542,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_nonneg | [] | [
144,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.BisimO.imp | [] | [
479,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Order/Hom/Bounded.lean | BotHom.cancel_left | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.48941\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nδ : Type ?u.48953\ninst✝³ : Bot α\ninst✝² : Bot β\ninst✝¹ : Bot γ\ninst✝ : Bot δ\ng : BotHom β γ\nf₁ f₂ : BotHom α β\nhg : Injective ↑g\nh : comp g f₁ = comp g f₂\na : α\n⊢ ↑g (↑f₁ a) = ↑g (↑f₂ a)",
... | [
484,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Data/Real/Irrational.lean | one_lt_natDegree_of_irrational_root | [
{
"state_after": "x : ℝ\np : ℤ[X]\nhx : Irrational x\np_nonzero : p ≠ 0\nx_is_root : ↑(aeval x) p = 0\nrid : ¬1 < natDegree p\n⊢ False",
"state_before": "x : ℝ\np : ℤ[X]\nhx : Irrational x\np_nonzero : p ≠ 0\nx_is_root : ↑(aeval x) p = 0\n⊢ 1 < natDegree p",
"tactic": "by_contra rid"
},
{
"state... | [
515,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.closedEmbedding_comap_of_surjective | [] | [
755,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Antitone.continuousWithinAt_Ioi_iff_rightLim_eq | [] | [
364,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.map_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝² : DivisionRing R\np q : R[X]\ninst✝¹ : Semiring S\ninst✝ : Nontrivial S\nf : R →+* S\n⊢ (∀ (n : ℕ), coeff (map f p) n = coeff 0 n) ↔ ∀ (n : ℕ), coeff p n = coeff 0 n",
"state_before": "R : Type u\nS : Type v\nk : Type y... | [
142,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/Function/ContinuousMapDense.lean | MeasureTheory.Memℒp.exists_hasCompactSupport_integral_rpow_sub_le | [
{
"state_after": "α : Type u_1\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : TopologicalSpace α\ninst✝⁵ : NormalSpace α\ninst✝⁴ : BorelSpace α\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\nμ : Measure α\np✝ : ℝ≥0∞\ninst✝² : NormedSpace ℝ E\ninst✝¹ : LocallyCompactSpace α\ninst✝ : Measure.Regular μ\np : ℝ\nhp : 0 < p\nf... | [
214,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | contDiff_iff_iteratedDeriv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.124644\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn✝ : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx : 𝕜\nn : ℕ∞\n⊢ ContDiff 𝕜... | [
265,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Logic/Relation.lean | Relation.comp_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11378\nγ : Type ?u.11381\nδ : Type ?u.11384\nr✝ : α → β → Prop\np : β → γ → Prop\nq : γ → δ → Prop\nr : α → Prop → Prop\nthis : (fun x x_1 => x ↔ x_1) = fun x x_1 => x = x_1\n⊢ (r ∘r fun x x_1 => x ↔ x_1) = r",
"tactic": "rw [this, ... | [
156,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.contDiffAt_log | [] | [
89,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBounded_principal | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.5475\nγ : Type ?u.5478\nι : Type ?u.5481\nr : α → α → Prop\nf g : Filter α\ns : Set α\n⊢ IsBounded r (𝓟 s) ↔ ∃ t, ∀ (x : α), x ∈ s → r x t",
"tactic": "simp [IsBounded, subset_def]"
}
] | [
87,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Part.lean | Part.some_mod_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.73852\nγ : Type ?u.73855\ninst✝ : Mod α\na b : α\n⊢ some a % some b = some (a % b)",
"tactic": "simp [mod_def]"
}
] | [
800,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.ofConjAct_one | [] | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | LipschitzWith.compLp_zero | [
{
"state_after": "α : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.2123310\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ng : E → F\nc : ℝ≥0\nhg : LipschitzWith c g\ng0 : g 0 = 0\n⊢ ↑↑(co... | [
913,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_cons_ne | [] | [
189,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_sub | [] | [
340,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.zeroth_convergent'_aux_eq_zero | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
src/lean/Init/SimpLemmas.lean | beq_self_eq_true' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\n⊢ (a == a) = true",
"tactic": "simp [BEq.beq]"
}
] | [
149,
97
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
149,
9
] |
Mathlib/Topology/Compactification/OnePoint.lean | Continuous.homeoOfEquivCompactToT2.t1_counterexample | [] | [
509,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kronecker_smul | [] | [
322,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Algebra/AddTorsor.lean | Set.singleton_vsub_self | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nP : Type u_2\ninst✝ : AddGroup G\nT : AddTorsor G P\np : P\n⊢ {p} -ᵥ {p} = {0}",
"tactic": "rw [Set.singleton_vsub_singleton, vsub_self]"
}
] | [
198,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_eq_empty | [] | [
242,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_mul | [] | [
358,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Init/Data/Nat/Lemmas.lean | Nat.bit1_lt_bit0 | [
{
"state_after": "n m : ℕ\nh : n < succ m\nthis✝ : n ≤ m\nthis : succ (n + n) ≤ succ (m + m)\n⊢ succ (n + n) ≤ succ (m + m)",
"state_before": "n m : ℕ\nh : n < succ m\nthis✝ : n ≤ m\nthis : succ (n + n) ≤ succ (m + m)\n⊢ succ (n + n) ≤ succ m + m",
"tactic": "rw [succ_add]"
},
{
"state_after": "... | [
195,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
11
] |
Mathlib/FieldTheory/Tower.lean | FiniteDimensional.trans | [] | [
103,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.isOpen_preimage | [] | [
307,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_diff_null | [] | [
228,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.add_nsmul_modEq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn✝ : ℕ\nz : ℤ\nn : ℕ\n⊢ a - (a + n • p) = -↑n • p",
"tactic": "simp"
}
] | [
126,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.invFun_eq_of_injective_of_rightInverse | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\ninst✝ : Nonempty α\nf : α → β\na : α\nb✝ : β\ng : β → α\nhf : Injective f\nhg : RightInverse g f\nb : β\n⊢ f (invFun f b) = b",
"state_before": "α : Sort u_1\nβ : Sort u_2\ninst✝ : Nonempty α\nf : α → β\na : α\nb✝ : β\ng : β → α\nhf : Injective f\nhg : RightInve... | [
451,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.add'_comm | [
{
"state_after": "R : Type u_1\ninst✝¹ : Semiring R\nS : Submonoid R\ninst✝ : OreSet S\nr₁ r₂ : R\ns₁ s₂ : { x // x ∈ S }\n⊢ Quotient.mk (oreEqv R S) (r₂ * ↑(oreDenom (↑s₂) s₁) + r₁ * oreNum (↑s₂) s₁, s₂ * oreDenom (↑s₂) s₁) =\n Quotient.mk (oreEqv R S) (r₁ * ↑(oreDenom (↑s₁) s₂) + r₂ * oreNum (↑s₁) s₂, s₁ *... | [
589,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
9
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | ContinuousOn.measurable_piecewise | [
{
"state_after": "α : Type u_1\nβ : Type ?u.930878\nγ : Type u_2\nγ₂ : Type ?u.930884\nδ : Type ?u.930887\nι : Sort y\ns✝ t✝ u : Set α\ninst✝¹⁵ : TopologicalSpace α\ninst✝¹⁴ : MeasurableSpace α\ninst✝¹³ : OpensMeasurableSpace α\ninst✝¹² : TopologicalSpace β\ninst✝¹¹ : MeasurableSpace β\ninst✝¹⁰ : OpensMeasurabl... | [
853,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
842,
1
] |
Mathlib/GroupTheory/GroupAction/Group.lean | smul_left_cancel_iff | [] | [
172,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
src/lean/Init/Prelude.lean | Or.intro_right | [] | [
527,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
526,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Filter.EventuallyEq.fderivWithin_eq_nhds | [] | [
962,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_of_empty | [] | [
1507,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1506,
1
] |
Mathlib/Algebra/Star/Unitary.lean | unitary.star_mem_iff | [] | [
75,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Iic_iff_exists_Icc_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 : NoMinOrder α\ninst✝ : DenselyOrdered α\na : α\ns : Set α\n⊢ (∃ u, ↑toDual a < ↑toDual u ∧ ↑ofDual ⁻¹' Icc u a ⊆ ↑ofDual ⁻¹' s) ↔ ∃ l, l < a ∧ Icc l a ⊆ s",
"state_bef... | [
1839,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1834,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.exists_iUnion_eq_diff | [
{
"state_after": "case intro\nι : Type u_1\nM : Type ?u.56100\nn : ℕ\nI J : Box ι\ni : ι\nx : ℝ\ninst✝ : Finite ι\nπ : Prepartition I\ns : Finset (ι × ℝ)\nhs : π ⊓ splitMany I s = filter (splitMany I s) fun J => ↑J ⊆ Prepartition.iUnion π\n⊢ ∃ π', Prepartition.iUnion π' = ↑I \\ Prepartition.iUnion π",
"stat... | [
359,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | csInf_one | [] | [
121,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Polynomial/Taylor.lean | Polynomial.taylor_zero' | [
{
"state_after": "case h.h.a\nR : Type u_1\ninst✝ : Semiring R\nr : R\nf : R[X]\nn✝¹ n✝ : ℕ\n⊢ coeff (↑(LinearMap.comp (taylor 0) (monomial n✝¹)) 1) n✝ = coeff (↑(LinearMap.comp LinearMap.id (monomial n✝¹)) 1) n✝",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : R\nf : R[X]\n⊢ taylor 0 = LinearMap.id... | [
62,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.of_mul_right | [] | [
392,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/Nat/Cast/WithTop.lean | Nat.cast_withBot | [] | [
27,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.sbtw_of_collinear_of_dist_center_lt_radius | [] | [
392,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
1
] |
Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.IsSheafFor.valid_glue | [] | [
623,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderWith.comp_holderOnWith | [] | [
212,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | StrictMonoOn.continuousWithinAt_left_of_surjOn | [] | [
209,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_lt_sub_of_lt_of_le | [] | [
1134,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1132,
11
] |
Mathlib/Topology/DenseEmbedding.lean | DenseInducing.extend_eq' | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type u_3\nγ : Type u_1\nδ : Type ?u.8090\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ni : α → β\ndi✝ : DenseInducing i\ninst✝² : TopologicalSpace δ\nf✝ : γ → α\ng : γ → δ\nh : δ → β\ninst✝¹ : TopologicalSpace γ\ninst✝ : T2Space γ\nf : α → γ\ndi : Den... | [
177,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.C_inj | [] | [
254,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.finset_sup_compact_of_compact | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.14463\nα✝ : Type ?u.14466\ninst✝¹ : CompleteLattice α✝\nf✝ : ι → α✝\nα : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\nf : β → α\ns : Finset β\nh : ∀ (x : β), x ∈ s → IsCompactElement (f x)\n⊢ IsCompactElement (Finset.sup s f)",
"tactic": "c... | [
200,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_of_sub_pos | [
{
"state_after": "a b : Int\nh✝ : 0 < a - b\nh : 0 + b < a - b + b\n⊢ b < a",
"state_before": "a b : Int\nh : 0 < a - b\n⊢ b < a",
"tactic": "have h := Int.add_lt_add_right h b"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : 0 < a - b\nh : 0 + b < a - b + b\n⊢ b < a",
"... | [
940,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
938,
11
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousAt_ciInf | [] | [
1021,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.continuousWithinAt_Iio_iff_leftLim_eq | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : LinearOrder α\ninst✝⁴ : ConditionallyCompleteLinearOrder β\ninst✝³ : TopologicalSpace β\ninst✝² : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderTopology α\nh' : 𝓝[Iio x] x = ⊥\n⊢ ContinuousWithinA... | [
196,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Init/Logic.lean | InvImage.irreflexive | [] | [
500,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.id_tsnd | [] | [
74,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.hasSum_sub | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.416023\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E → F\np pf pg ... | [
451,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.isUnit_iff_isUnit_det | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.86247\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\n⊢ IsUnit A ↔ IsUnit (det A)",
"tactic": "simp only [← nonempty_invertible_iff_isUnit, (invertibleEquivDetInvertible A)... | [
202,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Category/GroupCat/Basic.lean | GroupCat.ofHom_apply | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_def | [] | [
180,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.colorable_of_fintype | [] | [
211,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Rel.lean | Rel.image_id | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.15405\nγ : Type ?u.15408\nr : Rel α β\ns : Set α\nx : α\n⊢ x ∈ image Eq s ↔ x ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.15405\nγ : Type ?u.15408\nr : Rel α β\ns : Set α\n⊢ image Eq s = s",
"tactic": "ext x"
},
{
"state_after": "no goals"... | [
160,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousSubmodule_mul | [
{
"state_after": "σ : Type u_2\nτ : Type ?u.119978\nR : Type u_1\nS : Type ?u.119984\ninst✝ : CommSemiring R\nm n : ℕ\n⊢ ∀ (m_1 : MvPolynomial σ R),\n m_1 ∈ homogeneousSubmodule σ R m →\n ∀ (n_1 : MvPolynomial σ R), n_1 ∈ homogeneousSubmodule σ R n → m_1 * n_1 ∈ homogeneousSubmodule σ R (m + n)",
"s... | [
110,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
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