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 |
|---|---|---|---|---|---|---|
src/lean/Init/Data/List/Basic.lean | List.replicate_eq_replicateTR | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\n⊢ ∀ (x : Type u_1), replicate = replicateTR",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\n⊢ @replicate = @replicateTR",
"tactic": "apply funext"
},
{
"state_after": "case h\nα✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u_1\n... | [
754,
51
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
752,
10
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.zsmul_apply | [] | [
331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.exists_eq_mul_self | [
{
"state_after": "case intro\nk : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\nz : k\n⊢ ∃ z_1, z ^ 2 = z_1 * z_1",
"state_before": "k : Type u\ninst✝¹ : Field k\ninst✝ : IsAlgClosed k\nx : k\n⊢ ∃ z, x = z * z",
"tactic": "rcases exists_pow_nat_eq x zero_lt_two with ⟨z, rfl⟩"
},
{
"state_afte... | [
97,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Data/List/Basic.lean | List.mem_of_mem_getLast? | [] | [
814,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.eq_biInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.61264\nγ : Type ?u.61267\nι : Sort u_2\nι' : Sort ?u.61273\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'\nh : HasBasis l p s\nx✝ : Set α\n⊢ x✝ ∈ l ↔ ∃ i, p i ∧ x✝ ∈ 𝓟 (s i)",
... | [
754,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_sum_fiber_lt_of_sum_lt_nsmul | [] | [
358,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Analysis/Calculus/UniformLimitsDeriv.lean | hasFDerivAt_of_tendstoUniformlyOn | [] | [
431,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/ModelTheory/LanguageMap.lean | FirstOrder.Language.card_withConstants | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\ninst✝ : Structure L M\nα : Type w'\n⊢ card (L[[α]]) = lift (card L) + lift (#α)",
"tactic": "rw [withConstants, card_sum, card_constantsOn]"
}
] | [
463,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_one | [] | [
126,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.le_limsup_of_frequently_le | [
{
"state_after": "α✝ : Type ?u.190748\nβ✝ : Type ?u.190751\nγ : Type ?u.190754\nι : Type ?u.190757\nα : Type u_1\nβ : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder β\nf : Filter α\nu : α → β\nb : β\nhu : autoParam (IsBoundedUnder (fun x x_1 => x ≤ x_1) f u) _auto✝\n⊢ (∃ᶠ (x : α) in f, b ≤ u x) → b ≤ limsup... | [
1144,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.Normal.subgroupOf | [] | [
3401,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3399,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_union_distrib_right | [] | [
1078,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1077,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.toIdeal_homogeneousCore_le | [] | [
196,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_def | [] | [
553,
60
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
553,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_smul_vadd_smul_vadd_of_nonpos_of_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.542740\nP : Type u_3\nP' : Type ?u.542746\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx : P\nv : V\nr₁ r₂ : R\nhr₁ : r₁ ≤ 0\nhr₂ : r₂ ≤ r₁\n⊢ Wbtw R x (r₁ • v +ᵥ x)... | [
785,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.one_eq_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type ?u.206405\ninst✝ : CommSemiring R\nI J K L : Ideal R\n⊢ 1 = ⊤",
"tactic": "erw [Submodule.one_eq_range, LinearMap.range_id]"
}
] | [
444,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_bit0 | [] | [
1117,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.symm_trans_source_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.11860\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.11871\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne✝ : Pretrivialization F proj\nx : Z\ne e' : Pretrivialization F proj\n⊢ (LocalEquiv.trans (LocalEquiv.symm... | [
219,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.lift_lt_continuum | [
{
"state_after": "no goals",
"state_before": "c : Cardinal\n⊢ lift c < 𝔠 ↔ c < 𝔠",
"tactic": "rw [← lift_continuum.{u,v}, lift_lt]"
}
] | [
70,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/WideEqualizers.lean | CategoryTheory.Limits.wideCoequalizer.hom_ext | [] | [
757,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
] |
Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.lcm_mono | [] | [
76,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_comp_succAbove | [
{
"state_after": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni : Fin (n + 1)\nx : β\np : Fin n → β\n⊢ ∀ (x_1 : Fin n), insertNth i x p (↑(succAbove i) x_1) = p x_1",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni : Fin (n + 1)\nx : β\np : Fin n → β\n⊢ ∀ (x_1 : Fin n), (insertNth i x p... | [
693,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.zip_eq | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β → δ\ns₁ : Stream' α\ns₂ : Stream' β\n⊢ head (zip f s₁ s₂) :: tail (zip f s₁ s₂) = f (head s₁) (head s₂) :: zip f (tail s₁) (tail s₂)",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β → δ\ns₁ : Stream' α\ns₂ : Stream' β\n⊢ zip f s... | [
223,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_eq_pi_div_two_sub_arcsin | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.homothety_norm | [
{
"state_after": "case intro\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.2620779\nE : Type u_3\nEₗ : Type ?u.2620785\nF : Type u_4\nFₗ : Type ?u.2620791\nG : Type ?u.2620794\nGₗ : Type ?u.2620797\n𝓕 : Type ?u.2620800\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : NormedAddCommGrou... | [
1506,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1500,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BoundedLatticeHom.asBoolRing_comp | [] | [
571,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.one_imI | [] | [
871,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
9
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_pi_empty | [
{
"state_after": "ι✝ : Type ?u.6064426\nι' : Type ?u.6064429\nα✝ : ι✝ → Type ?u.6064434\ninst✝¹ : Fintype ι✝\nm✝ : (i : ι✝) → OuterMeasure (α✝ i)\nι : Type u\nα : ι → Type v\ninst✝ : IsEmpty ι\nm : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ne : ((i : ι) → α i) ≃ᵐ Unit := MeasurableEquiv.ofUni... | [
833,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
827,
1
] |
Mathlib/Data/Option/Basic.lean | Option.some_orElse' | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Data/Sigma/Order.lean | Sigma.Lex.le_def | [] | [
147,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.ω_pow_formula | [
{
"state_after": "p' : ℕ\nh : sZMod (p' + 2) (p' + 2 - 2) = 0\n⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1",
"state_before": "p' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\n⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1",
"tactic": "dsimp [lucasLehmerResidue]... | [
432,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_top | [] | [
553,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
9
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_op_rel_iff_and | [
{
"state_after": "case empty\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.57392\nop : β → β → β\nhc : IsCommutative β op\nha : IsAssociative β op\nf : α → β\nb : β\ns : Finset α\na : α\nr : β → β → Prop\nhr : ∀ {x y z : β}, r x (op y z) ↔ r x y ∧ r x z\nc : β\n⊢ r c (fold op b f ∅) ↔ r c b ∧ ∀ (x : α), x ∈ ∅ → r c ... | [
182,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/CategoryTheory/Limits/ConeCategory.lean | CategoryTheory.Limits.IsTerminal.from_eq_liftConeMorphism | [] | [
115,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.one_le_rpow_of_pos_of_le_one_of_neg | [
{
"state_after": "case intro\nz : ℝ\nhz : z < 0\nx : ℝ≥0\nhx1 : 0 < ↑x\nhx2 : ↑x ≤ 1\n⊢ 1 ≤ ↑x ^ z",
"state_before": "x : ℝ≥0∞\nz : ℝ\nhx1 : 0 < x\nhx2 : x ≤ 1\nhz : z < 0\n⊢ 1 ≤ x ^ z",
"tactic": "lift x to ℝ≥0 using ne_of_lt (lt_of_le_of_lt hx2 coe_lt_top)"
},
{
"state_after": "case intro\nz :... | [
719,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.sum_lt_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.161632\nr : α → α → Prop\nι : Type u\nf : ι → Cardinal\nc : Cardinal\nhc : IsRegular c\nhι : (#ι) < c\n⊢ lift (#ι) < c",
"tactic": "rwa [lift_id]"
}
] | [
1120,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.algebraMap_eq_inl_hom | [] | [
600,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | GroupTopology.ext' | [] | [
1884,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1883,
1
] |
Mathlib/Topology/Order/Basic.lean | le_of_tendsto_of_tendsto' | [] | [
183,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.mul_empty | [] | [
242,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.lt_three | [
{
"state_after": "p q r : ℕ+\nhpq : p ≤ q\nhqr : q ≤ r\nH : 1 < sumInv {p, q, r}\nh3 : 0 < 3\n⊢ p < 3",
"state_before": "p q r : ℕ+\nhpq : p ≤ q\nhqr : q ≤ r\nH : 1 < sumInv {p, q, r}\n⊢ p < 3",
"tactic": "have h3 : (0 : ℚ) < 3 := by norm_num"
},
{
"state_after": "p q r : ℕ+\nhpq : p ≤ q\nhqr : ... | [
197,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_symm_le | [
{
"state_after": "x y : ℕ∞\n⊢ ↑withTopEquiv (↑withTopEquiv.symm x) ≤ ↑withTopEquiv (↑withTopEquiv.symm y) ↔ x ≤ y",
"state_before": "x y : ℕ∞\n⊢ ↑withTopEquiv.symm x ≤ ↑withTopEquiv.symm y ↔ x ≤ y",
"tactic": "rw [← withTopEquiv_le]"
},
{
"state_after": "no goals",
"state_before": "x y : ℕ∞\... | [
737,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.lipschitz_compContinuous | [] | [
389,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Order/Basic.lean | closure_Iio' | [] | [
2230,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2229,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopy.extend_apply_of_one_le | [
{
"state_after": "F✝ : Type ?u.11079\nX : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nf₀ f₁ : C(X, Y)\nF : Homotopy f₀ f₁\nt : ℝ\nht : 1 ≤ t\nx : X\n⊢ ↑(↑(extend F) t) x = ↑F (1, x)",
"state_... | [
183,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.continuousAt | [] | [
246,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
11
] |
Mathlib/Data/Int/Order/Basic.lean | Int.lt_of_toNat_lt | [] | [
526,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
525,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₈_int_eq_if_mod_eight | [
{
"state_after": "n : ℤ\nhelp : ∀ (m : ℤ), 0 ≤ m → m < 8 → ↑χ₈ ↑m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 7 then 1 else -1\n⊢ ↑χ₈ ↑n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1",
"state_before": "n : ℤ\n⊢ ↑χ₈ ↑n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 7 then 1 else -1",
... | [
170,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Std/Logic.lean | exists_eq_left | [] | [
457,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
456,
9
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_one | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ descFactorial n 1 = n",
"tactic": "rw [descFactorial_succ, descFactorial_zero, mul_one, tsub_zero]"
}
] | [
363,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.isOpen_iff | [
{
"state_after": "s : Set Ordinal\na o : Ordinal\nho : o ∈ s\n⊢ s ∈ 𝓝 o ↔ IsLimit o → ∃ a, a < o ∧ Set.Ioo a o ⊆ s",
"state_before": "s : Set Ordinal\na : Ordinal\n⊢ IsOpen s ↔ ∀ (o : Ordinal), o ∈ s → IsLimit o → ∃ a, a < o ∧ Set.Ioo a o ⊆ s",
"tactic": "refine isOpen_iff_mem_nhds.trans <| forall₂_con... | [
85,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Logic/Basic.lean | xor_not_right | [
{
"state_after": "no goals",
"state_before": "a b : Prop\n⊢ Xor' a ¬b ↔ (a ↔ b)",
"tactic": "by_cases a <;> simp [*]"
}
] | [
297,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
9
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.limit_le | [] | [
270,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_Ioo | [] | [
458,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_left_comm | [
{
"state_after": "no goals",
"state_before": "a b c : Int\n⊢ a + (b + c) = b + (a + c)",
"tactic": "rw [← Int.add_assoc, Int.add_comm a, Int.add_assoc]"
}
] | [
284,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
283,
11
] |
Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Structure.FG.cg | [] | [
255,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.boxProd_neighborFinset | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.86875\nG : SimpleGraph α\nH : SimpleGraph β\nx : α × β\ninst✝² : Fintype ↑(neighborSet G x.fst)\ninst✝¹ : Fintype ↑(neighborSet H x.snd)\ninst✝ : Fintype ↑(neighborSet (G □ H) x)\nthis : Fintype ↑(neighborSet (G □ H) x) := boxProdFintypeNeighborSet x\n⊢ ... | [
240,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_prodAssoc | [] | [
921,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
920,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.continuous_imK | [] | [
224,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_inv_one_add_sq | [
{
"state_after": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, 1 / (1 + x ^ 2)) = arctan b - arctan a",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, (1 + x ^ 2)⁻¹) = arctan b - arctan a",
"tactic": "simp only [← one_div]"
},
{
"state_after": "case refine'_1\na b : ℝ\nn : ℕ\n⊢ deriv arctan = f... | [
548,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinOn.iInf_eq | [] | [
697,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.C_zero | [] | [
968,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Order/GameAdd.lean | Acc.sym2_gameAdd | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.6233\nrα : α → α → Prop\nrβ : β → β → Prop\na✝ b✝ : α\nhb✝ : Acc rα b✝\na : α\nh✝ : ∀ (y : α), rα y a → Acc rα y\niha : ∀ (y : α), rα y a → ∀ {b : α}, Acc rα b → Acc (Sym2.GameAdd rα) (Quotient.mk (Sym2.Rel.setoid α) (y, b))\nb : α\nhb : Acc rα b\n⊢ Acc (S... | [
216,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_eq_on_Ico | [] | [
789,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.map_mod_divByMonic | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np q : R[X]\ninst✝ : CommRing S\nf : R →+* S\nhq : Monic q\n✝ : Nontrivial S\n⊢ map f (p /ₘ q) = map f p /ₘ map f q ∧ map f (p %ₘ q) = map f p %ₘ map f q",
"state_before": "R : Type u\nS : Type v\nT : Type ... | [
374,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.union_union | [] | [
803,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Topology/Algebra/Order/UpperLower.lean | IsUpperSet.closure | [] | [
68,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
11
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIso_inv_snd_snd | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasPullbacks C\nU V₁ V₂ : C\nf : X ⟶ Y\ni : U ⟶ Y\ni₁ : V₁ ⟶ pullback f i\ni₂ : V₂ ⟶ pullback f i\ninst✝ : HasPullback i₁ i₂\n⊢ (Iso.mk (lift (snd ≫ fst) (snd ≫ snd) (_ : (snd ≫ fst) ≫ i₁ = (snd ≫ snd) ≫ i₂))\n (lift (fst ≫ i₁ ≫ f... | [
186,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.not_le_delta | [] | [
82,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | tsub_le_tsub_left | [] | [
125,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atTop_of_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.215087\nι' : Type ?u.215090\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.215099\ninst✝ : LinearOrderedSemifield α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\nhr : 0 < r\nh : Tendsto f l atTop\n⊢ Tendsto (fun x => r⁻¹ * (r * f x)) l atTop",
"tactic": "s... | [
1006,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.unop_sum | [] | [
1796,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1794,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.807876\nβ : Type ?u.807879\na b c d : ℝ≥0∞\nr p✝ q : ℝ≥0\np : ℝ\n⊢ ENNReal.ofReal p = 0 ↔ p ≤ 0",
"tactic": "simp [ENNReal.ofReal]"
}
] | [
2118,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2118,
1
] |
Mathlib/Order/Atoms.lean | isAtom_dual_iff_isCoatom | [] | [
131,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/List/Infix.lean | List.tail_suffix | [
{
"state_after": "α : Type u_1\nβ : Type ?u.2600\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ drop 1 l <:+ l",
"state_before": "α : Type u_1\nβ : Type ?u.2600\nl✝ l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\nl : List α\n⊢ tail l <:+ l",
"tactic": "rw [← drop_one]"
},
{
"state_after": "no goals... | [
175,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Matrix/Basic.lean | AlgEquiv.mapMatrix_symm | [] | [
1638,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_eq_iff' | [] | [
306,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Topology/Instances/NNReal.lean | NNReal.hasSum_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → ℝ≥0\nr : ℝ≥0\n⊢ HasSum (fun a => ↑(f a)) ↑r ↔ HasSum f r",
"tactic": "simp only [HasSum, ← coe_sum, tendsto_coe]"
}
] | [
155,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/List/Sigma.lean | List.nodup_enum_map_fst | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\nl : List α\n⊢ Nodup (map Prod.fst (enum l))",
"tactic": "simp [List.nodup_range]"
}
] | [
156,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.inf_principal_neBot_iff | [] | [
683,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.nonempty_closedBall | [] | [
515,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.isColimit_desc | [] | [
746,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.eq_inv_of_inv_hom_id | [] | [
366,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_symm_none | [] | [
163,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackAssoc_inv_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁷ : Category C\nD : Type u₂\ninst✝⁶ : Category D\nW X Y Z X₁ X₂ X₃ Y₁ Y₂ : C\nf₁ : X₁ ⟶ Y₁\nf₂ : X₂ ⟶ Y₁\nf₃ : X₂ ⟶ Y₂\nf₄ : X₃ ⟶ Y₂\ninst✝⁵ : HasPullback f₁ f₂\ninst✝⁴ : HasPullback f₃ f₄\ninst✝³ : HasPullback (pullback.snd ≫ sorryAx (sorryAx C... | [
2448,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2445,
1
] |
Mathlib/Data/Analysis/Topology.lean | Ctop.Realizer.mem_interior_iff | [] | [
157,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.flipₗᵢ'_symm | [] | [
845,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.compl_inv | [] | [
230,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Tactic/CancelDenoms.lean | CancelDenoms.div_subst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Field α\nn1 n2 k e1 e2 t1 : α\nh1 : n1 * e1 = t1\nh2 : n2 / e2 = 1\nh3 : n1 * n2 = k\n⊢ k * (e1 / e2) = t1",
"tactic": "rw [← h3, mul_assoc, mul_div_left_comm, h2, ← mul_assoc, h1, mul_comm, one_mul]"
}
] | [
45,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_eq_left | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.76166\nα : Type u_1\nβ : Type ?u.76172\nπ : ι → Type ?u.76177\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ a ∆ b = a ↔ a ∆ b = a ∆ ⊥",
"tactic": "rw [symmDiff_bot]"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.... | [
549,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Star.lean | differentiableAt_star_iff | [] | [
78,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Ioi | [] | [
85,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Subsequent.mk_right' | [
{
"state_after": "no goals",
"state_before": "xl xr : Type u_1\nxL : xl → PGame\nxR : xr → PGame\nj : RightMoves (mk xl xr xL xR)\n⊢ Subsequent (xR j) (mk xl xr xL xR)",
"tactic": "pgame_wf_tac"
}
] | [
305,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | LinearLocallyFiniteOrder.le_of_lt_succFn | [
{
"state_after": "ι : Type u_1\ninst✝ : LinearOrder ι\nj i : ι\nhij : ∃ c, c ∈ lowerBounds (Set.Ioi i) ∧ j < c\n⊢ j ≤ i",
"state_before": "ι : Type u_1\ninst✝ : LinearOrder ι\nj i : ι\nhij : j < succFn i\n⊢ j ≤ i",
"tactic": "rw [lt_isGLB_iff (succFn_spec i)] at hij"
},
{
"state_after": "case in... | [
116,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.continuousAt_extend_symm | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_4\nE : Type u_3\nM : Type u_1\nH : Type u_2\nE' : Type ?u.144430\nM' : Type ?u.144433\nH' : Type ?u.144436\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : Topologic... | [
863,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
861,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_sub_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℂ\n⊢ sin (x - ↑π / 2) = -cos x",
"tactic": "simp [sub_eq_add_neg, sin_add]"
}
] | [
1282,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.sigmaUncurry_apply | [] | [
344,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
] |
Mathlib/Data/Fintype/Basic.lean | Function.Embedding.right_inv_of_invOfMemRange | [] | [
540,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.contDiffWithinAt | [] | [
473,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
11
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Ioc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ Neg.neg '' Ioc a b = Ico (-b) (-a)",
"tactic": "simp"
}
] | [
309,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
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