file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Algebra/Hom/Aut.lean | MulAut.conj_inv_apply | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.mkContinuousLinear_norm_le' | [
{
"state_after": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E i)\nins... | [
1087,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | nndist_triangle_right | [] | [
398,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.closedBall_inv_subset_polar_closedBall | [] | [
263,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/CategoryTheory/GradedObject.lean | CategoryTheory.GradedObject.eqToHom_apply | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nβ : Type w\nX Y : β → C\nh : X = Y\nb : β\n⊢ X b = Y b",
"tactic": "rw [h]"
},
{
"state_after": "C : Type u\ninst✝ : Category C\nβ : Type w\nX : β → C\nb : β\n⊢ eqToHom (_ : X = X) b = eqToHom (_ : X b = X b)",
"st... | [
119,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.hasSum_fst_expSeries | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nR : Type u_2\nM : Type u_3\ninst✝¹⁵ : TopologicalSpace R\ninst✝¹⁴ : TopologicalSpace M\ninst✝¹³ : Field 𝕜\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup M\ninst✝¹⁰ : Algebra 𝕜 R\ninst✝⁹ : Module R M\ninst✝⁸ : Module Rᵐᵒᵖ M\ninst✝⁷ : SMulCommClass R R... | [
57,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_compl | [] | [
1628,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1627,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nat_mul_two_pi_sub | [] | [
376,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.forall_const | [] | [
516,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_setOf_im_lt | [
{
"state_after": "no goals",
"state_before": "a : ℝ\n⊢ frontier {z | z.im < a} = {z | z.im = a}",
"tactic": "simpa only [frontier_Iio] using frontier_preimage_im (Iio a)"
}
] | [
163,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_sup | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.862790\nR' : Type ?u.862793\n𝕜 : Type u_1\n𝕜₂ : Type ?u.862799\n𝕜₃ : Type ?u.862802\n𝕝 : Type ?u.862805\nE : Type u_2\nE₂ : Type ?u.862811\nE₃ : Type ?u.862814\nF : Type ?u.862817\nG : Type ?u.862820\nι : Type ?u.862823\ninst✝² : SeminormedRing �... | [
716,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_C | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nr : R\n⊢ Finset.gcd (support (↑C r)) (coeff (↑C r)) = ↑normalize r",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\nr : R\n⊢ content (↑C r) = ↑nor... | [
100,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Std/Logic.lean | exists_eq' | [] | [
454,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
454,
9
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.map_comp_inr | [
{
"state_after": "no goals",
"state_before": "N : Type u_4\nG : Type u_1\nH : Type ?u.270290\ninst✝⁴ : Group N\ninst✝³ : Group G\ninst✝² : Group H\nφ : G →* MulAut N\nN₁ : Type u_2\nG₁ : Type u_3\ninst✝¹ : Group N₁\ninst✝ : Group G₁\nφ₁ : G₁ →* MulAut N₁\nf₁ : N →* N₁\nf₂ : G →* G₁\nh : ∀ (g : G), MonoidHom... | [
308,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | essSup_mono_ae | [] | [
160,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_subset_left | [
{
"state_after": "α : Type u_1\nα' : Type ?u.42795\nβ : Type u_3\nβ' : Type ?u.42801\nγ : Type u_2\nγ' : Type ?u.42807\nδ : Type ?u.42810\nδ' : Type ?u.42813\nε : Type ?u.42816\nε' : Type ?u.42819\nζ : Type ?u.42822\nζ' : Type ?u.42825\nν : Type ?u.42828\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ninst✝⁶... | [
216,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_pos | [] | [
76,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_le | [] | [
1273,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1272,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.nat_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.81753\nβ : Type ?u.81756\nγ : Type ?u.81759\nσ : Type ?u.81762\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : ℕ →. ℕ\n⊢ Partrec f ↔ Nat.Partrec f",
"tactic": "simp [Partrec, map_id']"
}
] | [
487,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_mul_of_commute | [
{
"state_after": "f✝ g✝ f g : CircleDeg1Lift\nh : Commute f g\n⊢ Tendsto (fun x => transnumAuxSeq f x + transnumAuxSeq g x) atTop (𝓝 (τ (f * g)))",
"state_before": "f✝ g✝ f g : CircleDeg1Lift\nh : Commute f g\n⊢ τ (f * g) = τ f + τ g",
"tactic": "refine tendsto_nhds_unique ?_\n (f.tendsto_translationN... | [
735,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Nat.sum_range_choose | [
{
"state_after": "R : Type ?u.145590\nn : ℕ\nthis : ∑ m in range (n + 1), 1 ^ m * 1 ^ (n - m) * ↑(choose n m) = (1 + 1) ^ n\n⊢ ∑ m in range (n + 1), choose n m = 2 ^ n",
"state_before": "R : Type ?u.145590\nn : ℕ\n⊢ ∑ m in range (n + 1), choose n m = 2 ^ n",
"tactic": "have := (add_pow 1 1 n).symm"
},... | [
95,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_le_restrictScalars | [] | [
507,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.mk_one | [] | [
76,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balancedSz_up | [
{
"state_after": "α : Type ?u.9339\nl r₁ r₂ : ℕ\nh₁ : r₁ ≤ r₂\nh₂ : l + r₂ ≤ 1 ∨ r₂ ≤ delta * l\nH : BalancedSz l r₁\nh : ¬l + r₂ ≤ 1\n⊢ l ≤ delta * r₂ ∧ r₂ ≤ delta * l",
"state_before": "α : Type ?u.9339\nl r₁ r₂ : ℕ\nh₁ : r₁ ≤ r₂\nh₂ : l + r₂ ≤ 1 ∨ r₂ ≤ delta * l\nH : BalancedSz l r₁\n⊢ BalancedSz l r₂",
... | [
211,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_continuous_iff | [] | [
411,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.padicNorm_p | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : 1 < p\n⊢ padicNorm p ↑p = (↑p)⁻¹",
"tactic": "simp [padicNorm, (pos_of_gt hp).ne', padicValNat.self hp]"
}
] | [
89,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | DifferentiableWithinAt.div | [] | [
213,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_le_neg_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ 0 ≤ -x ↔ x ≤ 0",
"tactic": "rw [le_neg_iff, neg_zero]"
}
] | [
1376,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.add_one_lt_exp_of_pos | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℝ\nhx : 0 < x\n⊢ x + 1 < 1 + x + x ^ 2 / 2",
"tactic": "nlinarith"
}
] | [
1481,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_strict_mono | [] | [
185,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.mem_colon | [] | [
367,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | NormedField.exists_lt_norm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.372611\nγ : Type ?u.372614\nι : Type ?u.372617\ninst✝ : NontriviallyNormedField α\nr : ℝ\nw : α\nhw : 1 < ‖w‖\nn : ℕ\nhn : r < ‖w‖ ^ n\n⊢ r < ‖w ^ n‖",
"tactic": "rwa [norm_pow]"
}
] | [
732,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.comp_coimage_π_eq_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nP Q : C\nf : P ⟶ Q\nR : C\ng : Q ⟶ R\nh : f ≫ g = 0\n⊢ (f ≫ coimage.π g) ≫ Abelian.factorThruCoimage g = 0",
"tactic": "simp [h]"
}
] | [
352,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_iInter | [] | [
160,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.mul_div_cancel_left' | [
{
"state_after": "no goals",
"state_before": "m n k a b : ℕ\nHd : a ∣ b\n⊢ a * (b / a) = b",
"tactic": "rw [mul_comm, Nat.div_mul_cancel Hd]"
}
] | [
673,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
11
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.one_lt_card_iff_ne_bot | [] | [
172,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.congr_fun | [] | [
130,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.mapRange_eq_map | [
{
"state_after": "σ : Type u\nR✝ : Type v\ninst✝² : CommRing R✝\np✝ m : ℕ\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\np : MvPolynomial σ R\nf : R →+* S\n⊢ Finsupp.mapRange ↑↑f (_ : ↑↑f 0 = 0) p = ↑(map f) p",
"state_before": "σ : Type u\nR✝ : Type v\ninst✝² : CommRing R✝\np✝ m : ℕ\... | [
70,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.powerset_empty | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.epimorphisms.infer_property | [] | [
424,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.isoCoproduct_hom | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nf : J → C\ninst✝ : HasBiproduct f\nj : J\n⊢ ι f j ≫ (isoCoproduct f).hom = ι f j ≫ desc (Sigma.ι f)",
"tactic": "simp [← Iso.eq_comp_inv]"
}
] | [
506,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.one_add_natPred | [
{
"state_after": "no goals",
"state_before": "n : ℕ+\n⊢ 1 + natPred n = ↑n",
"tactic": "rw [natPred, add_tsub_cancel_iff_le.mpr <| show 1 ≤ (n : ℕ) from n.2]"
}
] | [
39,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | inner_matrix_row_row | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1855701\nι' : Type ?u.1855704\n𝕜 : Type u_3\ninst✝¹⁰ : IsROrC 𝕜\nE : Type ?u.1855713\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : InnerProductSpace 𝕜 E\nE' : Type ?u.1855733\ninst✝⁷ : NormedAddCommGroup E'\ninst✝⁶ : InnerProductSpace 𝕜 E'\nF : Type ?... | [
1014,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Bijective.injective | [] | [
93,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
11
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.dz_val | [
{
"state_after": "a : ℕ\na1 : 1 < a\nthis : 1 ≤ a * a\n⊢ ↑(a * a) - ↑1 = az a * az a - 1",
"state_before": "a : ℕ\na1 : 1 < a\nthis : 1 ≤ a * a\n⊢ ↑(Pell.d a1) = az a * az a - 1",
"tactic": "rw [Pell.d, Int.ofNat_sub this]"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\n... | [
185,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_lt_sub | [] | [
1126,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1125,
11
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.swap_apply_def | [] | [
1559,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1558,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.isOpen_ne_top | [] | [
57,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.div | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁶ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁵ : NormedAddCommGroup D\ninst✝¹⁴ : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace 𝕜 E\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁹ : ... | [
1739,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | FiniteField.pow_card_pow | [
{
"state_after": "case zero\nK : Type u_1\nR : Type ?u.348147\ninst✝¹ : GroupWithZero K\ninst✝ : Fintype K\na : K\n⊢ a ^ q ^ Nat.zero = a\n\ncase succ\nK : Type u_1\nR : Type ?u.348147\ninst✝¹ : GroupWithZero K\ninst✝ : Fintype K\na : K\nn : ℕ\nih : a ^ q ^ n = a\n⊢ a ^ q ^ Nat.succ n = a",
"state_before": ... | [
141,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.nonempty_support_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ Finset.Nonempty (support p) ↔ p ≠ 0",
"tactic": "rw [Ne.def, nonempty_iff_ne_empty, Ne.def, ← support_eq_empty]"
}
] | [
502,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subtype.mono_coe | [] | [
1138,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1137,
1
] |
Mathlib/Algebra/Group/Opposite.lean | MulOpposite.op_natCast | [] | [
183,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.coe_lTensorHom | [] | [
1028,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1027,
1
] |
Mathlib/Order/SuccPred/LinearLocallyFinite.lean | toZ_of_ge | [] | [
201,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.tan_eq_zero_iff | [
{
"state_after": "θ : ℂ\nh : 2 * sin θ * cos θ = sin (2 * θ)\n⊢ tan θ = 0 ↔ ∃ k, θ = ↑k * ↑π / 2",
"state_before": "θ : ℂ\n⊢ tan θ = 0 ↔ ∃ k, θ = ↑k * ↑π / 2",
"tactic": "have h := (sin_two_mul θ).symm"
},
{
"state_after": "θ : ℂ\nh : 2 * (sin θ * cos θ) = sin (2 * θ)\n⊢ tan θ = 0 ↔ ∃ k, θ = ↑k ... | [
72,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Algebra/GeomSum.lean | Commute.geom_sum₂_Ico | [
{
"state_after": "α : Type u\ninst✝ : DivisionRing α\nx y : α\nh : Commute x y\nhxy : x ≠ y\nm n : ℕ\nhmn : m ≤ n\nthis : x - y ≠ 0\n⊢ ∑ i in Ico m n, x ^ i * y ^ (n - 1 - i) = (x ^ n - y ^ (n - m) * x ^ m) / (x - y)",
"state_before": "α : Type u\ninst✝ : DivisionRing α\nx y : α\nh : Commute x y\nhxy : x ≠ ... | [
347,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
11
] |
Mathlib/ModelTheory/Quotients.lean | FirstOrder.Language.Term.realize_quotient_mk' | [
{
"state_after": "case var\nL : Language\nM : Type u_4\ns : Setoid M\nps : Prestructure L s\nβ : Type u_1\nx : β → M\n_a✝ : β\n⊢ realize (fun i => Quotient.mk s (x i)) (var _a✝) = Quotient.mk s (realize x (var _a✝))\n\ncase func\nL : Language\nM : Type u_4\ns : Setoid M\nps : Prestructure L s\nβ : Type u_1\nx :... | [
80,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_pi | [
{
"state_after": "case intro\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_1\ninst✝¹⁴ : Ring K\ninst✝¹³ : StrongRankCondition K\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : Module K V\ninst✝¹⁰ : Module.Free K V\ninst✝⁹ : AddCommGroup V'\ninst✝... | [
1012,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/Order/CompleteLattice.lean | Prod.iInf_mk | [] | [
1871,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1869,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Comp.lean | MvQPF.Comp.get_mk | [] | [
58,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
11
] |
Mathlib/Algebra/Associated.lean | Associated.irreducible_iff | [] | [
651,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.le_tsum | [] | [
861,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
11
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_sSup | [
{
"state_after": "case h\nι : Sort ?u.109989\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ns : Set (Subgraph G)\ne : Sym2 V\n⊢ e ∈ edgeSet (sSup s) ↔ e ∈ ⋃ (G' : Subgraph G) (_ : G' ∈ s), edgeSet G'",
"state_before": "ι : Sort ?u.109989\nV : Type u\nW : Type v\nG : SimpleGraph V\n... | [
561,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_atBot_iff_of_monotone | [] | [
1317,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1314,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.IntegrableOn.locallyIntegrableOn | [] | [
64,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubalgebra.lie_mem_sup_of_mem_normalizer | [
{
"state_after": "R : Type u_2\nL : Type u_1\nM : Type ?u.47924\nM' : Type ?u.47927\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : Lie... | [
152,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.linear_refl | [] | [
318,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.prod_source | [] | [
941,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
939,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_inf_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.41525\nδ : Type ?u.41528\nι : Sort ?u.41531\ns : Set α\nt : Set β\nf : Filter α\ng : Filter β\nf₁ f₂ : Filter α\ng₁ g₂ : Filter β\n⊢ f₁ ×ˢ g₁ ⊓ f₂ ×ˢ g₂ = (f₁ ⊓ f₂) ×ˢ (g₁ ⊓ g₂)",
"tactic": "simp only [SProd.sprod, Fil... | [
390,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_add | [] | [
1388,
36
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1386,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfLeftIso_x | [] | [
1781,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1781,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMin.on | [] | [
94,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_fintype | [] | [
174,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_add_closedBall_subset | [
{
"state_after": "case intro.intro.intro.intro\nR : Type ?u.878378\nR' : Type ?u.878381\n𝕜 : Type u_1\n𝕜₂ : Type ?u.878387\n𝕜₃ : Type ?u.878390\n𝕝 : Type ?u.878393\nE : Type u_2\nE₂ : Type ?u.878399\nE₃ : Type ?u.878402\nF : Type ?u.878405\nG : Type ?u.878408\nι : Type ?u.878411\ninst✝² : SeminormedRing 𝕜\... | [
764,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.coe_rpow | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.contSupp_supports | [
{
"state_after": "case halt\nS : Finset Λ'\nH : contSupp Cont'.halt ⊆ S\n⊢ Supports (contSupp Cont'.halt) S\n\ncase cons₁\nS : Finset Λ'\na✝¹ : Code\na✝ : Cont'\na_ih✝ : contSupp a✝ ⊆ S → Supports (contSupp a✝) S\nH : contSupp (Cont'.cons₁ a✝¹ a✝) ⊆ S\n⊢ Supports (contSupp (Cont'.cons₁ a✝¹ a✝)) S\n\ncase cons₂\... | [
2058,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2041,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_cos_add_sin_mul_I_coe_angle | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ ↑(arg (↑(Angle.cos θ) + ↑(Angle.sin θ) * I)) = θ",
"tactic": "rw [← one_mul (_ + _), ← ofReal_one, arg_mul_cos_add_sin_mul_I_coe_angle zero_lt_one]"
}
] | [
471,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_insert | [
{
"state_after": "F : Type ?u.361063\nα : Type u_1\nβ : Type ?u.361069\nγ : Type ?u.361072\nι : Type ?u.361075\nκ : Type ?u.361078\ninst✝ : LinearOrder α\ns✝ : Finset α\nH✝ : Finset.Nonempty s✝\nx a : α\ns : Finset α\nH : Finset.Nonempty s\n⊢ IsLeast (insert a ↑s) (min a (min' s H))",
"state_before": "F : T... | [
1484,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/CategoryTheory/Sites/Sieves.lean | CategoryTheory.Sieve.functorPullback_top | [] | [
723,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.toSubtype_π | [] | [
613,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Std/Data/List/Lemmas.lean | List.append_eq_append_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : List α\n⊢ a ++ b = c ++ d ↔ (∃ a', c = a ++ a' ∧ b = a' ++ d) ∨ ∃ c', a = c ++ c' ∧ d = c' ++ b",
"tactic": "induction a generalizing c with\n| nil => simp; exact (or_iff_left_of_imp fun ⟨_, ⟨e, rfl⟩, h⟩ => e ▸ h.symm).symm\n| cons a ... | [
135,
75
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
131,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.linearIndependent | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2133622\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_3\ndec_ι : DecidableEq ι\nv : ι → E\nhv : Orthonormal 𝕜 v\n⊢ ∀ ... | [
874,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.isTopologicalBasis_of_subbasis | [
{
"state_after": "α : Type u\ns : Set (Set α)\n⊢ IsTopologicalBasis ((fun f => ⋂₀ f) '' {f | Set.Finite f ∧ f ⊆ s})",
"state_before": "α : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nhs : t = generateFrom s\n⊢ IsTopologicalBasis ((fun f => ⋂₀ f) '' {f | Set.Finite f ∧ f ⊆ s})",
"tactic": "subst t"
... | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/MeasureTheory/Measure/Content.lean | MeasureTheory.Content.outerMeasure_pos_of_is_mul_left_invariant | [
{
"state_after": "case h.e'_4\nG : Type w\ninst✝³ : TopologicalSpace G\nμ : Content G\ninst✝² : T2Space G\ninst✝¹ : Group G\ninst✝ : TopologicalGroup G\nh3 :\n ∀ (g : G) {K : Compacts G},\n (fun s => ↑(toFun μ s)) (Compacts.map (fun b => g * b) (_ : Continuous fun b => g * b) K) =\n (fun s => ↑(toFun μ... | [
343,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.reduce_v | [
{
"state_after": "no goals",
"state_before": "u✝ x✝ : XgcdType\nu : XgcdType := x✝\nh : r u = 0\n⊢ v (reduce x✝) = v x✝",
"tactic": "rw [reduce_a h, finish_v u h]"
},
{
"state_after": "u✝ x✝ : XgcdType\nu : XgcdType := x✝\nh : ¬r u = 0\nthis : sizeOf (step u) < sizeOf u\n⊢ v (reduce x✝) = v x✝",... | [
397,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Eventually.exists_forall_of_atTop | [] | [
315,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/CategoryTheory/Bicategory/NaturalTransformation.lean | CategoryTheory.OplaxNatTrans.whiskerLeft_naturality_id | [
{
"state_after": "no goals",
"state_before": "B : Type u₁\ninst✝¹ : Bicategory B\nC : Type u₂\ninst✝ : Bicategory C\nF G H : OplaxFunctor B C\nη : OplaxNatTrans F G\nθ : OplaxNatTrans G H\na b c : B\na' : C\nf : a' ⟶ (↑G.toPrelaxFunctor).obj a\n⊢ f ◁ naturality θ (𝟙 a) ≫ f ◁ app θ a ◁ OplaxFunctor.mapId H ... | [
151,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/LinearAlgebra/Ray.lean | exists_pos_right_iff_sameRay | [
{
"state_after": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ (∃ r, 0 < r ∧ x = r • y) ↔ SameRay R y x",
"state_before": "R : Type u_2\ninst✝² : LinearOrderedField R\nM : Type u_1\ninst✝¹ : AddCommGroup M\ninst✝ :... | [
738,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.IsClique.card_le_chromaticNumber | [
{
"state_after": "case intro\nV : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝ : Finite V\ns : Finset V\nh : IsClique G ↑s\nval✝ : Fintype V\n⊢ Finset.card s ≤ chromaticNumber G",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝ : Finite V\ns : Finset V\n... | [
444,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombinationLineMapWeights_apply_right | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type ?u.438199\nP : Type ?u.438202\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.438858\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni j : ι\nh : i ≠ j\nc : k\n⊢ affineC... | [
728,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | exists_zpow_eq_one | [
{
"state_after": "case intro.intro\nG : Type u\nA : Type v\nx✝ y : G\na b : A\nn m : ℕ\ninst✝² : Group G\ninst✝¹ : AddGroup A\ninst✝ : Finite G\nx : G\nw : ℕ\nhw1 : w > 0\nhw2 : IsPeriodicPt ((fun x x_1 => x * x_1) x) w 1\n⊢ ∃ i x_1, x ^ i = 1",
"state_before": "G : Type u\nA : Type v\nx✝ y : G\na b : A\nn ... | [
806,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.additiveObjIsoBiproduct_naturality | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\nD : Type u₁\ninst✝³ : Category D\ninst✝² : Preadditive D\ninst✝¹ : HasFiniteBiproducts D\nF : Mat_ C ⥤ D\ninst✝ : Functor.Additive F\nM N : Mat_ C\nf : M ⟶ N\ni : N.ι\n⊢ (F.map f ≫ (additiveObjIsoBiproduct F N).hom) ≫ biproduct.π (fun i... | [
425,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀ | [] | [
319,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Std/Data/Array/Lemmas.lean | Array.get?_eq_data_get? | [] | [
60,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
59,
1
] |
Mathlib/CategoryTheory/Monoidal/Functor.lean | CategoryTheory.MonoidalFunctor.ε_hom_inv_id | [] | [
267,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.empty_mul | [] | [
231,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.kerLift_mk' | [] | [
360,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\na✝ b✝ : R\nm n : ℕ\ninst✝ : Semiring R\np q : R[X]\na b : AddMonoidAlgebra R ℕ\n⊢ { toFinsupp := a * b } = Polynomial.mul { toFinsupp := a } { toFinsupp := b }",
"tactic": "rw [mul_def]"
}
] | [
184,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.prod_repr_inl | [] | [
718,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
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