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/RingTheory/FractionalIdeal.lean | FractionalIdeal.canonicalEquiv_canonicalEquiv | [
{
"state_after": "case a\nR : Type u_2\ninst✝⁹ : CommRing R\nS : Submonoid R\nP : Type u_3\ninst✝⁸ : CommRing P\ninst✝⁷ : Algebra R P\nloc : IsLocalization S P\nP' : Type u_4\ninst✝⁶ : CommRing P'\ninst✝⁵ : Algebra R P'\nloc' : IsLocalization S P'\nP''✝ : Type ?u.928438\ninst✝⁴ : CommRing P''✝\ninst✝³ : Algebra... | [
935,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousWithinAt.zpow₀ | [] | [
343,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
8
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_eq_zero | [
{
"state_after": "b x y : ℝ\n⊢ (x = 0 ∨ x = 1 ∨ x = -1) ∨ b = 0 ∨ b = 1 ∨ b = -1 ↔ b = 0 ∨ b = 1 ∨ b = -1 ∨ x = 0 ∨ x = 1 ∨ x = -1",
"state_before": "b x y : ℝ\n⊢ logb b x = 0 ↔ b = 0 ∨ b = 1 ∨ b = -1 ∨ x = 0 ∨ x = 1 ∨ x = -1",
"tactic": "simp_rw [logb, div_eq_zero_iff, log_eq_zero]"
},
{
"state... | [
385,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_neg_eq_arg_sub_pi_of_im_pos | [
{
"state_after": "x : ℂ\nhi : 0 < x.im\n⊢ -arccos ((-x).re / ↑abs (-x)) = arccos (x.re / ↑abs x) - π",
"state_before": "x : ℂ\nhi : 0 < x.im\n⊢ arg (-x) = arg x - π",
"tactic": "rw [arg_of_im_pos hi, arg_of_im_neg (show (-x).im < 0 from Left.neg_neg_iff.2 hi)]"
},
{
"state_after": "no goals",
... | [
377,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.recOn_of_mul | [] | [
177,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Part.lean | Part.toOption_eq_none_iff | [] | [
310,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_int_cast_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Ring R\nn : ℤ\nk : ℕ\nf : R[X]\n⊢ (↑derivative^[k]) (↑n * f) = ↑n * (↑derivative^[k]) f",
"tactic": "induction' k with k ih generalizing f <;> simp [*]"
}
] | [
631,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_add_of_order_eq.aux | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\n_h : order φ ≠ order ψ\nH : order φ < order ψ\n⊢ order (φ + ψ) = order φ",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\n_h : order φ ≠ order ψ\nH : order φ < order ψ\n⊢ order (φ + ψ) ≤ order φ ⊓ order ψ... | [
2359,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2346,
9
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_zero | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | zpow_le_iff_le | [] | [
87,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictFDerivAt_exp_of_mem_ball | [] | [
120,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | le_tsub_of_add_le_left | [] | [
237,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_floor | [] | [
917,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Order/Max.lean | not_isTop | [] | [
222,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.encode_ofNatCode | [
{
"state_after": "no goals",
"state_before": "⊢ encodeCode (ofNatCode 0) = 0",
"tactic": "simp [ofNatCode, encodeCode]"
},
{
"state_after": "no goals",
"state_before": "⊢ encodeCode (ofNatCode 1) = 1",
"tactic": "simp [ofNatCode, encodeCode]"
},
{
"state_after": "no goals",
"... | [
188,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
9
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_cubic | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1382528\nha : a ≠ 0\n⊢ ↑3 = 3",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1382528\nha : a ≠ 0\n⊢ degree (↑C a * X ^ 3 + ↑C b * X ^ 2 + ... | [
1230,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1226,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.mem_doset_self | [] | [
50,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/Order/Monoid/WithZero/Defs.lean | WithZero.covariantClass_add_le | [
{
"state_after": "α : Type u\ninst✝² : AddZeroClass α\ninst✝¹ : Preorder α\ninst✝ : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\nh : ∀ (a : α), 0 ≤ a\na b c : WithZero α\nhbc : b ≤ c\n⊢ a + b ≤ a + c",
"state_before": "α : Type u\ninst✝² : AddZeroClass α\ninst✝¹ : Preorder α\ninst✝ : Cova... | [
121,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
11
] |
Mathlib/Data/Nat/Choose/Central.lean | Nat.two_le_centralBinom | [] | [
69,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Parity.lean | IsSquare_sq | [] | [
129,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.not_mem_of_not_mem_closure | [] | [
319,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.mem_diff_shiftr_find | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.169884\nπ : ι → Type ?u.169889\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nK : CompactExhaustion α\nx : α\n⊢ ¬CompactExhaustion.find (shiftr K) x ≤ CompactExhaustion.find K x",
"tactic": "simp on... | [
1503,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1501,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type ?u.125421\nF : Type u_2\nF' : Type u_3\nG : Type ?u.125430\n𝕜 : Type ?u.125433\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\nin... | [
290,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_add | [] | [
1098,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.map_div_left_eq_self | [] | [
468,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.asq_pos | [
{
"state_after": "a : ℕ\na1 : 1 < a\nthis : a * 1 ≤ a * a\n⊢ a ≤ a * a",
"state_before": "a : ℕ\na1 : 1 < a\n⊢ a ≤ a * a",
"tactic": "have := @Nat.mul_le_mul_left 1 a a (le_of_lt a1)"
},
{
"state_after": "no goals",
"state_before": "a : ℕ\na1 : 1 < a\nthis : a * 1 ≤ a * a\n⊢ a ≤ a * a",
... | [
180,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_eq_iff_covby | [
{
"state_after": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : PredOrder α\nb : α\ninst✝ : NoMinOrder α\n⊢ pred b ⋖ b",
"state_before": "α : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : PredOrder α\na b : α\ninst✝ : NoMinOrder α\n⊢ pred b = a → a ⋖ b",
"tactic": "rintro rfl"
},
{
"state_after"... | [
847,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
1
] |
Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.ofHasUnitMulPowIrreducibleFactorization | [
{
"state_after": "R✝ : Type ?u.108992\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nhR : HasUnitMulPowIrreducibleFactorization R\nthis : UniqueFactorizationMonoid R := HasUnitMulPowIrreducibleFactorization.toUniqueFactorizationMonoid hR\n⊢ DiscreteValuationRing R",
"state_before": "R✝ : Type ?u.1089... | [
319,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_finset_of_monotone | [
{
"state_after": "ι : Type ?u.269296\nι' : Type ?u.269299\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.269308\ninst✝ : Preorder β\nf : β → Finset α\nh : Monotone f\nh' : ∀ (x : α), ∃ n, x ∈ f n\n⊢ ∀ (i : α), ∀ᶠ (a : β) in atTop, f a ∈ Ici {i}",
"state_before": "ι : Type ?u.269296\nι' : Type ?u.269299\nα : Type ... | [
1379,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
] |
Mathlib/Algebra/Group/Basic.lean | exists_npow_eq_one_of_zpow_eq_one | [
{
"state_after": "case ofNat\nα : Type ?u.63936\nβ : Type ?u.63939\nG : Type u_1\ninst✝ : Group G\na b c d x : G\nn : ℕ\nhn : Int.ofNat n ≠ 0\nh : x ^ Int.ofNat n = 1\n⊢ ∃ n, 0 < n ∧ x ^ n = 1\n\ncase negSucc\nα : Type ?u.63936\nβ : Type ?u.63939\nG : Type u_1\ninst✝ : Group G\na b c d x : G\nn : ℕ\nhn : Int.ne... | [
889,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | differentiableWithinAt_inv | [] | [
89,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.smul_vec3 | [
{
"state_after": "no goals",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nR : Type u_1\ninst✝ : SMul R α\nx : R\na₀ a₁ a₂ : α\n⊢ x • ![a₀, a₁, a₂] = ![x • a₀, x • a₁, x • a₂]",
"tactic": "rw [smul_cons, smul_cons, smul_cons, smul_empty]"
}
] | [
485,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_fst | [] | [
836,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Units.mk0_mul | [
{
"state_after": "case a\nα : Type ?u.18576\nM₀ : Type ?u.18579\nG₀ : Type u_1\nM₀' : Type ?u.18585\nG₀' : Type ?u.18588\nF : Type ?u.18591\nF' : Type ?u.18594\ninst✝¹ : MonoidWithZero M₀\ninst✝ : GroupWithZero G₀\na b c x y : G₀\nhxy : x * y ≠ 0\n⊢ ↑(mk0 (x * y) hxy) = ↑(mk0 x (_ : x ≠ 0) * mk0 y (_ : y ≠ 0))"... | [
281,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Topology/Constructions.lean | CofiniteTopology.isClosed_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.17786\nδ : Type ?u.17789\nε : Type ?u.17792\nζ : Type ?u.17795\ns : Set (CofiniteTopology α)\n⊢ IsClosed s ↔ s = univ ∨ Set.Finite s",
"tactic": "simp only [← isOpen_compl_iff, isOpen_iff', compl_compl, compl_empty_iff]"
... | [
291,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.smul_toProd | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_le_of_one_lt_of_pos | [] | [
770,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_inter_subset_left | [] | [
346,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_zero' | [
{
"state_after": "case h\n𝕜 : Type ?u.24181\nE : Type u_1\nF : Type ?u.24187\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\nx : E\n⊢ gauge 0 x = OfNat.ofNat 0 x",
"state_before": "𝕜 : Type ?u.24181\nE : Type u_1\nF : Type ?u.24187\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set ... | [
117,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.image_mul_prod | [] | [
351,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_sub | [
{
"state_after": "no goals",
"state_before": "a✝ d e : Int\n⊢ a✝ * d - a✝ * e = a✝ * (d - e)",
"tactic": "rw [Int.mul_sub]"
}
] | [
619,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
618,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_le_norm_add_norm_div | [
{
"state_after": "𝓕 : Type ?u.86263\n𝕜 : Type ?u.86266\nα : Type ?u.86269\nι : Type ?u.86272\nκ : Type ?u.86275\nE : Type u_1\nF : Type ?u.86281\nG : Type ?u.86284\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nu v : E\n⊢ ‖v‖ ≤ ... | [
587,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Adj.ne | [] | [
211,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
11
] |
Mathlib/Analysis/Convex/Segment.lean | Prod.image_mk_segment_right | [
{
"state_after": "case h.mk\n𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.327345\nι : Type ?u.327348\nπ : ι → Type ?u.327353\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx : E\ny₁ y₂ : F\nx' : E\ny' : F\n⊢ (x', y') ∈ (fun ... | [
618,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sqrtTwoAddSeries_zero | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ sqrtTwoAddSeries x 0 = x",
"tactic": "simp"
}
] | [
682,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.optionSubtype_apply_symm_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.18695\ninst✝ : DecidableEq β\nx : β\ne : { e // ↑e none = x }\nb : { y // y ≠ x }\n⊢ some\n (↑(↑{\n toFun := fun e =>\n { toFun := fun a => { val := ↑↑e (some a), property := (_ : ↑↑e (some a) ≠ x) },\n ... | [
237,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_inter | [] | [
1659,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1658,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_Iic | [] | [
214,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.nhdsWithin_compl_infty_eq | [
{
"state_after": "case refine'_1\nX : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ ∀ (i : Set (OnePoint X)), ∞ ∈ i ∧ IsOpen i → ∃ i', (IsClosed i' ∧ IsCompact i') ∧ some '' i'ᶜ ⊆ i ∩ {∞}ᶜ\n\ncase refine'_2\nX : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\n⊢ ... | [
318,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.IsPrime.isPrimary | [] | [
1852,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1851,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | PicardLindelof.FunSpace.dist_iterate_next_le | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nv : PicardLindelof E\nf : FunSpace v\ninst✝ : CompleteSpace E\nf₁ f₂ : FunSpace v\nn : ℕ\nt : ↑(Icc v.tMin v.tMax)\n⊢ (↑v.L * abs (↑t - ↑v.t₀)) ^ n / ↑n ! * dist f₁ f₂ ≤ (↑v.L * tDist v) ^ n / ↑n ! * dist f₁ f₂",
"state... | [
338,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.copy_eq | [] | [
277,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.pow_apply_eq | [
{
"state_after": "case inl\nι : Type ?u.1658946\nα : Type u_1\nβ : Type ?u.1658952\nf g : Perm α\ns t : Set α\na b x y : α\nn : ℕ\nhf : IsCycleOn f ↑{a}\nha : a ∈ {a}\n⊢ ↑(f ^ n) a = a ↔ card {a} ∣ n\n\ncase inr\nι : Type ?u.1658946\nα : Type u_1\nβ : Type ?u.1658952\nf g : Perm α\ns✝ t : Set α\na b x y : α\ns ... | [
869,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | Complex.tendsto_euler_sin_prod | [
{
"state_after": "z : ℂ\nA :\n Tendsto\n (fun n =>\n ((↑π * z * ∏ j in Finset.range n, (1 - z ^ 2 / (↑j + 1) ^ 2)) *\n ∫ (x : ℝ) in 0 ..π / 2, Complex.cos (2 * z * ↑x) * ↑(cos x) ^ (2 * n)) /\n ↑(∫ (x : ℝ) in 0 ..π / 2, cos x ^ (2 * n)))\n atTop (𝓝 (Complex.sin (↑π * z)))\n⊢ Tendsto... | [
331,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean | charmatrix_apply_natDegree_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝³ : CommRing R\nn G : Type v\ninst✝² : DecidableEq n\ninst✝¹ : Fintype n\nα β : Type v\ninst✝ : DecidableEq α\nM : Matrix n n R\ni j : n\n⊢ natDegree (charmatrix M i j) ≤ if i = j then 1 else 0",
"tactic": "split_ifs with h <;> simp [h, natD... | [
57,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/ContinuousOn.lean | DenseRange.nhdsWithin_neBot | [] | [
410,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Topology/Order.lean | nhds_iInf | [] | [
661,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.one_mem_divisors | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 1 ∈ divisors n ↔ n ≠ 0",
"tactic": "simp"
}
] | [
104,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_atBot_eq_of_gc | [] | [
1517,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1514,
1
] |
Mathlib/Data/List/Basic.lean | List.eq_cons_of_mem_head? | [
{
"state_after": "ι : Type ?u.41922\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx a : α\nl : List α\nh : a = x\n⊢ a :: l = x :: tail (a :: l)",
"state_before": "ι : Type ?u.41922\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx a : α\nl : List α\nh : x ∈ head? (a :: l)... | [
879,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Data/W/Cardinal.lean | WType.cardinal_mk_le_max_aleph0_of_finite | [
{
"state_after": "α : Type u\nβ : α → Type u\ninst✝ : ∀ (a : α), Finite (β a)\nh : IsEmpty α\n⊢ (#WType β) ≤ max (#α) ℵ₀",
"state_before": "α : Type u\nβ : α → Type u\ninst✝ : ∀ (a : α), Finite (β a)\n⊢ IsEmpty α → (#WType β) ≤ max (#α) ℵ₀",
"tactic": "intro h"
},
{
"state_after": "α : Type u\nβ... | [
84,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.dist_left | [] | [
407,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
11
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.mem_cycleFactorsFinset_iff | [
{
"state_after": "case intro.intro\nι : Type ?u.2735472\nα : Type u_1\nβ : Type ?u.2735478\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ f p : Perm α\nl : List (Perm α)\nhl : List.Nodup l\nhl' : List.toFinset l = cycleFactorsFinset f\n⊢ p ∈ cycleFactorsFinset f ↔ IsCycle p ∧ ∀ (a : α), a ∈ support p → ↑p a = ↑... | [
1413,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_eq_right | [
{
"state_after": "no goals",
"state_before": "a b : Cardinal\nhb : ℵ₀ ≤ b\nha : a ≤ b\n⊢ a + b = b",
"tactic": "rw [add_comm, add_eq_left hb ha]"
}
] | [
784,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.congr_left | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.4752\nγ : Type ?u.4755\na b c : α\nh : Quotient.mk (Rel.setoid α) (b, a) = Quotient.mk (Rel.setoid α) (c, a)\n⊢ b = c\n\ncase mpr\nα : Type u_1\nβ : Type ?u.4752\nγ : Type ?u.4755\na b c : α\nh : b = c\n⊢ Quotient.mk (Rel.setoid α) (b, a) = Quotient.mk (Rel.s... | [
165,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Algebra/Group/WithOne/Basic.lean | MulEquiv.withOneCongr_symm | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/List/Nodup.lean | List.disjoint_of_nodup_append | [] | [
223,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Std/Data/List/Lemmas.lean | List.cons_ne_nil | [] | [
20,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
1
] |
src/lean/Init/Core.lean | Iff.trans | [] | [
669,
43
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
666,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.a_mono | [
{
"state_after": "case intro.intro\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nL : F\nr ε δ : ℝ\nh : ε ≤ δ\nx r' : ℝ\nr'r : r' ∈ Ioc (r / 2) r\nhr' : ∀ (y : ℝ), y ∈ Icc x (x + r') → ∀ (z : ℝ), z ∈ Icc x (x + r') → ‖f z - f y - (z - y) • L‖ ≤ ε * r\n⊢ x ∈ A f L r ... | [
516,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.CommSq.cone_snd | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_mul_X | [] | [
1026,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.rTensorHomToHomRTensor_apply | [] | [
852,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/LinearAlgebra/Matrix/ZPow.lean | Matrix.Commute.mul_zpow | [
{
"state_after": "no goals",
"state_before": "n' : Type u_1\ninst✝² : DecidableEq n'\ninst✝¹ : Fintype n'\nR : Type u_2\ninst✝ : CommRing R\nA B : M\nh : Commute A B\nn : ℕ\n⊢ (A * B) ^ ↑n = A ^ ↑n * B ^ ↑n",
"tactic": "simp [h.mul_pow n, -mul_eq_mul]"
},
{
"state_after": "no goals",
"state_... | [
314,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.map_lift'_eq2 | [] | [
307,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Std/Data/String/Lemmas.lean | String.data_take | [
{
"state_after": "no goals",
"state_before": "s : String\nn : Nat\n⊢ (take s n).data = List.take n s.data",
"tactic": "rw [take_eq]"
}
] | [
1099,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1099,
9
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.multiplicity_add_eq_min | [
{
"state_after": "case inl\nα : Type u_1\ninst✝¹ : Ring α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nh : multiplicity p a ≠ multiplicity p b\nhab : multiplicity p a < multiplicity p b\n⊢ multiplicity p (a + b) = min (multiplicity p a) (multiplicity p b)\n\ncase inr.inl\nα : Type u_1\ninst✝¹ : Ring α... | [
467,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.map_tmul | [] | [
726,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Data/Nat/Choose/Sum.lean | Commute.add_pow | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nx y : R\nh : Commute x y\nn : ℕ\nt : ℕ → ℕ → R := fun n m => x ^ m * y ^ (n - m) * ↑(Nat.choose n m)\n⊢ (x + y) ^ n = ∑ m in range (n + 1), x ^ m * y ^ (n - m) * ↑(Nat.choose n m)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nx y : R\nh : Commute x ... | [
71,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | extChartAt_preimage_mem_nhdsWithin' | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.219932\nM' : Type ?u.219935\nH' : Type ?u.219938\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : Topologi... | [
1208,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1205,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous.prod_mk_left | [] | [
1630,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1628,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_X_pow | [] | [
1263,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_nhds_left | [] | [
797,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.StronglyMeasurable.smul_const | [] | [
478,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
11
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.unique_ext_iff | [] | [
279,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_congr_meas | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.307127\nγ : Type ?u.307130\nδ : Type ?u.307133\nι : Type ?u.307136\nR : Type ?u.307139\nR' : Type ?u.307142\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t✝ : Set... | [
1803,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1798,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_le_add_iff_left | [] | [
780,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
779,
11
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_min | [] | [
353,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsGreatest.isLUB | [] | [
283,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_comp_C | [] | [
1607,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1606,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mul_right_not_lt | [
{
"state_after": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\nh : a ≠ 0\n⊢ ¬b * a ≺ b",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na b : R\nh : a ≠ 0\n⊢ ¬a * b ≺ b",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDomai... | [
154,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_nat_cast | [] | [
523,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.indicator | [] | [
342,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_ne_zero | [
{
"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[X]\nι : Type ?u.514573\n⊢ leadingCoeff p ≠ 0 ↔ p ≠ 0",
"tactic": "rw [Ne.def, leadingCoeff_eq_zero]"
}
] | [
668,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Data/Set/Image.lean | Subtype.preimage_val_eq_preimage_val_iff | [] | [
1453,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1451,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_union_filter_of_codisjoint | [] | [
2956,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2954,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_linear | [
{
"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[X]\nι : Type ?u.910503\nha : a ≠ 0\n⊢ leadingCoeff (↑C a * X + ↑C b) = a",
"tactic": "rw [add_comm, leadingCoeff_add_of_degree_lt (degree_C_lt_degree_C_mul_X ha),\n leadingCoeff_C_mul... | [
1170,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.stepAux_read | [
{
"state_after": "Γ : Type u_3\ninst✝² : Inhabited Γ\nΛ : Type u_2\ninst✝¹ : Inhabited Λ\nσ : Type u_1\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nM : Λ → Stmt₁\nencdec : ∀ (a : Γ), dec (enc a) = a\nf : Γ → Stmt Bool Λ' σ\nv : σ\n... | [
1850,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1822,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.tendsto_lift₂_nhdsWithin | [
{
"state_after": "X : Type u_1\nY : Type u_2\nZ : Type ?u.107519\nα : Type u_3\nι : Type ?u.107525\nπ : ι → Type ?u.107530\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx✝ y✝ z : X\ns✝ : Set X\nf✝ : X → Y\nt : Set (SeparationQuo... | [
604,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
9
] |
Mathlib/FieldTheory/Subfield.lean | Subfield.comap_top | [] | [
812,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
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