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/MeasureTheory/Measure/Lebesgue/EqHaar.lean | MeasureTheory.Measure.add_haar_submodule | [
{
"state_after": "case intro\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : IsAddHaarMeasure μ\ns : Submodule ℝ E\nhs : s ≠ ⊤\nx : E\nhx : ¬x ∈ s\n⊢ ↑↑μ ↑s = 0",
"state_before":... | [
182,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_pair_fin | [
{
"state_after": "k : Type u_1\nV : Type u_3\nP : Type u_2\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type ?u.492907\ns : Finset ι\nι₂ : Type ?u.492913\ns₂ : Finset ι₂\ninst✝ : Invertible 2\np : Fin 2 → P\n⊢ centroid k {0, 1} p = 2⁻¹ • (p 1 -ᵥ p 0) +ᵥ p... | [
883,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/List/Basic.lean | List.indexOf_get | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.92215\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : indexOf a (b :: l) < length (b :: l)\n⊢ get (b :: l) { val := indexOf a (b :: l), isLt := h } = a",
"tactic": "by_cases h' : a ... | [
1407,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.fun_support_eq | [] | [
195,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Regular/Pow.lean | IsRegular.pow_iff | [] | [
66,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/Monotone/Odd.lean | monotone_of_odd_of_monotoneOn_nonneg | [
{
"state_after": "G : Type u_2\nH : Type u_1\ninst✝¹ : LinearOrderedAddCommGroup G\ninst✝ : OrderedAddCommGroup H\nf : G → H\nh₁ : ∀ (x : G), f (-x) = -f x\nh₂ : MonotoneOn f (Ici 0)\nx : G\nhx : x ∈ Iic 0\ny : G\nhy : y ∈ Iic 0\nhxy : x ≤ y\n⊢ -f y ≤ -f x",
"state_before": "G : Type u_2\nH : Type u_1\ninst... | [
49,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_of_ne | [] | [
156,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_bot | [] | [
370,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_mul | [] | [
702,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_move | [] | [
1108,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fib_one | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Std/Classes/LawfulMonad.lean | LawfulMonad.mk' | [
{
"state_after": "m : Type u → Type v\ninst✝ : Monad m\nid_map : ∀ {α : Type u} (x : m α), id <$> x = x\npure_bind : ∀ {α β : Type u} (x : α) (f : α → m β), pure x >>= f = f x\nbind_assoc : ∀ {α β γ : Type u} (x : m α) (f : α → m β) (g : β → m γ), x >>= f >>= g = x >>= fun x => f x >>= g\nmap_const : autoParam ... | [
36,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
12,
1
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_iff | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type ?u.361200\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι✝ : Type ?u.361850\nι : Type u_1\np : ι → V\ns : Finset ι\nw : ι → k\nhw : ∑ i in s, w i = 0\n⊢ (↑(Finset.weightedVSub s p) w... | [
493,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithBot.coe_add | [] | [
558,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.comp_comp | [] | [
576,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_lt_exp | [] | [
1520,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.principal_one | [] | [
104,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.log_mul_moebius_eq_vonMangoldt | [
{
"state_after": "no goals",
"state_before": "⊢ log * ↑μ = Λ",
"tactic": "rw [← vonMangoldt_mul_zeta, mul_assoc, coe_zeta_mul_coe_moebius, mul_one]"
}
] | [
137,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Logic/Equiv/List.lean | Encodable.decode_list_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Encodable α\n⊢ decodeList 0 = some []",
"tactic": "rw [decodeList]"
}
] | [
74,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Std/Data/List/Lemmas.lean | List.mem_range'_1 | [
{
"state_after": "m s n : Nat\n⊢ (∃ i, i < n ∧ m = s + i) ↔ s ≤ m ∧ m < s + n",
"state_before": "m s n : Nat\n⊢ m ∈ range' s n ↔ s ≤ m ∧ m < s + n",
"tactic": "simp [mem_range']"
},
{
"state_after": "no goals",
"state_before": "m s n : Nat\n⊢ (∃ i, i < n ∧ m = s + i) ↔ s ≤ m ∧ m < s + n",
... | [
1826,
93
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1823,
9
] |
Mathlib/RingTheory/HahnSeries.lean | Polynomial.algebraMap_hahnSeries_injective | [] | [
1330,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.not_dvd_of_pos_of_lt | [
{
"state_after": "case intro\nm k✝ l k : ℕ\nh1 : 0 < m * k\nh2 : m * k < m\n⊢ False",
"state_before": "m n k l : ℕ\nh1 : 0 < n\nh2 : n < m\n⊢ ¬m ∣ n",
"tactic": "rintro ⟨k, rfl⟩"
},
{
"state_after": "case intro.inl\nm k l : ℕ\nh1 : 0 < m * 0\nh2 : m * 0 < m\n⊢ False\n\ncase intro.inr\nm k✝ l k :... | [
487,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/CategoryTheory/Monoidal/End.lean | CategoryTheory.μ_inv_hom_app | [] | [
105,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.smul_mem_pointwise_smul | [] | [
72,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.coe_nat_den | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn : ℕ\n⊢ (↑n).den = 1",
"tactic": "rw [← Int.cast_ofNat, coe_int_den]"
}
] | [
539,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | Convex.exists_nhdsWithin_lipschitzOnWith_of_hasFDerivWithinAt | [] | [
517,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.le_to_int | [
{
"state_after": "α : Type ?u.990763\nm n : ZNum\n⊢ ¬↑n < ↑m ↔ m ≤ n",
"state_before": "α : Type ?u.990763\nm n : ZNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"tactic": "rw [← not_lt]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.990763\nm n : ZNum\n⊢ ¬↑n < ↑m ↔ m ≤ n",
"tactic": "exact not... | [
1402,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
] |
Mathlib/Order/WithBot.lean | WithTop.toDual_lt_iff | [] | [
886,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_of | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.1314142\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\nA : Type u₃\ninst✝³ : Semiring A\ninst✝² : Algebra k A\nB : Type ?u.1314179\ninst✝¹ : Semiring B\ninst✝ : Algebra k B\nF : G →* A\nx : G\n⊢ ↑(↑(lift k G A) F) (↑(of k G) x... | [
917,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
916,
1
] |
Mathlib/Data/Int/Dvd/Basic.lean | Int.coe_nat_dvd_left | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nz : ℤ\n⊢ ↑n ∣ z ↔ n ∣ natAbs z",
"tactic": "rcases natAbs_eq z with (eq | eq) <;> rw [eq] <;> simp [←coe_nat_dvd]"
}
] | [
38,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Std/Data/List/Lemmas.lean | List.set_succ | [] | [
820,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
819,
9
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.top_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.89016\nβ : Type ?u.89019\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nn : ℕ\nh : 0 < n\nm : ℕ\nx✝ : Nat.succ 0 ≤ m\nhm : ⊤ ^ m = ⊤\n⊢ ⊤ ^ (m + 1) = ⊤",
"tactic": "rw [pow_succ, hm, top_mul_top]"
}
] | [
577,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_def | [] | [
182,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Algebra/Order/Floor.lean | round_eq_zero_iff | [
{
"state_after": "F : Type ?u.281474\nα : Type u_1\nβ : Type ?u.281480\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nx : α\n⊢ x ∈ Ico (0 - 1 / 2) (1 - 1 / 2) ↔ x ∈ Ico (-(1 / 2)) (1 / 2)",
"state_before": "F : Type ?u.281474\nα : Type u_1\nβ : Type ?u.281480\ninst✝¹ : LinearOrderedField α\ninst✝ : Fl... | [
1465,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1463,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.coe_coe_symm | [] | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Hom/Units.lean | Group.isUnit | [] | [
40,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.IsCycleOn.zpow_apply_eq | [
{
"state_after": "ι : Type ?u.1696537\nα : Type u_1\nβ : Type ?u.1696543\nf g : Perm α\ns✝ t : Set α\na b x y : α\ns : Finset α\nhf : IsCycleOn f ↑s\nha : a ∈ s\nn : ℕ\n⊢ ↑(f⁻¹ ^ (n + 1)) a = a ↔ ↑(card s) ∣ Int.negSucc n",
"state_before": "ι : Type ?u.1696537\nα : Type u_1\nβ : Type ?u.1696543\nf g : Perm ... | [
877,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Std/Data/List/Basic.lean | List.sections_eq_nil_of_isEmpty | [
{
"state_after": "α : Type u_1\nl : List α\nL : List (List α)\nh : isEmpty l = true ∨ foldr (fun a r => isEmpty a || r) false L = true\n⊢ sections (l :: L) = []",
"state_before": "α : Type u_1\nl : List α\nL : List (List α)\nh : any (l :: L) isEmpty = true\n⊢ sections (l :: L) = []",
"tactic": "simp onl... | [
920,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
915,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_dite_eq' | [
{
"state_after": "case inl\nι : Type ?u.413230\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\ns : Finset α\na : α\nb : (x : α) → x = a → β\nh : a ∈ s\n⊢ (∏ x in s, if h : x = a then b x h else 1) = b a (_ : a = a)\n\ncase inr\nι : Typ... | [
1078,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1066,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.Quotient.alg_map_eq | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.liftPropWithinAt_univ | [] | [
218,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_eq_of_forall_le_of_forall_lt_exists_gt | [] | [
613,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_trans_source | [] | [
722,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
721,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.hasCoequalizer_epi_comp | [] | [
1333,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1330,
1
] |
Mathlib/Algebra/Order/Sub/Defs.lean | lt_tsub_of_add_lt_right | [] | [
382,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_add_of_order_eq | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\nh : order φ ≠ order ψ\n⊢ order (φ + ψ) ≤ order φ ⊓ order ψ",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nφ✝ φ ψ : PowerSeries R\nh : order φ ≠ order ψ\n⊢ order (φ + ψ) = order φ ⊓ order ψ",
"tactic": "refine' le_antisymm ... | [
2371,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2364,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.coe_neg | [] | [
316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | NormedSpace.vonNBornology_eq | [
{
"state_after": "𝕜 : Type u_2\n𝕜' : Type ?u.259865\nE : Type u_1\nE' : Type ?u.259871\nF : Type ?u.259874\nι : Type ?u.259877\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\n⊢ ∀ (s : Set E), Bornology.IsBounded s ↔ Bornology.IsBounded s",
"state_before":... | [
316,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Std/Logic.lean | and_and_left | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ a ∧ b ∧ c ↔ (a ∧ b) ∧ a ∧ c",
"tactic": "rw [and_and_and_comm, and_self]"
}
] | [
193,
34
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
192,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concatRec_concat | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nmotive : (u v : V) → Walk G u v → Sort u_1\nHnil : {u : V} → motive u u nil\nHconcat : {u v w : V} → (p : Walk G u v) → (h : Adj G v w) → motive u v p → motive u w (concat p h)\nu v w : V\np :... | [
478,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.length_thinkN | [] | [
607,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformEmbedding.comp | [] | [
173,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Topology/ContinuousFunction/Units.lean | ContinuousMap.continuous_isUnit_unit | [
{
"state_after": "X : Type u_1\nM : Type ?u.349183\nR : Type u_2\n𝕜 : Type ?u.349189\ninst✝² : TopologicalSpace X\ninst✝¹ : NormedRing R\ninst✝ : CompleteSpace R\nf : C(X, R)\nh : ∀ (x : X), IsUnit (↑f x)\nx : X\n⊢ ContinuousAt (fun x => ↑((fun x => IsUnit.unit (_ : IsUnit (↑f x))) x)⁻¹) x",
"state_before"... | [
82,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/LocalAtTarget.lean | Set.restrictPreimage_embedding | [] | [
46,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iInf₂_sup_eq | [] | [
211,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/SetTheory/Cardinal/Divisibility.lean | Cardinal.prime_of_aleph0_le | [
{
"state_after": "case refine'_1\na b : Cardinal\nn m : ℕ\nha : ℵ₀ ≤ a\n⊢ ¬IsUnit a\n\ncase refine'_2\na b✝ : Cardinal\nn m : ℕ\nha : ℵ₀ ≤ a\nb c : Cardinal\nhbc : a ∣ b * c\n⊢ a ∣ b ∨ a ∣ c",
"state_before": "a b : Cardinal\nn m : ℕ\nha : ℵ₀ ≤ a\n⊢ Prime a",
"tactic": "refine' ⟨(aleph0_pos.trans_le ha)... | [
91,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.trans | [] | [
564,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.forget_map | [] | [
407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_eq_mul_right_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.7173\nM₀ : Type u_1\nG₀ : Type ?u.7179\nM₀' : Type ?u.7182\nG₀' : Type ?u.7185\nF : Type ?u.7188\nF' : Type ?u.7191\ninst✝ : CancelMonoidWithZero M₀\na b c : M₀\n⊢ a * c = b * c ↔ a = b ∨ c = 0",
"tactic": "by_cases hc : c = 0 <;> [simp [hc]; sim... | [
180,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Part.lean | Part.div_mem_div | [
{
"state_after": "α : Type u_1\nβ : Type ?u.59915\nγ : Type ?u.59918\ninst✝ : Div α\na b : Part α\nma mb : α\nha : ma ∈ a\nhb : mb ∈ b\n⊢ ∃ a_1, a_1 ∈ a ∧ ∃ a, a ∈ b ∧ a_1 / a = ma / mb",
"state_before": "α : Type u_1\nβ : Type ?u.59915\nγ : Type ?u.59918\ninst✝ : Div α\na b : Part α\nma mb : α\nha : ma ∈ a... | [
758,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_add | [
{
"state_after": "case a.h\nl : Type ?u.266590\nm : Type u_2\nn : Type u_1\no : Type u_3\nm' : o → Type ?u.266604\nn' : o → Type ?u.266609\nR : Type ?u.266612\nS : Type ?u.266615\nα : Type v\nβ : Type w\nγ : Type ?u.266622\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype n\nL : Matrix m n α\nM N : Matrix ... | [
1003,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
11
] |
Mathlib/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.underlyingIso_top_hom | [
{
"state_after": "case h.e'_2\nC : Type u₁\ninst✝¹ : Category C\nX Y Z : C\nD : Type u₂\ninst✝ : Category D\nB : C\n⊢ (underlyingIso (𝟙 B)).hom = (underlyingIso (𝟙 B)).hom ≫ 𝟙 B",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nX Y Z : C\nD : Type u₂\ninst✝ : Category D\nB : C\n⊢ (underlyingIso (𝟙 B)... | [
238,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | exists_lt_of_csInf_lt | [] | [
954,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/Data/Finset/Slice.lean | Set.Sized.mono | [] | [
53,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.DeleteFar.mono | [] | [
1219,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.le_pow_clog | [] | [
330,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_add_measure_iff | [] | [
2873,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2871,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iInter | [] | [
147,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_comm | [] | [
264,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Std/Data/Option/Lemmas.lean | Option.guard_eq_some | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\np : α✝ → Prop\na b : α✝\ninst✝ : DecidablePred p\n⊢ guard p a = some b ↔ a = b ∧ p a",
"tactic": "by_cases h : p a <;> simp [Option.guard, h]"
}
] | [
175,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
174,
9
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.symm_dual_id | [] | [
1427,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1426,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ioo | [] | [
182,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_val | [] | [
928,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/RingTheory/Adjoin/Field.lean | lift_of_splits | [
{
"state_after": "case refine'_1\nF✝ : Type ?u.30572\ninst✝⁵ : Field F✝\nF : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra F K\ninst✝ : Algebra F L\ns : Finset K\nx✝ : ∀ (x : K), x ∈ ∅ → IsIntegral F x ∧ Splits (algebraMap F L) (minpoly F x)\n⊢ None... | [
97,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/NumberTheory/LegendreSymbol/MulCharacter.lean | MulChar.IsQuadratic.comp | [
{
"state_after": "R : Type u\ninst✝² : CommRing R\nR' : Type v\ninst✝¹ : CommRing R'\nR'' : Type w\ninst✝ : CommRing R''\nχ : MulChar R R'\nhχ : IsQuadratic χ\nf : R' →+* R''\na : R\n⊢ ↑(ringHomComp χ f) a = 0 ∨ ↑(ringHomComp χ f) a = 1 ∨ ↑(ringHomComp χ f) a = -1",
"state_before": "R : Type u\ninst✝² : Com... | [
487,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_withDensity_eq_lintegral_mul | [
{
"state_after": "case h_ind\nα : Type u_1\nβ : Type ?u.1781918\nγ : Type ?u.1781921\nδ : Type ?u.1781924\nm m0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nh_mf : Measurable f\n⊢ ∀ (c : ℝ≥0∞) ⦃s : Set α⦄,\n MeasurableSet s →\n (∫⁻ (a : α), indicator s (fun x => c) a ∂Measure.withDensity μ f) = ∫⁻ ... | [
1775,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1765,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_top | [] | [
1209,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1208,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.243376\nE : Type ?u.243379\nF : Type ?u.243382\nG : Type ?u.243385\nE' : Type u_2\nF' : Type u_3\nG' : Type ?u.243394\nE'' : Type ?u.243397\nF'' : Type ?u.243400\nG'' : Type ?u.243403\nR : Type ?u.243406\nR' : Type ?u.243409\n𝕜 : Type ... | [
1196,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1194,
1
] |
Mathlib/Dynamics/Ergodic/Ergodic.lean | Ergodic.ae_empty_or_univ_of_preimage_ae_le | [] | [
169,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.add_right | [] | [
155,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
21
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.zero_vecMul | [
{
"state_after": "case h\nl : Type ?u.844759\nm : Type u_1\nn : Type u_2\no : Type ?u.844768\nm' : o → Type ?u.844773\nn' : o → Type ?u.844778\nR : Type ?u.844781\nS : Type ?u.844784\nα : Type v\nβ : Type w\nγ : Type ?u.844791\ninst✝¹ : NonUnitalNonAssocSemiring α\ninst✝ : Fintype m\nA : Matrix m n α\nx✝ : n\n⊢... | [
1727,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1725,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mk_mem_iff | [] | [
721,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Std/Tactic/Ext.lean | Std.Tactic.Ext.$extName | [] | [
85,
49
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
84,
31
] |
Mathlib/Control/Basic.lean | fish_pipe | [] | [
120,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/Calculus/Deriv/Polynomial.lean | Polynomial.hasStrictDerivAt | [
{
"state_after": "case h_add\n𝕜 : Type u\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx✝ : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nR : Type ... | [
74,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Data/Int/Order/Basic.lean | Int.toNat_eq_zero | [] | [
545,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Topology/Constructions.lean | IsClosed.prod | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.63391\nδ : Type ?u.63394\nε : Type ?u.63397\nζ : Type ?u.63400\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
788,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/RingTheory/Polynomial/Content.lean | Polynomial.content_X_mul | [
{
"state_after": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsDomain R\ninst✝ : NormalizedGCDMonoid R\np : R[X]\n⊢ Multiset.gcd (Multiset.map (coeff (X * p)) (support (X * p)).val) =\n Multiset.gcd (Multiset.map (coeff p) (support p).val)",
"state_before": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : I... | [
133,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.inv_mul | [
{
"state_after": "u : Lean.Level\nR✝ : Type ?u.353952\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : DivisionRing R\na₁ : R\na₂ : ℕ\na₃ : R\n⊢ (a₁ ^ a₂ * a₃)⁻¹ = a₃⁻¹ * (a₁⁻¹ ^ a₂ * Nat.rawCast 1)",
"state_before": "u : Lean.Level\nR✝ : Type ?u.353952\nα : Q(Type ... | [
886,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | IsClosed.reProdIm | [] | [
213,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Order/LocallyFinite.lean | WithTop.Ioo_coe_coe | [] | [
1141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.testBit_two_pow | [
{
"state_after": "case pos\nn m : ℕ\nh : n = m\n⊢ (testBit (2 ^ n) m = true) = (n = m)\n\ncase neg\nn m : ℕ\nh : ¬n = m\n⊢ (testBit (2 ^ n) m = true) = (n = m)",
"state_before": "n m : ℕ\n⊢ (testBit (2 ^ n) m = true) = (n = m)",
"tactic": "by_cases h : n = m"
},
{
"state_after": "case pos.refl\n... | [
163,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.closedBall_mem_nhds_of_mem | [] | [
1021,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/Algebra/Group/Opposite.lean | isUnit_op | [] | [
479,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Algebra/Star/Module.lean | skewAdjointPart_comp_subtype_selfAdjoint | [] | [
161,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.mk_mem_sigma | [] | [
71,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_ne_nil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\np : Walk G u v\n⊢ support p ≠ []",
"tactic": "cases p <;> simp"
}
] | [
562,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.add_snd | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictMono_comp_ofDual_iff | [] | [
182,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.symm_target | [] | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
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