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/Group/Units.lean | divp_eq_one_iff_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c a : α\nu : αˣ\n⊢ a /ₚ u * ↑u = 1 * ↑u ↔ a = ↑u",
"tactic": "rw [divp_mul_cancel, one_mul]"
}
] | [
499,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/Order/Antisymmetrization.lean | OrderHom.coe_antisymmetrization | [] | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.range_face_points | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nn : ℕ\ns : Simplex k P n\nfs : Finset (Fin (n + 1))\nm : ℕ\nh : Finset.card fs = m + 1\n⊢ Set.range (face s h).points = s.points '' ... | [
865,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.coe_monoidHom_refl | [] | [
464,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Order/SymmDiff.lean | inf_himp_bihimp | [] | [
584,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal_injective | [] | [
556,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_C | [] | [
1436,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_monoidHom_of_continuous | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\ninst✝⁶ : UniformSpace α\ninst✝⁵ : Group α\ninst✝⁴ : UniformGroup α\nhom : Type u_1\ninst✝³ : UniformSpace β\ninst✝² : Group β\ninst✝¹ : UniformGroup β\ninst✝ : MonoidHomClass hom α β\nf : hom\nh : Continuous ↑f\nthis : Tendsto (↑f) (�... | [
435,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.coeff_list_prod_of_natDegree_le | [
{
"state_after": "case nil\nR : Type u\nι : Type w\ns : Finset ι\nS : Type u_1\ninst✝ : Semiring S\nl : List S[X]\nn : ℕ\nhl✝ : ∀ (p : S[X]), p ∈ l → natDegree p ≤ n\nhl : ∀ (p : S[X]), p ∈ [] → natDegree p ≤ n\n⊢ coeff (List.prod []) (List.length [] * n) = List.prod (List.map (fun p => coeff p n) [])\n\ncase c... | [
110,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.coe_one | [] | [
268,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Data/Set/MulAntidiagonal.lean | Set.mulAntidiagonal_mono_left | [] | [
42,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
41,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivWithinAt_iff_tendsto | [] | [
313,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.norm_coe_le_norm | [] | [
217,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Order/Monotone/Basic.lean | antitone_iff_forall_lt | [] | [
440,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | HasDerivAt.eventually_ne | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Fi... | [
112,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/RingTheory/Finiteness.lean | Ideal.FG.map | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.327753\nM : Type ?u.327756\ninst✝⁴ : Semiring R✝\ninst✝³ : AddCommMonoid M\ninst✝² : Module R✝ M\nR : Type u_1\nS : Type u_2\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nI : Ideal R\nh : FG I\nf : R →+* S\n⊢ FG (Ideal.map f I)",
"tactic": "classica... | [
482,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Data/Nat/Pairing.lean | Nat.pair_lt_pair_left | [
{
"state_after": "case pos\na₁ a₂ b : ℕ\nh : a₁ < a₂\nh₁ : a₁ < b\n⊢ b * b + a₁ < if a₂ < b then b * b + a₂ else a₂ * a₂ + (a₂ + b)\n\ncase neg\na₁ a₂ b : ℕ\nh : a₁ < a₂\nh₁ : ¬a₁ < b\n⊢ a₁ * a₁ + (a₁ + b) < if a₂ < b then b * b + a₂ else a₂ * a₂ + (a₂ + b)",
"state_before": "a₁ a₂ b : ℕ\nh : a₁ < a₂\n⊢ pai... | [
141,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | ContinuousAt.div | [] | [
193,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
8
] |
Std/Data/Int/Lemmas.lean | Int.le_add_of_neg_add_le | [
{
"state_after": "a b c : Int\nh✝ : -b + a ≤ c\nh : b + (-b + a) ≤ b + c\n⊢ a ≤ b + c",
"state_before": "a b c : Int\nh : -b + a ≤ c\n⊢ a ≤ b + c",
"tactic": "have h := Int.add_le_add_left h b"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : -b + a ≤ c\nh : b + (-b + a) ≤ ... | [
976,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
974,
11
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.and_eq_false_eq_eq_false_or_eq_false | [
{
"state_after": "no goals",
"state_before": "a b : Bool\n⊢ ((a && b) = false) = (a = false ∨ b = false)",
"tactic": "cases a <;> cases b <;> simp"
}
] | [
100,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.mem_disjUnion | [] | [
652,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
650,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.bit1_apply_ne | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.83546\nm : Type ?u.83549\nn : Type u_1\no : Type ?u.83555\nm' : o → Type ?u.83560\nn' : o → Type ?u.83565\nR : Type ?u.83568\nS : Type ?u.83571\nα : Type v\nβ : Type w\nγ : Type ?u.83578\ninst✝² : DecidableEq n\ninst✝¹ : AddZeroClass α\ninst✝ : One α... | [
594,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_comp_map | [] | [
349,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Heyting/Hom.lean | HeytingHom.id_apply | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Algebra/Order/Nonneg/Ring.lean | Nonneg.bot_eq | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Topology/Connected.lean | Set.Subsingleton.isPreconnected | [] | [
97,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_prod_one | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nι : Type ?u.132367\nM : Type u_3\nN : Type ?u.132373\ninst✝ : MulZeroOneClass M\ns : Set α\nt : Set β\nx : α\ny : β\n⊢ (if x ∈ s ∧ y ∈ t then OfNat.ofNat 1 (x, y) else 0) =\n (if x ∈ s then OfNat.ofNat 1 x else 0) * if y ∈ t then OfNat.ofNat 1 y else 0",
"sta... | [
728,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/GroupTheory/Perm/Basic.lean | Equiv.Perm.one_apply | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mulEquivOfMulEquiv_eq | [] | [
1579,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1576,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.add_conj | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (z + ↑(starRingEnd ℂ) z).re = (↑(2 * z.re)).re ∧ (z + ↑(starRingEnd ℂ) z).im = (↑(2 * z.re)).im",
"tactic": "simp [two_mul, ofReal']"
}
] | [
676,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.roots.le_of_dvd | [
{
"state_after": "case intro\nR : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np k : R[X]\nh : p * k ≠ 0\n⊢ roots p ≤ roots (p * k)",
"state_before": "R : Type u\nS : Type v\nT : Type w\na b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np q : R[X]\nh : q ≠ ... | [
633,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_C_mul_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nx : R\nn : ℕ\n⊢ coeff (↑C x * X) n = if n = 1 then x else 0",
"tactic": "rw [← pow_one X, coeff_C_mul_X_pow]"
}
] | [
163,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_sdiff | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.132431\n𝕜 : Type ?u.132434\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nG₁ G₂ : SimpleGraph V\ninst✝³ : Fintype ↑(edgeSet G)\ninst✝² : Fintype ↑(edgeSet G₁)\ninst✝¹ : Fintype ↑(edgeSet G₂)\... | [
938,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | generateFrom_piiUnionInter_le | [
{
"state_after": "α : Type u_1\nι : Type u_2\nm : MeasurableSpace α\nπ : ι → Set (Set α)\nh : ∀ (n : ι), generateFrom (π n) ≤ m\nS : Set ι\n⊢ ∀ (t : Set α), t ∈ piiUnionInter π S → MeasurableSet t",
"state_before": "α : Type u_1\nι : Type u_2\nm : MeasurableSpace α\nπ : ι → Set (Set α)\nh : ∀ (n : ι), gener... | [
481,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.norm_symm_pos | [] | [
1962,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1960,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.forall | [] | [
2040,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2038,
11
] |
Mathlib/Topology/UniformSpace/AbstractCompletion.lean | AbstractCompletion.continuous_extend | [] | [
156,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.Rel.is_equivalence | [] | [
85,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_sup_sdiff_cancel | [] | [
724,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean | CategoryTheory.CommSq.right_adjoint_hasLift_iff | [
{
"state_after": "C : Type u_1\nD : Type u_4\ninst✝¹ : Category C\ninst✝ : Category D\nG : C ⥤ D\nF : D ⥤ C\nA B : C\nX Y : D\ni : A ⟶ B\np : X ⟶ Y\nu : G.obj A ⟶ X\nv : G.obj B ⟶ Y\nsq : CommSq u (G.map i) p v\nadj : G ⊣ F\n⊢ Nonempty (LiftStruct (_ : CommSq (↑(Adjunction.homEquiv adj A X) u) i (F.map p) (↑(Ad... | [
72,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | Orientation.volumeForm_apply_le | [] | [
285,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/CategoryTheory/Limits/Creates.lean | CategoryTheory.hasColimitsOfShape_of_hasColimitsOfShape_createsColimitsOfShape | [] | [
212,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Topology/Basic.lean | closure_union | [] | [
522,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_inter_mul_diff' | [
{
"state_after": "case hst\nα : Type u_1\nβ : Type ?u.358627\nι : Type ?u.358630\nG : Type ?u.358633\nM : Type u_2\nN : Type ?u.358639\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t✝ t : Set α\nh : Set.Finite (s ∩ mulSupport f)\n⊢ Disjoint (s ∩ t) (s \\ t)\n\ncase hs\nα : Type u_1\nβ : ... | [
1017,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisors_zero | [
{
"state_after": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ divisors 0 ↔ a✝ ∈ ∅",
"state_before": "n : ℕ\n⊢ divisors 0 = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ divisors 0 ↔ a✝ ∈ ∅",
"tactic": "simp"
}
] | [
163,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.ofInt'_eq | [
{
"state_after": "α : Type ?u.1057236\nn : ℕ\n⊢ Num.toZNumNeg ↑(n + 1) = -↑(n + 1)",
"state_before": "α : Type ?u.1057236\nn : ℕ\n⊢ ofInt' -[n+1] = ↑-[n+1]",
"tactic": "show Num.toZNumNeg (n + 1 : ℕ) = -(n + 1 : ℕ)"
},
{
"state_after": "α : Type ?u.1057236\nn : ℕ\n⊢ succ (Num.toZNum ↑n) = succ ↑... | [
1542,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1536,
1
] |
Mathlib/Data/List/Basic.lean | List.concat_cons | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Algebra/Associated.lean | Associates.prime_mk | [
{
"state_after": "α : Type u_1\nβ : Type ?u.318602\nγ : Type ?u.318605\nδ : Type ?u.318608\ninst✝ : CommMonoidWithZero α\np : α\n⊢ (Associates.mk p ≠ 0 ∧\n ¬IsUnit (Associates.mk p) ∧\n ∀ (a : α) (b : Associates α),\n Associates.mk p ∣ Associates.mk a * b → Associates.mk p ∣ Associates.mk a... | [
1027,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_le_of_le_mul | [
{
"state_after": "case pos\nα : Type ?u.287943\nβ : Type ?u.287946\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≤ b * c\nh0 : c = 0\n⊢ a / c ≤ b\n\ncase neg\nα : Type ?u.287943\nβ : Type ?u.287946\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nh : a ≤ b * c\nh0 : ¬c = 0\n⊢ a / c ≤ b",
"state_before": "α : Type ?u.287943\nβ : Type ?u... | [
1590,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.norm_le_dual_bound | [
{
"state_after": "case pos\n𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nM : ℝ\nhMp : 0 ≤ M\nhM : ∀ (f : Dual 𝕜 E), ‖↑f x‖ ≤ M * ‖f‖\nh : x = 0\n⊢ ‖x‖ ≤ M\n\ncase neg\n𝕜 : Type v\ninst✝² : IsROrC 𝕜\nE : Type u\ninst✝¹ : NormedAddCommGroup E\nins... | [
147,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Std/Data/List/Lemmas.lean | List.getElem_eq_get | [] | [
544,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
544,
9
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_le_sub_left | [
{
"state_after": "n m k a : Nat\nh : n ≤ n + a\n⊢ k - n - a ≤ k - n",
"state_before": "n m k a : Nat\nh : n ≤ n + a\n⊢ k - (n + a) ≤ k - n",
"tactic": "rw [← Nat.sub_sub]"
},
{
"state_after": "no goals",
"state_before": "n m k a : Nat\nh : n ≤ n + a\n⊢ k - n - a ≤ k - n",
"tactic": "appl... | [
409,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
407,
11
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.linearEquivFunOnFintype_symm_single | [
{
"state_after": "R : Type u\ninst✝⁶ : Semiring R\nι : Type v\ndec_ι : DecidableEq ι\nM : ι → Type w\ninst✝⁵ : (i : ι) → AddCommMonoid (M i)\ninst✝⁴ : (i : ι) → Module R (M i)\nN : Type u₁\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nφ : (i : ι) → M i →ₗ[R] N\nψ ψ' : (⨁ (i : ι), M i) →ₗ[R] N\ninst✝¹ : Fintyp... | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | isClosed_setOf_map_smul | [
{
"state_after": "M : Type u_4\nα✝ : Type ?u.23804\nβ✝ : Type ?u.23807\ninst✝⁹ : TopologicalSpace α✝\ninst✝⁸ : Monoid M\ninst✝⁷ : MulAction M α✝\ninst✝⁶ : ContinuousConstSMul M α✝\nN : Type u_1\ninst✝⁵ : Monoid N\nα : Type u_2\nβ : Type u_3\ninst✝⁴ : MulAction M α\ninst✝³ : MulAction N β\ninst✝² : TopologicalSp... | [
189,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Icc_union_Ioo | [] | [
1569,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1568,
1
] |
Mathlib/Data/Option/NAry.lean | Option.map₂_assoc | [
{
"state_after": "no goals",
"state_before": "α : Type u_5\nβ : Type u_6\nγ : Type u_4\nf✝ : α → β → γ\na : Option α\nb : Option β\nc : Option γ\nδ : Type u_1\nε : Type u_2\nε' : Type u_3\nf : δ → γ → ε\ng : α → β → δ\nf' : α → ε' → ε\ng' : β → γ → ε'\nh_assoc : ∀ (a : α) (b : β) (c : γ), f (g a b) c = f' a... | [
127,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.strongMono_of_strongMono | [
{
"state_after": "C : Type u\ninst✝² : Category C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\ninst✝¹ : StrongMono (f ≫ g)\nX Y : C\nz : X ⟶ Y\ninst✝ : Epi z\n⊢ HasLiftingProperty z f",
"state_before": "C : Type u\ninst✝¹ : Category C\nP Q R : C\nf : P ⟶ Q\ng : Q ⟶ R\ninst✝ : StrongMono (f ≫ g)\nX Y : C\nz : X ⟶ Y\n⊢ ... | [
139,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_self | [] | [
32,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.mul_lt_mul_of_pos_left | [] | [
829,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multicoequalizer.π_desc | [] | [
884,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.restrict | [] | [
140,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/RingTheory/Finiteness.lean | Submodule.fg_def | [
{
"state_after": "case intro.intro\nR : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nt' : Set M\nh : Set.Finite t'\n⊢ FG (span R t')",
"state_before": "R : Type u_1\nM : Type u_2\ninst✝² : Semiring R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nN : Submodule R... | [
57,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Fintype/Order.lean | Fintype.exists_ge | [] | [
209,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_abs_right | [] | [
702,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_of_not_mem | [] | [
88,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousCore'_eq_sSup | [
{
"state_after": "ι : Type u_2\nσ : Type u_3\nR : Type ?u.202181\nA : Type u_1\ninst✝⁵ : Semiring A\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : SetLike σ A\ninst✝¹ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝ : GradedRing 𝒜\nI : Ideal A\n⊢ IsLUB {J | IsHomogeneous 𝒜 J ∧ J ≤ I} (homogeneousCore' 𝒜 I... | [
522,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Real.lean | QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared | [] | [
100,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_compl | [] | [
884,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
8
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.dist_eq_zero_iff_eq_or_not_reachable | [
{
"state_after": "no goals",
"state_before": "V : Type u_1\nG : SimpleGraph V\nu v : V\n⊢ dist G u v = 0 ↔ u = v ∨ ¬Reachable G u v",
"tactic": "simp [dist, Nat.sInf_eq_zero, Reachable]"
}
] | [
74,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.length_eq | [
{
"state_after": "no goals",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝¹ l₂✝¹ l₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\n_x : α\nl₁ l₂ : List α\n_p : l₁ ~ l₂\nr : length l₁ = length l₂\n⊢ length (_x :: l₁) = length (_x :: l₂)",
"tactic": "simp [r]"
},
{
"state_after": "no goals",
"state_before": "... | [
156,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Antiperiodic.funext | [] | [
369,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.induction | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.12839\nγ : Type ?u.12842\np : Multiset α → Prop\nempty : p 0\ncons : ∀ ⦃a : α⦄ {s : Multiset α}, p s → p (a ::ₘ s)\ns✝ : Multiset α\nl : List α\n⊢ p (Quot.mk Setoid.r l)",
"state_before": "α : Type u_1\nβ : Type ?u.12839\nγ : Type ?u.12842\np : Multiset α... | [
157,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
11
] |
Mathlib/Data/Pi/Lex.lean | Pi.lt_toLex_update_self_iff | [
{
"state_after": "ι : Type u_1\nβ : ι → Type u_2\nr : ι → ι → Prop\ns : {i : ι} → β i → β i → Prop\ninst✝² : LinearOrder ι\ninst✝¹ : IsWellOrder ι fun x x_1 => x < x_1\ninst✝ : (i : ι) → PartialOrder (β i)\nx y : (i : ι) → β i\ni : ι\na : β i\n⊢ ↑toLex x < ↑toLex (update x i a) → x i < a",
"state_before": "... | [
152,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.empty_not_mem_classes | [] | [
117,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.one_left | [] | [
86,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.prod | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nht : Set.Finite t\na✝ : Fintype ↑s\n⊢ Set.Finite (s ×ˢ t)",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\nt : Set β\nhs : Set.Finite s\nht : Set.Finite t\n⊢ Set.Finite (s ×ˢ t)",... | [
914,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
11
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_aleph0_eq | [] | [
576,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Order/Filter/Archimedean.lean | atBot_hasCountableBasis_of_archimedean | [] | [
121,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Invertible.lean | nonempty_invertible_iff_isUnit | [] | [
225,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.bit0_apply | [] | [
574,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.trStmts₁_supports | [
{
"state_after": "S : Finset Λ'\nq : Λ'\nH₁ : Λ'.Supports S q\nHS₁ : trStmts₁ q ⊆ S\nW : ∀ {q : Λ'}, q ∈ trStmts₁ q\n⊢ Supports (trStmts₁ q) S",
"state_before": "S : Finset Λ'\nq : Λ'\nH₁ : Λ'.Supports S q\nHS₁ : trStmts₁ q ⊆ S\n⊢ Supports (trStmts₁ q) S",
"tactic": "have W := fun {q} => trStmts₁_self q... | [
1975,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1953,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.scalar_apply_ne | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.445575\nm : Type ?u.445578\nn : Type u_1\no : Type ?u.445584\nm' : o → Type ?u.445589\nn' : o → Type ?u.445594\nR : Type ?u.445597\nS : Type ?u.445600\nα : Type v\nβ : Type w\nγ : Type ?u.445607\ninst✝² : Semiring α\ninst✝¹ : DecidableEq n\ninst✝ : F... | [
1260,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/MeasureTheory/MeasurableSpaceDef.lean | Measurable.comp' | [] | [
563,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_eq_bsup | [] | [
1446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_trim | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.268461\nβ : Type ?u.268464\nE : Type u_2\nF : Type ?u.268470\ninst✝³ : MeasurableSpace α✝\ninst✝² : NormedAddCommGroup E\nf✝ g : α✝ → E\ns✝ t : Set α✝\nμ✝ ν : Measure α✝\nl l' : Filter α✝\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nα : Type ... | [
596,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_eq_card_basis' | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\ninst✝ : FiniteDimensional K V\nι : Type w\nh : Basis ι K V\nthis : IsNoetherian K V\n⊢ ↑(finrank K V) = (#ι)",
"state_before": "K : T... | [
233,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.rpow_sum_le_const_mul_sum_rpow | [
{
"state_after": "case inl\nι : Type u\ns : Finset ι\nf : ι → ℝ≥0\np : ℝ\nhp✝ : 1 ≤ p\nhp : 1 = p\n⊢ (∑ i in s, f i) ^ p ≤ ↑(card s) ^ (p - 1) * ∑ i in s, f i ^ p\n\ncase inr\nι : Type u\ns : Finset ι\nf : ι → ℝ≥0\np : ℝ\nhp✝ : 1 ≤ p\nhp : 1 < p\n⊢ (∑ i in s, f i) ^ p ≤ ↑(card s) ^ (p - 1) * ∑ i in s, f i ^ p",... | [
447,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsCycle.not_of_nil | [] | [
1006,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1006,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.le_pred_of_lt | [] | [
608,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mem_support_single | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.52813\nγ : Type ?u.52816\nι : Type ?u.52819\nM : Type u_2\nM' : Type ?u.52825\nN : Type ?u.52828\nP : Type ?u.52831\nG : Type ?u.52834\nH : Type ?u.52837\nR : Type ?u.52840\nS : Type ?u.52843\ninst✝ : Zero M\na✝ a'✝ : α\nb✝ : M\na a' : ... | [
393,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Fintype/Sigma.lean | Finset.univ_sigma_univ | [] | [
35,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_apply_eq | [
{
"state_after": "case inl\nr : ℝ\nhn : r < 0\n⊢ sign r = -1 ∨ sign r = 0 ∨ sign r = 1\n\ncase inr.inl\n\n⊢ sign 0 = -1 ∨ sign 0 = 0 ∨ sign 0 = 1\n\ncase inr.inr\nr : ℝ\nhp : 0 < r\n⊢ sign r = -1 ∨ sign r = 0 ∨ sign r = 1",
"state_before": "r : ℝ\n⊢ sign r = -1 ∨ sign r = 0 ∨ sign r = 1",
"tactic": "obt... | [
58,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.monotone_map | [] | [
139,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | expNegInvGlue.continuous_polynomial_eval_inv_mul | [] | [
146,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/CategoryTheory/Idempotents/HomologicalComplex.lean | CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem | [] | [
60,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Order/Heyting/Basic.lean | sdiff_le_inf_hnot | [] | [
1001,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Logic/Nontrivial.lean | nontrivial_iff_exists_ne | [] | [
80,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.zero_bind | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.toReal_one | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Option/Basic.lean | Option.bind_eq_none' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2567\nδ : Type ?u.2570\no : Option α\nf : α → Option β\n⊢ Option.bind o f = none ↔ ∀ (b : β) (a : α), a ∈ o → ¬b ∈ f a",
"tactic": "simp only [eq_none_iff_forall_not_mem, mem_def, bind_eq_some, not_exists, not_and]"
... | [
96,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.