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/Data/Set/Basic.lean | Set.strictAntiOn_iff_strictAnti | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nf : α → β\n⊢ StrictAntiOn f s ↔ StrictAnti fun a => f ↑a",
"tactic": "simp [StrictAnti, StrictAntiOn]"
}
] | [
2668,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2666,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.coprime_classification' | [
{
"state_after": "case intro.intro.intro.intro.intro\nx✝ y✝ z✝ : ℤ\nh✝ : PythagoreanTriple x✝ y✝ z✝\nx y z : ℤ\nh : PythagoreanTriple x y z\nh_coprime : Int.gcd x y = 1\nh_parity : x % 2 = 1\nh_pos : 0 < z\nm n : ℤ\nht1 : x = m ^ 2 - n ^ 2 ∧ y = 2 * m * n ∨ x = 2 * m * n ∧ y = m ^ 2 - n ^ 2\nht2 : z = m ^ 2 + n... | [
675,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.conePointUniqueUpToIso_inv | [
{
"state_after": "J : Type w\nC : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nf : J → C\ninst✝ : HasBiproduct f\nb : Bicone f\nhb : Bicone.IsBilimit b\nj : J\nj' : Discrete J\n⊢ (ι f j ≫ (IsLimit.conePointUniqueUpToIso hb.isLimit (isLimit f)).inv) ≫ (Bicone.toCone b).π.app j' =\n (ι f j ≫ desc ... | [
898,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.disjoint_right_ordSeparatingSet | [] | [
185,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.dual | [] | [
221,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
11
] |
Mathlib/Data/Complex/Basic.lean | Complex.ext | [] | [
61,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.nhdsWithin_basis_ball | [] | [
1026,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.Adj.ne | [] | [
131,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
11
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_inter | [
{
"state_after": "case pos\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t u : Set Ω\nhs : Set.Finite s\nhst : s ∩ t = ∅\n⊢ ↑↑(condCount s) (t ∩ u) = ↑↑(condCount (s ∩ t)) u * ↑↑(condCount s) t\n\ncase neg\nΩ : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonC... | [
150,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_neg | [] | [
642,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.support_transfer | [
{
"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\nH : SimpleGraph V\nhp : ∀ (e : Sym2 V), e ∈ edges p → e ∈ edgeSet H\n⊢ support (Walk.transfer p H hp) = support p",
"tactic": "indu... | [
1703,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | Module.End.ker_pow_le_ker_pow_finrank | [
{
"state_after": "case pos\nK : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : FiniteDimensional K V\nf : End K V\nm : ℕ\nh_cases : m < finrank K V\n⊢ LinearMap.ker (f ^ m) ≤ LinearMap.ker (f ^ finrank K V)\n\ncase neg\nK : Type u\nV : Type v\ninst✝³ : Divisio... | [
1526,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1521,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | affineCombination_mem_affineSpan | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ninst✝ : Nontrivial k\ns : Finset ι\nw : ι → k\nh : ∑ i in s, w i = 1\np : ι → P\n⊢ ↑(Finset.affineCombination k s p) ... | [
1040,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_lt_zero | [] | [
228,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.norm_setToL1_le_mul_norm' | [] | [
1239,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupSeminorm.toFun_eq_coe | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | ConcaveOn.quasiconcaveOn | [] | [
170,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.biUnion_image_sup_right | [] | [
191,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.coe_bipartiteBelow | [] | [
66,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.continuousAt_inv_infDist_pt | [
{
"state_after": "case inl\nι : Sort ?u.66671\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nt u : Set α\nx y : α\nΦ : α → β\nh : ¬x ∈ closure ∅\n⊢ ContinuousAt (fun x => (infDist x ∅)⁻¹) x\n\ncase inr\nι : Sort ?u.66671\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\... | [
614,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.isDiag_zero | [] | [
70,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.homeomorph_mk_coe | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_eq_toNNReal_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.32929\nβ : Type ?u.32932\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y : ℝ≥0∞\nhx : x ≠ ⊤\nhy : y ≠ ⊤\n⊢ ENNReal.toNNReal x = ENNReal.toNNReal y ↔ x = y",
"tactic": "simp only [ENNReal.toNNReal_eq_toNNReal_iff x y, hx, hy, and_false, false_and, or_false]"
... | [
390,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.epi_of_epi | [] | [
167,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.disjiUnion_map | [
{
"state_after": "case intro.intro\nα : Type ?u.54766\nβ : Type ?u.54769\nγ : Type ?u.54772\nf✝ : α ↪ β\ns✝ s : Finset α\nt : α → Finset β\nf : β ↪ γ\nh : Set.PairwiseDisjoint (↑s) t\na : α\nha : a ∈ ↑s\nb : α\nhb : b ∈ ↑s\nhab : a ≠ b\nxa : β\nhfa : xa ∈ t a\nhxa : ↑f xa ∈ (fun a => map f (t a)) a\nhxb : ↑f xa... | [
292,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafification_map | [] | [
519,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.rightUnitor_inv_hom | [
{
"state_after": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX : Action V G\n⊢ 𝟙 X.V ≫ (ρ_ X.V).inv ≫ (𝟙 X.V ⊗ 𝟙 (𝟙_ V)) = (ρ_ X.V).inv",
"state_before": "V : Type (u + 1)\ninst✝¹ : LargeCategory V\nG : MonCat\ninst✝ : MonoidalCategory V\nX : Action V G\n⊢ (ρ_ X)... | [
550,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_indicator | [
{
"state_after": "ι : Type ?u.16911495\n𝕜 : Type ?u.16911498\nE : Type u_1\nF : Type ?u.16911504\nA : Type ?u.16911507\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c d : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\na₁ a₂ a₃ : ℝ\nh : a₂ ∈ Icc a₁ a₃\nthis : {x | x ≤ a₂} ... | [
1009,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
8
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_def | [] | [
216,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_closure | [] | [
264,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.integral_eq_tsum' | [] | [
428,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
1
] |
Mathlib/Data/Fin/Tuple/Monotone.lean | strictMono_vecEmpty | [] | [
50,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Spectrum.lean | spectrum.subset_polynomial_aeval | [
{
"state_after": "case intro.intro\n𝕜 : Type u\nA : Type v\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\na : A\np : 𝕜[X]\nk : 𝕜\nhk : k ∈ σ a\n⊢ (fun x => eval x p) k ∈ σ (↑(aeval a) p)",
"state_before": "𝕜 : Type u\nA : Type v\ninst✝² : Field 𝕜\ninst✝¹ : Ring A\ninst✝ : Algebra 𝕜 A\na : ... | [
98,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/PNat/Factors.lean | PNat.factorMultiset_gcd | [
{
"state_after": "case a\nm n : ℕ+\n⊢ factorMultiset (gcd m n) ≤ factorMultiset m ⊓ factorMultiset n\n\ncase a\nm n : ℕ+\n⊢ factorMultiset m ⊓ factorMultiset n ≤ factorMultiset (gcd m n)",
"state_before": "m n : ℕ+\n⊢ factorMultiset (gcd m n) = factorMultiset m ⊓ factorMultiset n",
"tactic": "apply le_a... | [
378,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | IsCompact.exists_forall_ge | [] | [
264,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.int_cast_modEq_int_cast | [
{
"state_after": "α : Type u_1\ninst✝¹ : AddCommGroupWithOne α\ninst✝ : CharZero α\na b z : ℤ\n⊢ (∃ z_1, ↑b - ↑a = ↑(z_1 * z)) ↔ ∃ z_1, b - a = z_1 • z",
"state_before": "α : Type u_1\ninst✝¹ : AddCommGroupWithOne α\ninst✝ : CharZero α\na b z : ℤ\n⊢ ↑a ≡ ↑b [PMOD ↑z] ↔ a ≡ b [PMOD z]",
"tactic": "simp_r... | [
324,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_eq_preimage_infEdist | [] | [
1046,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sin_sq_add_cos_sq | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sin x ^ 2 + cos x ^ 2 = cosh (x * I) ^ 2 - sinh (x * I) ^ 2",
"tactic": "rw [cosh_mul_I, sinh_mul_I, mul_pow, I_sq, mul_neg_one, sub_neg_eq_add, add_comm]"
}
] | [
1022,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1020,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.Quotient.mk_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\nr : R\nx y : M\ninst✝² : Ring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np p' : Submodule R M\n⊢ mk x = 0 ↔ x ∈ p",
"tactic": "simpa using (Quotient.eq' p : mk x = 0 ↔ _)"
}
] | [
104,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime.mul_add_mul_ne_mul | [
{
"state_after": "m n a b : ℕ\ncop : coprime m n\nha : a ≠ 0\nhb : b ≠ 0\nh : a * m + b * n = m * n\n⊢ False",
"state_before": "m n a b : ℕ\ncop : coprime m n\nha : a ≠ 0\nhb : b ≠ 0\n⊢ a * m + b * n ≠ m * n",
"tactic": "intro h"
},
{
"state_after": "case intro\nm n b : ℕ\ncop : coprime m n\nhb ... | [
293,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | pow_div_pow_eventuallyEq_atBot | [
{
"state_after": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\np q : ℕ\n⊢ ∀ (x : 𝕜), x < 0 → (fun x => x ^ p / x ^ q) x = (fun x => x ^ (↑p - ↑q)) x",
"state_before": "𝕜 : Type u_1\ninst✝ : LinearOrderedField 𝕜\np q : ℕ\n⊢ (fun x => x ^ p / x ^ q) =ᶠ[atBot] fun x => x ^ (↑p - ↑q)",
"tactic": "apply ... | [
55,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Nat/Multiplicity.lean | Nat.multiplicity_two_factorial_lt | [
{
"state_after": "h2 : _root_.Prime 2\n⊢ ∀ {n : ℕ}, n ≠ 0 → multiplicity 2 n ! < ↑n",
"state_before": "⊢ ∀ {n : ℕ}, n ≠ 0 → multiplicity 2 n ! < ↑n",
"tactic": "have h2 := prime_two.prime"
},
{
"state_after": "case refine'_1\nh2 : _root_.Prime 2\n⊢ 0 ≠ 0 → multiplicity 2 0! < ↑0\n\ncase refine'_... | [
290,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/CategoryTheory/Endomorphism.lean | CategoryTheory.Aut.Aut_mul_def | [] | [
153,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderivWithin_csin | [] | [
409,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.and_frequently | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.160111\nι : Sort x\np q : α → Prop\nf : Filter α\nhp : ∀ᶠ (x : α) in f, p x\nhq : ∃ᶠ (x : α) in f, q x\n⊢ ∃ᶠ (x : α) in f, p x ∧ q x",
"tactic": "simpa only [and_comm] using hq.and_eventually hp"
}
] | [
1289,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1287,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_range | [] | [
627,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.inv_I | [
{
"state_after": "case pos\nK : Type u_1\nE : Type ?u.6057953\ninst✝ : IsROrC K\nh : I = 0\n⊢ I⁻¹ = -I\n\ncase neg\nK : Type u_1\nE : Type ?u.6057953\ninst✝ : IsROrC K\nh : ¬I = 0\n⊢ I⁻¹ = -I",
"state_before": "K : Type u_1\nE : Type ?u.6057953\ninst✝ : IsROrC K\n⊢ I⁻¹ = -I",
"tactic": "by_cases h : (I ... | [
602,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimitRecOn_pred' | [] | [
385,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_div_right | [] | [
489,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.associator_naturality_middle | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf : a ⟶ b\ng g' : b ⟶ c\nη : g ⟶ g'\nh : c ⟶ d\n⊢ (f ◁ η) ▷ h ≫ (α_ f g' h).hom = (α_ f g h).hom ≫ f ◁ η ▷ h",
"tactic": "simp"
}
] | [
360,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.lt_neg_of_pos_of_infinitesimal | [] | [
673,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/Order/Bounds/Basic.lean | Monotone.map_isLeast | [] | [
1295,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1294,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.skewProd_symm_apply | [] | [
2265,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2263,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Ico_eq_integral_Ioo | [] | [
660,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairHom_id | [] | [
122,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | ball_div_one | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ ball 1 δ / s = thickening δ s⁻¹",
"tactic": "simp [div_eq_mul_inv, ball_mul_one]"
}
] | [
227,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.exists_rat_pow_btwn_rat_aux | [
{
"state_after": "z x✝ y✝ : ℝ\nn : ℕ\nhn : n ≠ 0\nx y : ℝ\nh : x < y\nhy : 0 < y\nhn' : 0 < ↑n\n⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y",
"state_before": "z x✝ y✝ : ℝ\nn : ℕ\nhn : n ≠ 0\nx y : ℝ\nh : x < y\nhy : 0 < y\n⊢ ∃ q, 0 < q ∧ x < ↑q ^ n ∧ ↑q ^ n < y",
"tactic": "have hn' : 0 < (n : ℝ) := by exact... | [
684,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
672,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_nonpos_of_ae_restrict | [] | [
755,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousWithinAt.div' | [] | [
1135,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/Data/List/Permutation.lean | List.foldr_permutationsAux2 | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.20781\nt : α\nts : List α\nr : List (List α)\n⊢ foldr (fun y r => (permutationsAux2 t ts r y id).snd) r [] =\n (List.bind [] fun y => (permutationsAux2 t ts [] y id).snd) ++ r\n\ncase cons\nα : Type u_1\nβ : Type ?u.20781\nt : α\nts : List α\nr : List (Li... | [
181,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/Convex/SpecificFunctions/Basic.lean | strictConvexOn_rpow | [
{
"state_after": "p : ℝ\nhp : 1 < p\n⊢ ∀ {x y z : ℝ}, x ∈ Ici 0 → z ∈ Ici 0 → x < y → y < z → (y ^ p - x ^ p) / (y - x) < (z ^ p - y ^ p) / (z - y)",
"state_before": "p : ℝ\nhp : 1 < p\n⊢ StrictConvexOn ℝ (Ici 0) fun x => x ^ p",
"tactic": "apply strictConvexOn_of_slope_strict_mono_adjacent (convex_Ici ... | [
276,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sigmaFinsuppAddEquivPiFinsupp_apply | [] | [
1880,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1878,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.zero_left | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nZ X✝ Y P : C\nf : Z ⟶ X✝\ng : Z ⟶ Y\ninl : X✝ ⟶ P\ninr : Y ⟶ P\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX : C\n⊢ CommSq 0 0 (𝟙 X) 0",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before"... | [
704,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousAffineMap.coe_injective | [] | [
79,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.restrict_add | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.487868\nm inst✝⁴ : MeasurableSpace α\ninst✝³ : MeasurableSpace β\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\nv✝ : VectorMeasure α M\ninst✝ : ContinuousAdd M\nv w : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\n⊢ restrict (v + ... | [
757,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_apply | [] | [
797,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
796,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | NeZero.nat_of_injective | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.60026\nβ : Type ?u.60029\nR : Type u_1\nS : Type u_3\nF : Type u_2\ninst✝² : NonAssocSemiring R\ninst✝¹ : NonAssocSemiring S\nn : ℕ\nh✝ : NeZero ↑n\ninst✝ : RingHomClass F R S\nf : F\nhf : Function.Injective ↑f\nh : ↑n = 0\n⊢ ↑f ↑n = ↑f 0",
"tact... | [
279,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Data/List/Basic.lean | List.take_left' | [
{
"state_after": "ι : Type ?u.158941\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ l₁ l₂ : List α\nn : ℕ\nh : length l₁ = n\n⊢ take (length l₁) (l₁ ++ l₂) = l₁",
"state_before": "ι : Type ?u.158941\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ l₁ l₂ : List α\nn : ℕ\nh : length l₁ = n\n... | [
1947,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1946,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_one | [] | [
532,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtr.comp_continuous | [] | [
316,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.domDomCongr_eq_zero_iff | [] | [
787,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_neg | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.27269\nT : Type ?u.27272\nR : Type u_1\ninst✝ : CommRing R\nc₁ c₂ r x y z : R\na b c : ℍ[R,c₁,c₂]\n⊢ ↑(-x) = -↑x",
"tactic": "ext <;> simp"
}
] | [
264,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.toDeleteEdges_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' v' : V\ns : Set (Sym2 V)\np : Walk G u' v'\nh : ∀ (e : Sym2 V), e ∈ edges (Walk.copy p (_ : u' = u') (_ : v' = v')) → ¬e ∈ s\n⊢ ∀ (e : Sym2 V), e ∈ edges p → ¬e ∈ s",
"state_before": "V... | [
1830,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1825,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.add_succ_lt_add | [
{
"state_after": "m n k l : ℕ\nhab : m < n\nhcd : k < l\n⊢ m + (k + 1) < n + l",
"state_before": "m n k l : ℕ\nhab : m < n\nhcd : k < l\n⊢ m + k + 1 < n + l",
"tactic": "rw [add_assoc]"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nhab : m < n\nhcd : k < l\n⊢ m + (k + 1) < n ... | [
228,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.uniform_continuity | [] | [
375,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/MeasureTheory/Measure/Sub.lean | MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrict | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nh_meas_s : MeasurableSet s\n⊢ restrict (sInf {d | μ ≤ d + ν}) s = sInf {d | restrict μ s ≤ d + restrict ν s}",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nh_meas_s : MeasurableSet s\n⊢ re... | [
136,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.sum_cycleType | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\n⊢ sum (cycleType σ) = Finset.card (support σ)",
"tactic": "induction σ using cycle_induction_on with\n| base_one => simp\n| base_cycles σ hσ => rw [hσ.cycleType, coe_sum, List.sum_singleton... | [
153,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Arctan.lean | Real.neg_pi_div_two_lt_arctan | [] | [
161,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_of_not_le | [] | [
382,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
382,
11
] |
Mathlib/Data/List/AList.lean | AList.perm_erase | [] | [
241,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.coe_mk | [] | [
607,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Icc' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.149086\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\nh₂ : a ≤ d\nx : α\n⊢ x ∈ Icc a b ∪ Icc c d ↔ x ∈ Icc (min a c) (max b d)",
"state_before": "α : Type u_1\nβ : Type ?u.149086\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\nh₂... | [
1666,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1657,
1
] |
Mathlib/Data/Nat/Parity.lean | Function.Involutive.iterate_eq_id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → α\nn : ℕ\nhf : Involutive f\nhne : f ≠ id\nH : f^[n] = id\nhn : Odd n\n⊢ f = id",
"tactic": "rwa [hf.iterate_odd hn] at H"
}
] | [
330,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | integral_coe_re_add_coe_im | [
{
"state_after": "α : Type u_2\nβ : Type ?u.3318321\nE : Type ?u.3318324\nF : Type ?u.3318327\ninst✝⁹ : MeasurableSpace α\nι : Type ?u.3318333\ninst✝⁸ : NormedAddCommGroup E\nμ : MeasureTheory.Measure α\n𝕜 : Type u_1\ninst✝⁷ : IsROrC 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : Normed... | [
1177,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
src/lean/Init/Control/ExceptCps.lean | ExceptCpsT.run_bind_throw | [] | [
60,
140
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
60,
9
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | aux_hasSum_of_le_geometric | [
{
"state_after": "case inl\nα : Type ?u.447120\nβ : Type ?u.447123\nι : Type ?u.447126\ninst✝ : PseudoMetricSpace α\nr : ℝ\nhr : r < 1\nf : ℕ → α\nhu : ∀ (n : ℕ), dist (f n) (f (n + 1)) ≤ 0 * r ^ n\n⊢ HasSum (fun n => 0 * r ^ n) (0 / (1 - r))\n\ncase inr.intro\nα : Type ?u.447120\nβ : Type ?u.447123\nι : Type ?... | [
376,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Set/Image.lean | Set.disjoint_image_image | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type u_3\nβ : Type u_1\nγ : Type u_2\nf✝ : α → β\ns✝ t✝ : Set α\nf : β → α\ng : γ → α\ns : Set β\nt : Set γ\nh : ∀ (b : β), b ∈ s → ∀ (c : γ), c ∈ t → f b ≠ g c\nb : β\nhb : b ∈ s\nc : γ\nhc : c ∈ t\neq : f b = g c\n⊢ g c ∈ ⊥",
"state_before": "α : T... | [
1588,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Data/Subtype.lean | Subtype.equiv_iff | [] | [
233,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Std/Logic.lean | exists₂_congr | [] | [
386,
44
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
384,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_def_of_pos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx : 0 < x\ny : ℝ\n⊢ x ^ y = exp (log x * y)",
"tactic": "rw [rpow_def_of_nonneg (le_of_lt hx), if_neg (ne_of_gt hx)]"
}
] | [
58,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.eq_univ_iff_forall | [] | [
1524,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1523,
1
] |
Std/Data/List/Init/Lemmas.lean | List.head?_nil | [] | [
24,
54
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
24,
9
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.linearIndependent | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.456903\nR : Type u_2\nR₂ : Type ?u.456909\nK : Type ?u.456912\nM : Type u_3\nM' : Type ?u.456918\nM'' : Type ?u.456921\nV : Type u\nV' : Type ?u.456926\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCo... | [
562,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
11
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.IsCut.congr | [
{
"state_after": "case lt\nα✝ : Sort u_1\ncmp : α✝ → α✝ → Ordering\ncut : α✝ → Ordering\nx y : α✝\ninst✝¹ : IsCut cmp cut\ninst✝ : TransCmp cmp\nH : cmp x y = Ordering.eq\ney : cut y = Ordering.lt\n⊢ cut x = Ordering.lt\n\ncase eq\nα✝ : Sort u_1\ncmp : α✝ → α✝ → Ordering\ncut : α✝ → Ordering\nx y : α✝\ninst✝¹ :... | [
138,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
130,
1
] |
Mathlib/Topology/PathConnected.lean | ContinuousAt.path_extend | [] | [
262,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_le_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.21355\nα : Type u_1\nβ : Type ?u.21361\nπ : ι → Type ?u.21366\ninst✝ : GeneralizedCoheytingAlgebra α\na✝ b✝ c✝ d a b c : α\n⊢ a ∆ b ≤ c ↔ a ≤ b ⊔ c ∧ b ≤ a ⊔ c",
"tactic": "simp_rw [symmDiff, sup_le_iff, sdiff_le_iff]"
}
] | [
154,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_sin | [] | [
78,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Icc_iff_integrableOn_Ico' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.3185262\nE : Type u_2\nF : Type ?u.3185268\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : PartialOrder α\ninst✝ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\nhb : ↑↑μ {b} ≠ ⊤\nhab : a ≤ b\n⊢ IntegrableOn... | [
639,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.inv_univ | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.nil_append | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.