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/Rat/Lemmas.lean | Rat.inv_coe_nat_num | [] | [
291,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.coe_basis | [] | [
80,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.rightDual_leftDual | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.pow_card | [
{
"state_after": "K : Type ?u.1001241\nR : Type ?u.1001244\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : ZMod p\nh : x ^ Fintype.card (ZMod p) = x\n⊢ x ^ p = x",
"state_before": "K : Type ?u.1001241\nR : Type ?u.1001244\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : ZMod p\n⊢ x ^ p = x",
"tactic": "have h := FiniteF... | [
406,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | norm_cauchyPowerSeries_le | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nf : ℂ → E\nc : ℂ\nR : ℝ\nn : ℕ\n⊢ ‖cauchyPowerSeries f c R n‖ = (2 * π)⁻¹ * ‖∮ (z : ℂ) in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z‖",
"tactic": "simp [cauchyPower... | [
561,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_subset_preimage_of_inverse | [] | [
399,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Data/Set/Pointwise/Support.lean | mulSupport_comp_inv_smul | [
{
"state_after": "case h\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\ninst✝² : Group α\ninst✝¹ : MulAction α β\ninst✝ : One γ\nc : α\nf : β → γ\nx : β\n⊢ (x ∈ mulSupport fun x => f (c⁻¹ • x)) ↔ x ∈ c • mulSupport f",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\ninst✝² : Group α\ninst✝¹ : MulActi... | [
32,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
29,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂'_compl₂ | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.849082\nR₂ : Type ?u.849085\nM : Type ?u.849088\nM₁ : Type ?u.849091\nM₂ : Type ?u.849094\nM₁' : Type ?u.849097\nM₂' : Type ?u.849100\nn : Type u_2\nm : Type u_3\nn' : Type ?u.849109\nm' : Type u_4\nι : Type ?u.849115\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing R₁\ninst... | [
317,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Data/Sum/Order.lean | OrderIso.sumLexAssoc_apply_inl_inr | [] | [
666,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.mul_continuousOn | [
{
"state_after": "X : Type u_1\nY : Type ?u.2499165\nE : Type ?u.2499168\nR : Type u_2\ninst✝⁹ : MeasurableSpace X\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : MeasurableSpace Y\ninst✝⁶ : TopologicalSpace Y\ninst✝⁵ : NormedAddCommGroup E\nf✝ : X → E\nμ : Measure X\ns✝ : Set X\ninst✝⁴ : OpensMeasurableSpace X\nA K : S... | [
463,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.hrec_on₂_coe | [] | [
331,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_hnot_inf_hnot | [] | [
1106,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/Order/Heyting/Basic.lean | himp_inf_himp_inf_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.31071\nα : Type u_1\nβ : Type ?u.31077\ninst✝ : GeneralizedHeytingAlgebra α\na b c d : α\n⊢ (b ⇨ c) ⊓ (a ⇨ b) ⊓ a ≤ c",
"tactic": "simpa using @himp_le_himp_himp_himp"
}
] | [
394,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Series.lean | Complex.cos_eq_tsum' | [] | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_neg | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.281574\nG : Type ?u.281577\n𝕜 : Type ?u.281580\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
476,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Data/List/Count.lean | List.length_filter_lt_length_iff_exists | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl✝ : List α\np q : α → Bool\nl : List α\n⊢ length (filter p l) < length l ↔ ∃ x, x ∈ l ∧ ¬p x = true",
"tactic": "simpa [length_eq_countp_add_countp p l, countp_eq_length_filter] using\ncountp_pos (fun x => ¬p x) (l := l)"
}
] | [
119,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Sum/Interval.lean | Finset.mem_sumLift₂ | [
{
"state_after": "case mp\nα₁ : Type u_3\nα₂ : Type u_4\nβ₁ : Type u_5\nβ₂ : Type u_6\nγ₁ : Type u_1\nγ₂ : Type u_2\nf f₁ g₁ : α₁ → β₁ → Finset γ₁\ng f₂ g₂ : α₂ → β₂ → Finset γ₂\na : α₁ ⊕ α₂\nb : β₁ ⊕ β₂\nc : γ₁ ⊕ γ₂\n⊢ c ∈ sumLift₂ f g a b →\n (∃ a₁ b₁ c₁, a = inl a₁ ∧ b = inl b₁ ∧ c = inl c₁ ∧ c₁ ∈ f a₁ b₁... | [
62,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.comp | [] | [
169,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.cancel_right | [
{
"state_after": "α : Type u_1\nβ : Type u_3\nγ : Type u_2\nι : Sort ?u.48895\nπ : α → Type ?u.48900\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb✝ : β\nhf : EqOn (g₁ ∘ f) (g₂ ∘ f) s\nhf' : SurjOn f s t\nb : β\nhb : b ∈ t\n⊢ g₁ b = g₂... | [
887,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Algebra/Associated.lean | units_eq_one | [] | [
689,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
688,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_comp_C | [] | [
1407,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1406,
1
] |
Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.superpolynomialDecay_mul_param_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g g' : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : LinearOrderedField β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\n⊢ SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f",
"tactic": "simpa [mul_c... | [
294,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.right_ne | [] | [
255,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Order/Heyting/Basic.lean | PUnit.bot_eq | [] | [
1340,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Order/InitialSeg.lean | InitialSeg.eq_or_principal | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.20498\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\ninst✝ : IsWellOrder β s\nf : r ≼i s\nh : ¬∃ b, ∀ (x : β), s x b ↔ ∃ y, ↑f y = x\nb x : β\nx✝¹ : ∀ (y : β), s y x → Acc s y\nIH : ∀ (y : β), s y x → ∃ a, ↑f a = y\nhn : ∀ (x_1 : α), ¬↑f x_1 = x\... | [
184,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_symm_single_one | [] | [
147,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/GroupTheory/SpecificGroups/Dihedral.lean | DihedralGroup.exponent | [
{
"state_after": "case inl\n\n⊢ Monoid.exponent (DihedralGroup 0) = lcm 0 2\n\ncase inr\nn : ℕ\nhn : NeZero n\n⊢ Monoid.exponent (DihedralGroup n) = lcm n 2",
"state_before": "n : ℕ\n⊢ Monoid.exponent (DihedralGroup n) = lcm n 2",
"tactic": "rcases eq_zero_or_neZero n with (rfl | hn)"
},
{
"stat... | [
204,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | CompleteLattice.sup_continuous | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : OmegaCompletePartialOrder α\ninst✝ : CompleteLattice β\nf g : α →o β\nhf : Continuous f\nhg : Continuous g\n⊢ Continuous (sSup {f, g})",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : OmegaCompletePartialOrder α\ninst✝ : CompleteLattice β\nf g : α →o β\n... | [
504,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_nats | [] | [
760,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.sSup_apply | [] | [
414,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.equivOfEq_rfl | [
{
"state_after": "case h.a\nR : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nS✝ S : Subalgebra R A\na✝ : { x // x ∈ S }\n⊢ ↑(↑(equivOfEq S S (_ : S = S)) a✝) = ↑(↑AlgEquiv.refl a✝)",
"state_before": "R : Type u\... | [
1094,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1094,
1
] |
Mathlib/Order/Monotone/Monovary.lean | monovary_comm | [] | [
405,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/GroupTheory/Coset.lean | mem_own_leftCoset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Monoid α\ns : Submonoid α\na : α\nthis : a * 1 ∈ a *l ↑s\n⊢ a ∈ a *l ↑s",
"tactic": "simpa"
}
] | [
173,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | nonneg_of_mul_nonpos_right | [] | [
1192,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.cylinder_anti | [] | [
125,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.le_min | [] | [
1305,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1304,
11
] |
Std/Data/Int/DivMod.lean | Int.add_ediv_of_dvd_left | [
{
"state_after": "no goals",
"state_before": "a b c : Int\nH : c ∣ a\n⊢ (a + b) / c = a / c + b / c",
"tactic": "rw [Int.add_comm, Int.add_ediv_of_dvd_right H, Int.add_comm]"
}
] | [
183,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
182,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.dual_balance' | [
{
"state_after": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ dual\n (if size l + size r ≤ 1 then node' l x r\n else\n if delta * size l < size r then rotateL l x r\n else if delta * size r < size l then rotateR l x r else node' l x r) =\n if size l + size r ≤ 1 then node' (d... | [
350,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_add_toIcoMod_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocMod hp 0 (a - b) + toIcoMod hp 0 (b - a) = p",
"tactic": "rw [_root_.add_comm, toIcoMod_add_toIocMod_zero]"
}
] | [
789,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_append_left | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\nl₁ l₂ l : List α✝\n⊢ Disjoint (l₁ ++ l₂) l ↔ Disjoint l₁ l ∧ Disjoint l₂ l",
"tactic": "simp [Disjoint, or_imp, forall_and]"
}
] | [
1384,
38
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1383,
9
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.le_dedup | [] | [
122,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.Substructure.isElementary_of_exists | [] | [
482,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Order/Basic.lean | lt_of_lt_of_eq' | [] | [
199,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/Connected.lean | disjoint_or_subset_of_clopen | [] | [
938,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.mk0_eq_mk0_iff_exists_fraction_ring | [
{
"state_after": "R : Type u_1\nK : Type u_2\nL : Type ?u.1378419\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : DecidableEq L\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : Algebra K L\ninst✝⁴ : FiniteDimensional K L\ninst✝³ : Algebra R L\ninst✝² : IsScalarTower R K L\ninst✝... | [
293,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.tan_nat_mul_pi_sub | [] | [
1343,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.int_sub | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nx y : ℝ\nh : Irrational x\nm : ℤ\n⊢ Irrational (↑m - x)",
"tactic": "simpa only [Rat.cast_coe_int] using h.rat_sub m"
}
] | [
300,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_le_of_pow_eq_one | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\nhn : 0 < n\nh : x ^ n = 1\n⊢ IsPeriodicPt (fun x_1 => x * x_1) n 1",
"tactic": "rwa [isPeriodicPt_mul_iff_pow_eq_one]"
}
] | [
215,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.empty_mem_iff_bot | [] | [
684,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_of_forall_fin_meas_le' | [] | [
1187,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/Data/Int/Order/Lemmas.lean | Int.natAbs_le_iff_mul_self_le | [
{
"state_after": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a ≤ natAbs b ↔ ↑(natAbs a) ≤ ↑(natAbs b)",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\n⊢ natAbs a ≤ natAbs b ↔ a * a ≤ b * b",
"tactic": "rw [← abs_le_iff_mul_self_le, abs_eq_natAbs, abs_eq_natAbs]"
},
{
"state_after": "no goals",
"state_... | [
47,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisConnection.u_l_u_eq_u' | [] | [
181,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.mkPiField_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι)... | [
923,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_Ioi | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.187149\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.187155\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.187250\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.187340\ninst✝¹ : NormedAddCommGroup ... | [
462,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Algebra/Lie/OfAssociative.lean | LieSubalgebra.toEndomorphism_mk | [] | [
255,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Data/Vector.lean | Vector.toList_drop | [
{
"state_after": "case mk\nα : Type u\nβ : Type v\nφ : Type w\nn✝ n m : ℕ\nval✝ : List α\nproperty✝ : List.length val✝ = m\n⊢ toList (drop n { val := val✝, property := property✝ }) = List.drop n (toList { val := val✝, property := property✝ })",
"state_before": "α : Type u\nβ : Type v\nφ : Type w\nn✝ n m : ℕ... | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Slope.lean | slope_fun_def_field | [] | [
46,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Topology/LocalAtTarget.lean | inducing_iff_inducing_of_iSup_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set β\nι : Type ?u.37607\nU : ι → Opens β\nhU : iSup U = ⊤\nh : Continuous f\n⊢ (∀ (a : α), 𝓝 a = comap f (𝓝 (f a))) ↔\n ∀ (i : ι) (a : ↑(f ⁻¹' (U i).carrier)), 𝓝 a = comap Subtype.val (co... | [
137,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
src/lean/Init/Data/Nat/SOM.lean | Nat.SOM.Poly.mulMon_denote | [
{
"state_after": "ctx : Context\np : Poly\nk : Nat\nm : Mon\n⊢ denote ctx [] + denote ctx p * k * Mon.denote ctx m = denote ctx p * k * Mon.denote ctx m",
"state_before": "ctx : Context\np : Poly\nk : Nat\nm : Mon\n⊢ denote ctx (mulMon p k m) = denote ctx p * k * Mon.denote ctx m",
"tactic": "simp [mulM... | [
158,
136
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
151,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digitsAux_def | [
{
"state_after": "case zero\nn b : ℕ\nh : 2 ≤ b\nw : 0 < zero\n⊢ digitsAux b h zero = zero % b :: digitsAux b h (zero / b)\n\ncase succ\nn b : ℕ\nh : 2 ≤ b\nn✝ : ℕ\nw : 0 < succ n✝\n⊢ digitsAux b h (succ n✝) = succ n✝ % b :: digitsAux b h (succ n✝ / b)",
"state_before": "n✝ b : ℕ\nh : 2 ≤ b\nn : ℕ\nw : 0 < ... | [
66,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_mk'_spec | [
{
"state_after": "M : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_3\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nx : M\nv : P\ny : { x // x ∈ S }\n⊢ ↑g x * ↑(↑(IsUnit.liftRight (MonoidHom.restrict g... | [
981,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Topology/Separation.lean | t2Space_iff_disjoint_nhds | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝ : TopologicalSpace α\nx y : α\nx✝ : x ≠ y\n⊢ (∃ u v, IsOpen u ∧ IsOpen v ∧ x ∈ u ∧ y ∈ v ∧ Disjoint u v) ↔ Disjoint (𝓝 x) (𝓝 y)",
"state_before": "α : Type u\nβ : Type v\ninst✝ : TopologicalSpace α\n⊢ T2Space α ↔ ∀ (x y : α), x ≠ y → Disjoint (𝓝 x) (𝓝 y)",... | [
883,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
880,
1
] |
Mathlib/Data/Nat/Count.lean | Nat.count_injective | [
{
"state_after": "p : ℕ → Prop\ninst✝ : DecidablePred p\nm n : ℕ\nhm : p m\nhn : p n\nheq : count p m = count p n\nh : m ≠ n\n⊢ False",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nm n : ℕ\nhm : p m\nhn : p n\nheq : count p m = count p n\n⊢ m = n",
"tactic": "by_contra' h : m ≠ n"
},
{
... | [
140,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Computability/Primrec.lean | Primrec₂.encode_iff | [] | [
449,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Order/WithBot.lean | WithTop.untop'_eq_iff | [] | [
715,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Order/Monotone/Basic.lean | Monotone.iterate | [] | [
653,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
11
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.lintegral_mul_left_eq_self | [
{
"state_after": "case h.e'_3.h.e'_3\n𝕜 : Type ?u.5463\nM : Type ?u.5466\nα : Type ?u.5469\nG : Type u_1\nE : Type ?u.5475\nF : Type ?u.5478\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\nμ : Measure G\nf✝ : G → E\n... | [
68,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_lt_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.30052\nα : Type u_1\nβ : Type ?u.30058\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nhc : 0 < c\n⊢ b / c < a ↔ b < c * a",
"tactic": "rw [mul_comm, div_lt_iff hc]"
}
] | [
175,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.mk'_nonempty | [] | [
475,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/List/OfFn.lean | List.mem_ofFn | [
{
"state_after": "α : Type u\nn : ℕ\nf : Fin n → α\na : α\n⊢ (∃ n_1, f (↑(Fin.cast (_ : length (ofFn f) = n)) n_1) = a) ↔ ∃ y, f y = a",
"state_before": "α : Type u\nn : ℕ\nf : Fin n → α\na : α\n⊢ a ∈ ofFn f ↔ a ∈ Set.range f",
"tactic": "simp only [mem_iff_get, Set.mem_range, get_ofFn]"
},
{
"s... | [
205,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_sdiff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.39090\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : DecidableEq α\nh : s ⊆ t\n⊢ card (t \\ s) = card (t \\ s ∪ s) - card s",
"state_before": "α : Type u_1\nβ : Type ?u.39090\ns t : Finset α\nf : α → β\nn : ℕ\ninst✝ : DecidableEq α\nh : s ⊆ t\n⊢ card (t \\ s) = card t... | [
433,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_pos | [] | [
354,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/Fintype/Card.lean | Infinite.of_injective | [] | [
1014,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1013,
1
] |
Mathlib/CategoryTheory/FullSubcategory.lean | CategoryTheory.fullSubcategoryInclusion.map | [] | [
133,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Data/Nat/Lattice.lean | Nat.eq_Ici_of_nonempty_of_upward_closed | [] | [
104,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_eq_one | [] | [
498,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsUpperSet.not_top_mem | [] | [
298,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementaryEmbedding.coe_injective | [] | [
197,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.coe_ereal_ennreal | [] | [
2024,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2022,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_neg | [
{
"state_after": "F : Type ?u.170528\nα : Type u_1\nβ : Type ?u.170534\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na x : α\nhx : fract x ≠ 0\n⊢ 0 ≤ 1 - fract x ∧ 1 - fract x < 1 ∧ ∃ z, -x - (1 - fract x) = ↑z",
"state_before": "F : Type ?u.170528\nα : Type u_1\nβ : Type ?u.170534\ninst✝¹ : Li... | [
970,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_equiv_neg_iff | [
{
"state_after": "no goals",
"state_before": "x : PGame\n⊢ (0 ≈ -x) ↔ (0 ≈ x)",
"tactic": "rw [← neg_equiv_iff, neg_zero]"
}
] | [
1404,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.eq_nil_of_le | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : m ≤ n\n⊢ Ico n m = []",
"tactic": "simp [Ico, tsub_eq_zero_iff_le.mpr h]"
}
] | [
76,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.squarefree_two | [
{
"state_after": "⊢ List.Nodup (factors 2)\n\n\n⊢ 2 ≠ 0",
"state_before": "⊢ Squarefree 2",
"tactic": "rw [squarefree_iff_nodup_factors]"
},
{
"state_after": "⊢ List.Nodup [2]",
"state_before": "⊢ List.Nodup (factors 2)",
"tactic": "rw [Nat.factors_prime prime_two]"
},
{
"state_a... | [
258,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Topology/Basic.lean | Filter.le_lift'_closure | [] | [
579,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.ne_one | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : Irrational x\n⊢ x ≠ 1",
"tactic": "simpa only [Nat.cast_one] using h.ne_nat 1"
}
] | [
178,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.mop_inj | [] | [
105,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Std/Data/List/Lemmas.lean | List.mem_append_left | [] | [
147,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
146,
1
] |
Mathlib/Data/Tree.lean | Tree.left_node_right_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u\nh : nil ≠ nil\n⊢ node () (left nil) (right nil) = nil",
"tactic": "trivial"
}
] | [
167,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullback_fst_map_snd_isPullback | [
{
"state_after": "no goals",
"state_before": "C : Type ?u.598152\ninst✝² : Category C\nX Y Z : C\ninst✝¹ : HasPullbacks C\nU V₁ V₂ : C\nf : X ⟶ Y\ni : U ⟶ Y\ni₁ : V₁ ⟶ pullback f i\ni₂ : V₂ ⟶ pullback f i\ninst✝ : HasPullback i₁ i₂\n⊢ (i₁ ≫ snd) ≫ i = (i₁ ≫ fst) ≫ f",
"tactic": "simp [condition]"
},
... | [
197,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/GroupTheory/Torsion.lean | IsTorsion.subgroup | [] | [
93,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | AddCommGroup.modEq_iff_toIcoDiv_eq_toIocDiv_add_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\n⊢ a ≡ b [PMOD p] ↔ toIcoDiv hp a b = toIocDiv hp a b + 1",
"tactic": "rw [modEq_iff_toIcoMod_add_period_eq_toIocMod hp, toIcoMod, toIocMod, ← eq_sub_i... | [
672,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_iInf_of_ne | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.868335\nβ : Type ?u.868338\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nι✝ : Sort ?u.868355\nf✝ g : ι✝ → ℝ≥0∞\nι : Sort u_1\nf : ι → ℝ≥0∞\nx : ℝ≥0∞\nh0 : x ≠ 0\nh : x ≠ ⊤\n⊢ x * iInf f = ⨅ (i : ι), x * f i",
"tactic": "simpa only [mul_comm] using iInf_mul_of_ne... | [
2469,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2468,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.leadingCoeff_of_c_ne_zero' | [] | [
230,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.invUnitsSub_mul_X | [
{
"state_after": "case h.zero\nR : Type u_1\nS : Type ?u.96790\ninst✝¹ : Ring R\ninst✝ : Ring S\nu : Rˣ\n⊢ ↑(coeff R Nat.zero) (invUnitsSub u * X) = ↑(coeff R Nat.zero) (invUnitsSub u * ↑(C R) ↑u - 1)\n\ncase h.succ\nR : Type u_1\nS : Type ?u.96790\ninst✝¹ : Ring R\ninst✝ : Ring S\nu : Rˣ\nn : ℕ\n⊢ ↑(coeff R (N... | [
53,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.coe_map_subset_range | [] | [
111,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.ae_eq_trans | [] | [
431,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_disjUnion | [] | [
398,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.refl | [] | [
361,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.min_le_padicValRat_add | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhqr : q + r ≠ 0\nh : padicValRat p q ≤ padicValRat p r\n⊢ padicValRat p q ≤ padicValRat p (q + r)",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhqr : q + r ≠ 0\nh : padicValRat p q ≤ padicValRat p r\n⊢ min (padicValRat p q) (padicValRa... | [
380,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Prod.nnorm_def | [] | [
2406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2405,
1
] |
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