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/LinearAlgebra/LinearIndependent.lean | LinearIndependent.group_smul | [
{
"state_after": "ι : Type u'\nι' : Type ?u.270528\nR : Type u_2\nK : Type ?u.270534\nM : Type u_3\nM' : Type ?u.270540\nM'' : Type ?u.270543\nV : Type u\nV' : Type ?u.270548\nv✝ : ι → M\ninst✝¹⁰ : Ring R\ninst✝⁹ : AddCommGroup M\ninst✝⁸ : AddCommGroup M'\ninst✝⁷ : AddCommGroup M''\ninst✝⁶ : Module R M\ninst✝⁵ ... | [
532,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.neg_eq' | [] | [
72,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.totalSpaceMk_closedEmbedding | [
{
"state_after": "ι : Type ?u.6444\nB : Type u_1\nF : Type ?u.6450\nX : Type ?u.6453\ninst✝⁶ : TopologicalSpace X\ninst✝⁵ : TopologicalSpace B\ninst✝⁴ : TopologicalSpace F\nE : B → Type u_2\ninst✝³ : TopologicalSpace (TotalSpace E)\ninst✝² : (b : B) → TopologicalSpace (E b)\ninst✝¹ : FiberBundle F E\ninst✝ : T1... | [
283,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | Cube.zero_mem_boundary | [] | [
75,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.eq_one_of_dvd_coprimes | [
{
"state_after": "a b k : ℕ\nh_ab_coprime : gcd a b = 1\nhka : k ∣ a\nhkb : k ∣ b\n⊢ k = 1",
"state_before": "a b k : ℕ\nh_ab_coprime : coprime a b\nhka : k ∣ a\nhkb : k ∣ b\n⊢ k = 1",
"tactic": "rw [coprime_iff_gcd_eq_one] at h_ab_coprime"
},
{
"state_after": "a b k : ℕ\nh_ab_coprime : gcd a b ... | [
277,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Group/Ext.lean | LeftCancelMonoid.ext | [] | [
72,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_compose | [] | [
1867,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1866,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.exact_inr_fst | [] | [
167,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | RingHom.quotientKerEquivOfRightInverse.apply | [] | [
73,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_iUnion_of_mem | [] | [
160,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.nonempty_coeSort | [] | [
103,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
11
] |
Mathlib/Analysis/MeanInequalities.lean | NNReal.geom_mean_le_arith_mean_weighted | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ≥0\nhw' : ∑ i in s, w i = 1\n⊢ ∏ i in s, z i ^ ↑(w i) ≤ ∑ i in s, w i * z i",
"tactic": "exact_mod_cast\n Real.geom_mean_le_arith_mean_weighted _ _ _ (fun i _ => (w i).coe_nonneg)\n (by assumption_mod_cast) fun i _ =>... | [
187,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Vector3.lean | vectorAllP_nil | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/FieldTheory/Fixed.lean | FixedPoints.isIntegral | [
{
"state_after": "case intro\nM : Type u\ninst✝⁵ : Monoid M\nG : Type u\ninst✝⁴ : Group G\nF : Type v\ninst✝³ : Field F\ninst✝² : MulSemiringAction M F\ninst✝¹ : MulSemiringAction G F\nm : M\ninst✝ : Finite G\nx : F\nval✝ : Fintype G\n⊢ IsIntegral { x // x ∈ subfield G F } x",
"state_before": "M : Type u\ni... | [
261,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.liftOn_ofMem | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nq : Semiquot α\nf : α → β\na : α\naq : a ∈ q\n⊢ ∀ (h : ∀ (a : α), a ∈ q → ∀ (b : α), b ∈ q → f a = f b), liftOn q f h = f a",
"state_before": "α : Type u_1\nβ : Type u_2\nq : Semiquot α\nf : α → β\nh : ∀ (a : α), a ∈ q → ∀ (b : α), b ∈ q → f a = f b\na : α\naq :... | [
124,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Set/Basic.lean | Set.disjoint_compl_left_iff_subset | [] | [
1747,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.two_le_of_mem_cycleType | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nn : ℕ\nh : ∃ a, (IsCycle a ∧ ∀ (a_1 : α), a_1 ∈ support a → ↑a a_1 = ↑σ a_1) ∧ Finset.card (support a) = n\n⊢ 2 ≤ n",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nn : ℕ\nh : n ∈ cy... | [
100,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.pow_induction_on_left | [] | [
487,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
11
] |
Mathlib/MeasureTheory/PiSystem.lean | MeasurableSpace.DynkinSystem.generate_le | [] | [
695,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Mathlib/Algebra/Quandle.lean | ShelfHom.map_act | [] | [
375,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.fin_cons' | [
{
"state_after": "ι : Type u'\nι' : Type ?u.115828\nR : Type u_1\nK : Type ?u.115834\nM : Type u_2\nM' : Type ?u.115840\nM'' : Type ?u.115843\nV : Type u\nV' : Type ?u.115848\nv✝ : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMonoid M''\ninst✝² : Module R M\ni... | [
295,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Finite/Card.lean | Nat.card_eq | [
{
"state_after": "case inl\nα✝ : Type ?u.215\nβ : Type ?u.218\nγ : Type ?u.221\nα : Type u_1\nh✝ : Finite α\n⊢ Nat.card α = if h : Finite α then Fintype.card α else 0\n\ncase inr\nα✝ : Type ?u.215\nβ : Type ?u.218\nγ : Type ?u.221\nα : Type u_1\nh✝ : Infinite α\n⊢ Nat.card α = if h : Finite α then Fintype.card ... | [
57,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Algebra/CharZero/Defs.lean | Nat.cast_ne_one | [] | [
97,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Analysis/Calculus/Inverse.lean | approximatesLinearOn_empty | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.5815\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSp... | [
125,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | Polynomial.smul_eval_smul | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\ninst✝⁴ : Monoid M\nR : Type ?u.35641\ninst✝³ : Semiring R\ninst✝² : MulSemiringAction M R\nS : Type u_1\ninst✝¹ : CommSemiring S\ninst✝ : MulSemiringAction M S\nm : M\nf : S[X]\nx r : S\n⊢ eval (m • x) (m • ↑C r) = m • eval x (↑C r)",
"tactic":... | [
72,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.sin_eq_zero_iff | [
{
"state_after": "θ : ℂ\n⊢ (∃ k, θ - ↑π / 2 = (2 * ↑k + 1) * ↑π / 2) ↔ ∃ k, θ = ↑k * ↑π",
"state_before": "θ : ℂ\n⊢ sin θ = 0 ↔ ∃ k, θ = ↑k * ↑π",
"tactic": "rw [← Complex.cos_sub_pi_div_two, cos_eq_zero_iff]"
},
{
"state_after": "case mp\nθ : ℂ\n⊢ (∃ k, θ - ↑π / 2 = (2 * ↑k + 1) * ↑π / 2) → ∃ k... | [
59,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Set/Image.lean | Function.Injective.compl_image_eq | [
{
"state_after": "case h\nι : Sort ?u.105472\nα : Type u_1\nβ : Type u_2\nf : α → β\nhf : Injective f\ns : Set α\ny : β\n⊢ y ∈ (f '' s)ᶜ ↔ y ∈ f '' sᶜ ∪ range fᶜ",
"state_before": "ι : Sort ?u.105472\nα : Type u_1\nβ : Type u_2\nf : α → β\nhf : Injective f\ns : Set α\n⊢ (f '' s)ᶜ = f '' sᶜ ∪ range fᶜ",
... | [
1348,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1342,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_zero' | [] | [
1530,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.equiv_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nt₁ t₂ : Ordnode α\nh₁ : Sized t₁\nh₂ : Sized t₂\nh : toList t₁ = toList t₂\n⊢ size t₁ = size t₂",
"tactic": "rw [← length_toList h₁, h, length_toList h₂]"
}
] | [
567,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | hasFDerivAt_ring_inverse | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type ?u.1084130\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type ?u.1084230\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace 𝕜 F\nG : Type ?u.1084325\ninst✝⁶ : NormedAddCommGroup G... | [
525,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_inv | [] | [
303,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivaryOn_toDual_right | [] | [
284,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.coe_nodup | [] | [
35,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/RingTheory/Ideal/Prod.lean | Ideal.ideal_prod_prime_aux | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ✝ J' : Ideal S\nI : Ideal R\nJ : Ideal S\n⊢ I ≠ ⊤ ∧ J ≠ ⊤ → ¬IsPrime (prod I J)",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : Ring R\ninst✝ : Ring S\nI✝ I' : Ideal R\nJ✝ J' : Ideal S\nI : Ideal R\nJ : Ideal S\... | [
154,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/CategoryTheory/Sites/Plus.lean | CategoryTheory.GrothendieckTopology.plusMap_comp | [
{
"state_after": "case w.h\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\nP✝ : Cᵒᵖ ⥤ D\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q R : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nγ : Q ... | [
192,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.right_apply | [
{
"state_after": "no goals",
"state_before": "ε : Type u_1\np : ε → Prop\ninst✝ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // ¬p a }\na : ε\nh : ¬p a\n⊢ ↑(subtypeCongr ep en) a = ↑(↑en { val := a, property := h })",
"tactic": "simp [Perm.subtypeCongr.apply, h]"
}
] | [
576,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable | [
{
"state_after": "α : Type u_1\nι : Type u_3\nE : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup E\np : ℝ≥0∞\nf : ι → α → E\ng : α → E\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nhf : ∀ (n : ι), StronglyMeasurable (f n)\nhg : StronglyMeasurable g\nl : Filter ι\nhfg : Tendsto (fun n => sn... | [
307,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_eq_iff_star_eq | [] | [
113,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.toList_empty | [] | [
202,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.comapDomain_zero | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.304416\nι : Type ?u.304419\nM : Type u_3\nM' : Type ?u.304425\nN : Type ?u.304428\nP : Type ?u.304431\nG : Type ?u.304434\nH : Type ?u.304437\nR : Type ?u.304440\nS : Type ?u.304443\ninst✝ : Zero M\nf : α → β\nhif : optParam (Set.InjOn f (f ⁻¹' ↑... | [
738,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_lt_Ioc | [] | [
222,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Order/Circular.lean | sbtw_iff_not_btw | [
{
"state_after": "α : Type u_1\ninst✝ : CircularOrder α\na b c : α\n⊢ btw a b c ∧ ¬btw c b a ↔ ¬btw c b a",
"state_before": "α : Type u_1\ninst✝ : CircularOrder α\na b c : α\n⊢ sbtw a b c ↔ ¬btw c b a",
"tactic": "rw [sbtw_iff_btw_not_btw]"
},
{
"state_after": "no goals",
"state_before": "α ... | [
320,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inverse.lean | HasStrictDerivAt.of_local_left_inverse | [] | [
73,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Std/Data/List/Lemmas.lean | List.get_range | [
{
"state_after": "no goals",
"state_before": "n i : Nat\nH : i < length (range n)\n⊢ some (get (range n) { val := i, isLt := H }) = some i",
"tactic": "rw [← get?_eq_get _, get?_range (by simpa using H)]"
},
{
"state_after": "no goals",
"state_before": "n i : Nat\nH : i < length (range n)\n⊢... | [
1949,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1948,
9
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.map_add | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_3\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\nf : α → β\nhf : Measurable f\n⊢ map (v + w) f = map v f... | [
740,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
735,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.compl_add | [] | [
382,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.pred_castSucc_succ | [
{
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}
] | [
1592,
20
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1590,
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Mathlib/Order/Filter/Extr.lean | IsMaxOn.min | [] | [
605,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
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Mathlib/Data/Nat/Totient.lean | Nat.totient_div_of_dvd | [
{
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170,
57
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153,
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Mathlib/Order/Disjoint.lean | codisjoint_bot | [] | [
294,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/Data/List/Basic.lean | List.last_eq_of_concat_eq | [
{
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565,
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562,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.unop | [] | [
290,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Ioo | [
{
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"tactic": "simp [← Ioi_inter_Iio]"
}
] | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Algebra/AddTorsor.lean | vsub_ne_zero | [] | [
144,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
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Mathlib/Order/Filter/Basic.lean | Filter.EventuallyLE.diff | [] | [
1733,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
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Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.eq_of_eqOn_dense | [] | [
2918,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2917,
1
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SOppSide.right_not_mem | [] | [
187,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/Topology/Order/Basic.lean | not_tendsto_nhds_of_tendsto_atBot | [] | [
1564,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1562,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_app_one | [] | [
299,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
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Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_monomial | [] | [
212,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.mk'_ker | [
{
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202,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/Nat/Lemmas.lean | Nat.le_div_iff_mul_le | [
{
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276,
88
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267,
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Mathlib/Topology/SubsetProperties.lean | IsCompact.insert | [] | [
457,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.liftRel_mk_mk | [] | [
430,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Wequiv.refl | [
{
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"tactic": "cases' x with a ... | [
215,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
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Mathlib/Data/Fin/Interval.lean | Fin.card_Ioi | [
{
"state_after": "case b\nn : ℕ\na b : Fin n\n⊢ Fin n",
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},
{
"state_after": "no goals",
"state_before": "case b\nn : ℕ\na b : Fin n\n⊢ Fin n",
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186,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.map_quotient_self | [] | [
99,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.summable_of_lp | [
{
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201,
13
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197,
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single | [
{
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377,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/Data/Real/Irrational.lean | Irrational.add_int | [] | [
243,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
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Mathlib/Topology/ContinuousFunction/Weierstrass.lean | continuousMap_mem_polynomialFunctions_closure | [
{
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"state_before": "a b : ℝ\nf : C(↑(Set.Icc a b), ℝ)\n⊢ f ∈ Subalgebra.topologicalClosure (polynomialFunctions (Set.Icc a b))",
"tactic": "rw [polynomialFunctions_closure_eq_top _ _]"
},
{
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96,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
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Mathlib/Order/Hom/Basic.lean | OrderHomClass.mono | [] | [
160,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
11
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Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Complex.hasStrictDerivAt_exp | [] | [
76,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
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Mathlib/Order/GaloisConnection.lean | GaloisInsertion.l_inf_u | [
{
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"tactic": "simp only [g... | [
560,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | AffineIndependent.comp_embedding | [
{
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"tactic": "clas... | [
309,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
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Mathlib/Data/Rat/Defs.lean | Rat.eq_iff_mul_eq_mul | [
{
"state_after": "a b c p q : ℚ\n⊢ p.num /. ↑p.den = q.num /. ↑q.den ↔ p.num * ↑q.den = q.num * ↑p.den",
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"tactic": "conv =>\n lhs\n rw [← @num_den p, ← @num_den q]"
},
{
"state_after": "case z₂\na b c p q : ℚ\n⊢ ¬q.den... | [
393,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Topology/Constructions.lean | nhds_toMul | [] | [
136,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_inv | [] | [
529,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.add_apply | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.copy_nil | [
{
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"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu u' : V\... | [
152,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bitwise'_bit | [
{
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443,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
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Mathlib/Data/List/FinRange.lean | List.finRange_succ_eq_map | [
{
"state_after": "case a\nα : Type u\nn : ℕ\n⊢ map Fin.val (finRange (Nat.succ n)) = map Fin.val (0 :: map Fin.succ (finRange n))",
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},
{
"state... | [
37,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.TransvectionStruct.inv_mul | [
{
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211,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.div_subset_div | [] | [
638,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
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Mathlib/Init/Function.lean | Function.curry_uncurry | [] | [
144,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
9
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Mathlib/Computability/Primrec.lean | Primrec.nat_lt | [
{
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756,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
755,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.differentiableWithinAt | [] | [
282,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
11
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_sub_ordered | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nb : β\nf✝ g✝ : α → β\ninst✝² : CommSemiring β\nι : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : LinearOrder ι\ns : Finset ι\nf g : ι → R\n⊢ ∏ x in s, (f x + -g x) =\n ∏ i in s, f i +\n -∑ x in s, (g x * ∏ x in filt... | [
194,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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Mathlib/Algebra/CovariantAndContravariant.lean | Group.covariant_iff_contravariant | [
{
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164,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.uniq_cocone_morphism | [
{
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612,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.expand_mul | [] | [
77,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_add | [] | [
88,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Set/Function.lean | Set.MapsTo.val_restrict_apply | [] | [
353,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfpFamily_fp | [
{
"state_after": "ι : Type u\nf : ι → Ordinal → Ordinal\ni : ι\nH : IsNormal (f i)\na : Ordinal\n⊢ f i (sup (List.foldr f a)) = sup (List.foldr f a)",
"state_before": "ι : Type u\nf : ι → Ordinal → Ordinal\ni : ι\nH : IsNormal (f i)\na : Ordinal\n⊢ f i (nfpFamily f a) = nfpFamily f a",
"tactic": "unfold... | [
128,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Vector3.lean | Vector3.append_nil | [] | [
164,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.ext' | [
{
"state_after": "case mk\nF : PFunctor\ny : M F\napprox✝ : (n : ℕ) → CofixA F n\nconsistent✝ : AllAgree approx✝\nH : ∀ (i : ℕ), MIntl.approx { approx := approx✝, consistent := consistent✝ } i = MIntl.approx y i\n⊢ { approx := approx✝, consistent := consistent✝ } = y",
"state_before": "F : PFunctor\nx y : M... | [
225,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_le_of_lf | [
{
"state_after": "x y z : PGame\nh₁ : x ≤ y\nh₂ : ¬z ≤ y\n⊢ ¬z ≤ x",
"state_before": "x y z : PGame\nh₁ : x ≤ y\nh₂ : y ⧏ z\n⊢ x ⧏ z",
"tactic": "rw [← PGame.not_le] at h₂⊢"
},
{
"state_after": "no goals",
"state_before": "x y z : PGame\nh₁ : x ≤ y\nh₂ : ¬z ≤ y\n⊢ ¬z ≤ x",
"tactic": "exa... | [
560,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.blsub_id | [] | [
1917,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1916,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.rootMultiplicity_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ q p : R[X]\nx : R\n⊢ rootMultiplicity x p = 0 ↔ IsRoot p x → p = 0",
"tactic": "simp only [rootMultiplicity_eq_multiplicity, dite_eq_left_iff, PartENat.get_eq_iff_eq_coe,\... | [
565,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.inv_left_iff | [] | [
374,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
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