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/Finset/Basic.lean | List.toFinset_surj_on | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.461724\nγ : Type ?u.461727\ninst✝ : DecidableEq α\nl✝ l' : List α\na : α\nval✝ : Multiset α\nl : List α\nhl : Multiset.Nodup (Quot.mk Setoid.r l)\na✝ : { val := Quot.mk Setoid.r l, nodup := hl } ∈ Set.univ\n⊢ { val := Quot.mk Setoid.r l, nodup := hl } ∈ to... | [
3272,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3270,
1
] |
Mathlib/Order/Cover.lean | not_wcovby_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9689\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na b c : α\nh : a ≤ b\n⊢ ¬a ⩿ b ↔ ∃ c, a < c ∧ c < b",
"tactic": "simp_rw [Wcovby, h, true_and_iff, not_forall, exists_prop, not_not]"
}
] | [
101,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.image_source_eq_target | [] | [
336,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Topology/List.lean | List.continuous_prod | [] | [
180,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_lt_inter_not_lt | [
{
"state_after": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : SemilatticeSup α\na : α\n⊢ Bounded (fun x x_1 => x < x_1) (s ∩ {b | ¬b < a}) ↔ Bounded (fun x x_1 => x < x_1) s",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : SemilatticeSup α\na : α\n⊢ Unbounded (fun x x_1 => x ... | [
365,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Iio_iff_exists_mem_Ico_Ioo_subset | [] | [
1690,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1688,
1
] |
Mathlib/Order/Max.lean | IsMax.eq_of_le | [] | [
394,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
11
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.inductionOn | [] | [
204,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
8
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_pi | [
{
"state_after": "no goals",
"state_before": "⊢ tan π = 0",
"tactic": "rw [tan_periodic.eq, tan_zero]"
}
] | [
1008,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Subtype.dist_eq | [] | [
1643,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1642,
1
] |
Mathlib/Data/List/Dedup.lean | List.count_dedup | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : DecidableEq α\nl : List α\na : α\n⊢ count a (dedup l) = if a ∈ l then 1 else 0",
"tactic": "simp_rw [count_eq_of_nodup <| nodup_dedup l, mem_dedup]"
}
] | [
110,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Slope.lean | lineMap_slope_slope_sub_div_sub | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nE : Type u_2\nPE : Type u_3\ninst✝³ : Field k\ninst✝² : AddCommGroup E\ninst✝¹ : Module k E\ninst✝ : AddTorsor E PE\nf : k → PE\na b c : k\nh : a ≠ c\n⊢ ↑(lineMap (slope f a b) (slope f b c)) ((c - b) / (c - a)) = slope f a c",
"tactic": "field... | [
124,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Algebra/Ring/BooleanRing.lean | BooleanRing.inf_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13028\nγ : Type ?u.13031\ninst✝² : BooleanRing α\ninst✝¹ : BooleanRing β\ninst✝ : BooleanRing γ\na b : α\n⊢ a * b = b * a",
"tactic": "ring"
}
] | [
205,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_inter_subset | [] | [
483,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
480,
1
] |
Mathlib/Analysis/NormedSpace/Extend.lean | LinearMap.extendTo𝕜_apply | [] | [
158,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Algebra/Group/Opposite.lean | Units.coe_unop_opEquiv | [] | [
452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.id_apply | [] | [
171,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.map_range | [
{
"state_after": "G : Type u_3\nG' : Type ?u.474061\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.474070\ninst✝² : AddGroup A\nN : Type u_1\nP : Type u_2\ninst✝¹ : Group N\ninst✝ : Group P\nK : Subgroup G\ng : N →* P\nf : G →* N\n⊢ map g (map f ⊤) = map (comp g f) ⊤",
"state_before": "G : Type u_3\nG' :... | [
2651,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2650,
1
] |
Mathlib/Algebra/Hom/Aut.lean | AddAut.coe_mul | [] | [
199,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/List/Basic.lean | List.map_eq_foldr | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.129786\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\nl : List α\n⊢ map f l = foldr (fun a bs => f a :: bs) [] l",
"tactic": "induction l <;> simp [*]"
}
] | [
1771,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1770,
1
] |
Mathlib/MeasureTheory/Covering/VitaliFamily.lean | VitaliFamily.eventually_filterAt_subset_closedBall | [
{
"state_after": "α : Type u_1\ninst✝ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nx : α\nε : ℝ\nhε : 0 < ε\n⊢ ∃ ε_1, ε_1 > 0 ∧ ∀ (a : Set α), a ∈ setsAt v x → a ⊆ closedBall x ε_1 → a ⊆ closedBall x ε",
"state_before": "α : Type u_1\ninst✝ : MetricSpace α\nm0 : ... | [
261,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_add | [] | [
780,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_zero | [] | [
212,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
20
] |
Mathlib/RingTheory/PowerSeries/WellKnown.lean | PowerSeries.coeff_sin_bit0 | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nA' : Type ?u.351728\ninst✝⁷ : Ring A\ninst✝⁶ : Ring A'\ninst✝⁵ : Algebra ℚ A\ninst✝⁴ : Algebra ℚ A'\ninst✝³ : Ring A\ninst✝² : Ring A'\ninst✝¹ : Algebra ℚ A\ninst✝ : Algebra ℚ A'\nn : ℕ\nf : A →+* A'\n⊢ ↑(coeff A (bit0 n)) (sin A) = 0",
"tactic... | [
109,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.congr_fun | [] | [
670,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.dvd_add_left | [] | [
726,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
11
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_ofSurjective | [
{
"state_after": "case h\nR : Type u_1\nR₂ : Type u_2\nR₃ : Type ?u.1796089\nR₄ : Type ?u.1796092\nE : Type ?u.1796095\nE₂ : Type u_4\nE₃ : Type ?u.1796101\nE₄ : Type ?u.1796104\nF : Type u_3\n𝓕 : Type ?u.1796110\ninst✝³⁴ : Semiring R\ninst✝³³ : Semiring R₂\ninst✝³² : Semiring R₃\ninst✝³¹ : Semiring R₄\nσ₁₂ : ... | [
1090,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1087,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.pow_mem | [] | [
396,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
11
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.unique' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Monoid α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\na b : α\nk : ℕ\nhk : a ^ k ∣ b\nhsucc : ¬a ^ (k + 1) ∣ b\n⊢ k = Part.get (multiplicity a b) (_ : ∃ n, (fun n => ¬a ^ (n + 1) ∣ b) n)",
"tactic": "rw [← PartENat.natCast_inj, PartENat... | [
141,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/Filter.lean | Filter.inducing_nhds | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.23236\nα : Type ?u.23239\nβ : Type ?u.23242\nX : Type u_1\nY : Type ?u.23248\ninst✝ : TopologicalSpace X\nx : X\n⊢ (⨅ (s : Set X) (_ : IsOpen s) (_ : x ∈ s), 𝓟 s) = comap 𝓝 (𝓝 (𝓝 x))",
"tactic": "simp (config := { contextual := true }) only [... | [
217,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_X' | [] | [
119,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_im | [] | [
318,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | eq_of_fderiv_eq | [
{
"state_after": "no goals",
"state_before": "E : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nF : Type ?u.262038\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\n𝕜 : Type u_1\nG : Type u_3\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup G\ninst✝ :... | [
620,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_le_map | [] | [
1309,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1308,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_comm | [] | [
238,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Analysis/NormedSpace/Dual.lean | NormedSpace.smul_mem_polar | [
{
"state_after": "case pos\n𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\ns : Set E\nx' : Dual 𝕜 E\nc : 𝕜\nhc : ∀ (z : E), z ∈ s → ‖↑x' z‖ ≤ ‖c‖\nc_zero : c = 0\n⊢ c⁻¹ • x' ∈ polar 𝕜 s\n\ncase neg\n𝕜 : Type u_2\ninst✝² : Nontri... | [
237,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_inter_add_ncard_diff_eq_ncard | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.128103\ns✝ t✝ : Set α\na b x y : α\nf : α → β\ns t : Set α\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard (s ∩ t) + ncard (s \\ t) = ncard s",
"tactic": "simp_rw [← ncard_diff_add_ncard_eq_ncard (diff_subset s t) hs, sdiff_sdiff_rig... | [
544,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
9
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.vsub_nonempty | [] | [
633,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.isFixedPt_fixedPoint_iterate | [
{
"state_after": "α : Type u_1\ninst✝² : MetricSpace α\nK : ℝ≥0\nf : α → α\nhf✝ : ContractingWith K f\ninst✝¹ : Nonempty α\ninst✝ : CompleteSpace α\nn : ℕ\nhf : ContractingWith K (f^[n])\nx : α := fixedPoint (f^[n]) hf\n⊢ IsFixedPt f x",
"state_before": "α : Type u_1\ninst✝² : MetricSpace α\nK : ℝ≥0\nf : α ... | [
365,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_lintegral_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.1445604\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ✝ : { x // x ∈ kernel α β }\ns t✝ : Set β\nκ : { x // x ∈ kernel α β }\nhs : MeasurableSet s\na : α\nf : β → ℝ≥0∞\nt : Set β\n⊢ (∫⁻ (b : β) in t, f b ∂↑(kernel.rest... | [
517,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.sum_card | [
{
"state_after": "no goals",
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366,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/List/Basic.lean | List.insertNth_zero | [] | [
1596,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1595,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | generateFrom_pi | [] | [
148,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/Algebra/Module/LinearPMap.lean | LinearPMap.hasCore_def | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Computability/Partrec.lean | Computable₂.comp₂ | [] | [
554,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_le_prod_diam | [] | [
281,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_insert | [] | [
511,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_inter_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nα' : Type ?u.53422\nβ : Type u_3\nβ' : Type ?u.53428\nγ : Type u_2\nγ' : Type ?u.53434\nδ : Type ?u.53437\nδ' : Type ?u.53440\nε : Type ?u.53443\nε' : Type ?u.53446\nζ : Type ?u.53449\nζ' : Type ?u.53452\nν : Type ?u.53455\ninst✝⁸ : DecidableEq α'\... | [
272,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Control/Fix.lean | Part.fix_def' | [
{
"state_after": "α : Type u_2\nβ : α → Type u_1\nf : ((a : α) → Part (β a)) → (a : α) → Part (β a)\nx : α\nh' : ¬∃ i, (Fix.approx f i x).Dom\n⊢ (assert (∃ i, (Fix.approx f i x).Dom) fun h =>\n WellFounded.fix (_ : WellFounded (Upto.GT fun x_1 => (Fix.approx f x_1 x).Dom)) (fixAux f) Upto.zero x) =\n no... | [
115,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finrank_vectorSpan_insert_le | [
{
"state_after": "case pos\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : AffineSubspace k P\np : P\nhf : FiniteDimensional k { x // x ∈ direction s }\n⊢ finrank k { x // x ∈ vectorSpan k (insert p ↑s) } ≤ finrank k ... | [
711,
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683,
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Mathlib/Topology/Maps.lean | Inducing.inducing_iff | [
{
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Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_eq_nhds_of_re_neg_of_im_neg | [
{
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530,
99
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524,
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Mathlib/Order/Disjoint.lean | disjoint_comm | [] | [
48,
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Mathlib/LinearAlgebra/Ray.lean | Function.Injective.sameRay_map_iff | [
{
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175,
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173,
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Mathlib/Data/Set/Intervals/Group.lean | Set.mem_Icc_iff_abs_le | [] | [
142,
80
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140,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_X_pow | [
{
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553,
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550,
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Mathlib/Data/List/Cycle.lean | Cycle.nodup_reverse_iff | [] | [
668,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csInf_Ioc | [] | [
734,
44
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733,
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Mathlib/Data/Set/Basic.lean | Set.ite_right | [
{
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"tactic": "simp [Set.ite]"
}
] | [
2275,
73
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2275,
1
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Mathlib/Data/Int/Cast/Basic.lean | Int.cast_ofNat | [] | [
68,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
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Mathlib/Algebra/BigOperators/Order.lean | Finset.exists_le_of_prod_le' | [
{
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563,
41
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560,
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Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.eq_top_of_card_eq | [
{
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137,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
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Mathlib/Data/MvPolynomial/Rename.lean | MvPolynomial.renameEquiv_trans | [] | [
179,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
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Std/Data/Option/Lemmas.lean | Option.liftOrGet_none_right | [
{
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}
] | [
188,
18
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187,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.leadingCoeff_cubic | [
{
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1247,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1243,
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Mathlib/Data/PFun.lean | PFun.ext | [] | [
117,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Data/ZMod/Basic.lean | ZMod.coe_mul_inv_eq_one | [
{
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},
{
"state_after": "no goals",
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680,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
677,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_eq_iff_prime | [
{
"state_after": "p : ℕ\nhp : 0 < p\nh : φ p = p - 1\n⊢ Prime p",
"state_before": "p : ℕ\nhp : 0 < p\n⊢ φ p = p - 1 ↔ Prime p",
"tactic": "refine' ⟨fun h => _, totient_prime⟩"
},
{
"state_after": "case hp\np : ℕ\nhp : 0 < p\nh : φ p = p - 1\n⊢ 1 < p\n\np : ℕ\nh : φ p = p - 1\nhp : 1 < p\n⊢ Prime... | [
244,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.sub | [
{
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1230,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1228,
1
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_lt_iff | [] | [
378,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasFDerivAt.prod | [] | [
84,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
8
] |
Mathlib/RingTheory/MvPolynomial/WeightedHomogeneous.lean | MvPolynomial.weightedHomogeneousComponent_apply | [] | [
347,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Analysis/Calculus/Deriv/Pow.lean | HasDerivAt.pow | [
{
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112,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Topology/UniformSpace/Separation.lean | UniformSpace.comap_quotient_le_uniformity | [
{
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322,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Mathlib/LinearAlgebra/Alternating.lean | MultilinearMap.alternatization_apply | [
{
"state_after": "no goals",
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891,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
889,
1
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Mathlib/Data/List/Basic.lean | List.nthLe_pmap | [] | [
3207,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3202,
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Mathlib/Order/Heyting/Basic.lean | compl_iff_not | [] | [
1194,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1193,
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.surjective_proj | [] | [
264,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_eq_toFinset_card' | [
{
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"tactic": "simp [ncard_def, Nat.card_eq_fintype_card]"
}
] | [
76,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Topology/Constructions.lean | Embedding.prod_map | [
{
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825,
77
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822,
1
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Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Injective.injective_of_adjoint | [
{
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209,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Order/Bounded.lean | Set.bounded_ge_Ici | [] | [
203,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_lt_natDegree_iff | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.469198\nhp : p ≠ 0\nh : degree p < degree q\n⊢ natDegree p < natDegree q",
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617,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/Computability/Ackermann.lean | ack_lt_iff_right | [] | [
160,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/Order/SymmDiff.lean | bihimp_left_injective | [] | [
665,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Init/Logic.lean | dif_ctx_congr | [] | [
413,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/MeasureTheory/Covering/Differentiation.lean | VitaliFamily.aemeasurable_limRatio | [
{
"state_after": "α : Type u_1\ninst✝⁵ : MetricSpace α\nm0 : MeasurableSpace α\nμ : MeasureTheory.Measure α\nv : VitaliFamily μ\nE : Type ?u.2775341\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : SecondCountableTopology α\ninst✝² : BorelSpace α\ninst✝¹ : IsLocallyFiniteMeasure μ\nρ : MeasureTheory.Measure α\ninst✝ : ... | [
425,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Data/Int/Units.lean | Int.eq_one_or_neg_one_of_mul_eq_one | [] | [
54,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_div_distrib | [
{
"state_after": "no goals",
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738,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.cos_sub_sin_I | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos x - sin x * I = exp (-x * I)",
"tactic": "rw [neg_mul, ← cosh_sub_sinh, sinh_mul_I, cosh_mul_I]"
}
] | [
1015,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Order/Compare.lean | toDual_compares_toDual | [
{
"state_after": "case lt\nα : Type u_1\nβ : Type ?u.10829\ninst✝ : LT α\na b : α\n⊢ Compares lt (↑toDual a) (↑toDual b) ↔ Compares lt b a\n\ncase eq\nα : Type u_1\nβ : Type ?u.10829\ninst✝ : LT α\na b : α\n⊢ Compares eq (↑toDual a) (↑toDual b) ↔ Compares eq b a\n\ncase gt\nα : Type u_1\nβ : Type ?u.10829\ninst... | [
160,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | exists_hasDerivAt_eq_zero | [] | [
302,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.trNormal_supports | [
{
"state_after": "case zero'\nS : Finset Λ'\nk : Cont'\nHk : codeSupp Code.zero' k ⊆ S\n⊢ contSupp k ⊆ S\n\ncase succ\nS : Finset Λ'\nk : Cont'\nHk : codeSupp Code.succ k ⊆ S\n⊢ ∀ (s : Option Γ'),\n Λ'.Supports S\n (ite (s = some Γ'.consₗ) id (Λ'.clear (fun x => decide (x = Γ'.consₗ)) main) (unrev (Λ'.s... | [
1998,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1984,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.differentiable | [] | [
293,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
11
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.Set.sumCompl_apply_inr | [] | [
328,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_le_self | [] | [
861,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Topology/Constructions.lean | isClosedMap_ofAdd | [] | [
124,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_eq_empty_of_le | [] | [
119,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.div_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.320013\nβ : Type ?u.320016\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ a / b = 0 ↔ a = 0 ∨ b = ⊤",
"tactic": "simp [div_eq_mul_inv]"
}
] | [
1738,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1738,
9
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.curry_apply | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.528340\nι : Type ?u.528343\nM : Type u_3\nM' : Type ?u.528349\nN : Type ?u.528352\nP : Type ?u.528355\nG : Type ?u.528358\nH : Type ?u.528361\nR : Type ?u.528364\nS : Type ?u.528367\ninst✝¹ : AddCommMonoid M\ninst✝ : AddCommMonoid N\nf : α × β →₀ M\nx : ... | [
1225,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
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