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/RingTheory/HahnSeries.lean | HahnSeries.support_add_subset | [
{
"state_after": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddMonoid R\nx y : HahnSeries Γ R\na : Γ\nha : coeff x a + coeff y a ≠ 0\n⊢ a ∈ support x ∪ support y",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : PartialOrder Γ\ninst✝ : AddMonoid R\nx y : HahnSeries Γ R\na : Γ\nha : ... | [
385,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushout.hom_ext | [] | [
1313,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_comap_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ :... | [
852,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.exists_irreducible_of_natDegree_ne_zero | [] | [
983,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
981,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.comp_apply | [] | [
548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.lift_comp_inr | [
{
"state_after": "case h\nN : Type u_3\nG : Type u_1\nH : Type u_2\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nf₁ : N →* H\nf₂ : G →* H\nh :\n ∀ (g : G),\n MonoidHom.comp f₁ (MulEquiv.toMonoidHom (↑φ g)) = MonoidHom.comp (MulEquiv.toMonoidHom (↑MulAut.conj (↑f₂ g))) f₁\nx✝ : G\n... | [
244,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/GroupTheory/Congruence.lean | Con.ext_iff | [] | [
210,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Algebra/IsPrimePow.lean | Nat.Prime.isPrimePow | [] | [
84,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.add | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.522525\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g : E →... | [
547,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
544,
1
] |
Mathlib/Topology/Constructions.lean | frontier_prod_univ_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.61421\nδ : Type ?u.61424\nε : Type ?u.61427\nζ : Type ?u.61430\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : TopologicalSpace ε\ninst✝ : Topologic... | [
770,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
] |
Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.totalize_of_not_le | [] | [
194,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.one_nonempty | [] | [
116,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.isFiniteMeasure_withDensity_ofReal | [
{
"state_after": "α : Type u_1\nβ : Type ?u.734418\nγ : Type ?u.734421\nδ : Type ?u.734424\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ\nhfi : HasFiniteIntegral f\nx : α\n⊢ ENNReal.ofReal (f x) ≤ ↑‖f x‖₊",
"state_... | [
278,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mul_mul_apply | [
{
"state_after": "l : Type ?u.894994\nm : Type ?u.894997\nn : Type u_1\no : Type ?u.895003\nm' : o → Type ?u.895008\nn' : o → Type ?u.895013\nR : Type ?u.895016\nS : Type ?u.895019\nα : Type v\nβ : Type w\nγ : Type ?u.895026\ninst✝¹ : NonUnitalSemiring α\ninst✝ : Fintype n\nA B C : Matrix n n α\ni j : n\n⊢ (A ⬝... | [
1859,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1855,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_support_card_lt | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nh : f ≠ 0\n⊢ card (Finset.erase (support f) (natDegree f)) < card (support f)",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf : R[X]\nh : f ≠ 0\n⊢ card (support (eraseLead f)) < card (support f)",
"tactic": "rw [eraseLead_support]"
}... | [
114,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Order/Minimal.lean | maximals_idem | [] | [
189,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Reflexive.lean | CategoryTheory.right_comp_retraction | [] | [
105,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Order/GaloisConnection.lean | sSup_image2_eq_sInf_sSup | [] | [
394,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.prodEquivOfIsCompl_symm_apply_left | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\ninst✝⁹ : Ring R\nE : Type u_1\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module R E\nF : Type ?u.80375\ninst✝⁶ : AddCommGroup F\ninst✝⁵ : Module R F\nG : Type ?u.80891\ninst✝⁴ : AddCommGroup G\ninst✝³ : Module R G\np q : Submodule R E\nS : Type ?u.81854\ni... | [
124,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.sum_boole_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na✝ : α\nb : β\nf✝ g : α → β\ninst✝¹ : NonAssocSemiring β\ninst✝ : DecidableEq α\ns : Finset α\nf : α → β\na : α\n⊢ ∑ x in s, (if a = x then 1 else 0) * f x = if a ∈ s then f a else 0",
"tactic": "simp"... | [
81,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mkHom_f_1 | [] | [
1103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.mem_closedBall | [] | [
542,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
9
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.symm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.233556\nE : Type ?u.233559\nF : Type u_3\nG : Type ?u.233565\nE' : Type u_2\nF' : Type ?u.233571\nG' : Type ?u.233574\nE'' : Type ?u.233577\nF'' : Type ?u.233580\nG'' : Type ?u.233583\nR : Type ?u.233586\nR' : Type ?u.233589\n𝕜 : Type ... | [
1152,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.smul_mem | [] | [
162,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_arrow_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX Y Z : C\nf : X ⟶ Y\ninst✝ : HasImage f\n⊢ factorThruImageSubobject f ≫ arrow (imageSubobject f) = f",
"tactic": "simp [factorThruImageSubobject, imageSubobject_arrow]"
}
] | [
332,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.zero_fst | [] | [
207,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
9
] |
Mathlib/Algebra/Regular/Basic.lean | IsLeftRegular.right_of_commute | [] | [
87,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective.surjective_comp_right' | [] | [
786,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.ne_zero | [
{
"state_after": "ι : Type u'\nι' : Type ?u.83214\nR : Type u_1\nK : Type ?u.83220\nM : Type u_2\nM' : Type ?u.83226\nM'' : Type ?u.83229\nV : Type u\nV' : Type ?u.83234\nv : ι → M\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² ... | [
189,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.symm_dual_comp | [] | [
1587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | compRel_mono | [] | [
172,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.coe_sInf | [] | [
856,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.Monad.hasLimit_of_comp_forget_hasLimit | [] | [
129,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_of_mul_lt_mul_right' | [] | [
149,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_subset_cthickening | [
{
"state_after": "ι : Sort ?u.109089\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set α\nx✝ : α\nδ : ℝ\nE : Set α\nx : α\nhx : x ∈ thickening δ E\n⊢ x ∈ cthickening δ E",
"state_before": "ι : Sort ?u.109089\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ✝ ε : ℝ\ns t : Set ... | [
1119,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.map_add_one | [] | [
163,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Group/TypeTags.lean | toAdd_mul | [] | [
156,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Topology/Separation.lean | nhdsSet_le_iff | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns t : Set α\n⊢ 𝓝ˢ s ≤ 𝓝ˢ t → s ⊆ t",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T1Space α\ns t : Set α\n⊢ 𝓝ˢ s ≤ 𝓝ˢ t ↔ s ⊆ t",
"tactic": "refine' ⟨_, fun h => monotone_nhdsSe... | [
687,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.typein_top | [
{
"state_after": "case intro\nα✝ : Type ?u.72894\nβ✝ : Type ?u.72897\nγ : Type ?u.72900\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u_1\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : IsWellOrder β s\nf : r ≺i s\nx✝ : ↑{b | s b f.top}\nb : α\nh : ↑f.toRelEmbedd... | [
457,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Algebra/Ring/Defs.lean | ite_mul_zero_left | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nR : Type x\nα : Type u_1\ninst✝¹ : MulZeroClass α\nP : Prop\ninst✝ : Decidable P\na b : α\n⊢ (if P then a * b else 0) = (if P then a else 0) * b",
"tactic": "by_cases h : P <;> simp [h]"
}
] | [
230,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.toLin'_one | [] | [
147,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_of_set' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.71931\nδ : Type ?u.71934\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ne : LocalHomeomorph α β\ne' : LocalHomeomorph β γ\ns : Set β\nhs : IsOpen s\n⊢ Lo... | [
874,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
873,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.mul_im | [] | [
133,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | RingHom.map_prod | [] | [
265,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
11
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_zero | [
{
"state_after": "𝕜 : Type ?u.20500\nE : Type u_1\nF : Type ?u.20506\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\n⊢ sInf {r | r ∈ Ioi 0 ∧ r⁻¹ • 0 ∈ s} = 0",
"state_before": "𝕜 : Type ?u.20500\nE : Type u_1\nF : Type ?u.20506\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na... | [
106,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Fintype/Lattice.lean | Finset.fold_inf_univ | [] | [
47,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/List/Basic.lean | List.cons_subset_of_subset_of_mem | [] | [
328,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | Submonoid.top_closure_mul_self_eq | [] | [
422,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.pred_succ_iterate_of_not_isMax | [
{
"state_after": "case zero\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : SuccOrder α\ninst✝ : PredOrder α\na b i : α\nn : ℕ\nhin✝ : ¬IsMax ((succ^[n - 1]) i)\nhin : ¬IsMax ((succ^[Nat.zero - 1]) i)\n⊢ (pred^[Nat.zero]) ((succ^[Nat.zero]) i) = i\n\ncase succ\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : S... | [
979,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Topology/Constructions.lean | set_pi_mem_nhds | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.284993\nδ : Type ?u.284996\nε : Type ?u.284999\nζ : Type ?u.285002\nι : Type u_1\nπ : ι → Type u_2\nκ : Type ?u.285013\ninst✝¹ : TopologicalSpace α\ninst✝ : (i : ι) → TopologicalSpace (π i)\nf : α → (i : ι) → π i\ni : Set ι\ns : (a : ι) → Set (π a)\nx : (a :... | [
1346,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Order/Atoms.lean | isAtomic_of_orderBot_wellFounded_lt | [] | [
320,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/List/Infix.lean | List.dropLast_prefix | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.1312\nl l₁ l₂ l₃ : List α\na b : α\nm n : ℕ\n⊢ dropLast [] ++ [] = []",
"tactic": "rw [dropLast, List.append_nil]"
}
] | [
172,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/RingTheory/Ideal/Cotangent.lean | Ideal.to_quotient_square_range | [
{
"state_after": "R : Type u\nS : Type v\nS' : Type w\ninst✝⁶ : CommRing R\ninst✝⁵ : CommSemiring S\ninst✝⁴ : Algebra S R\ninst✝³ : CommSemiring S'\ninst✝² : Algebra S' R\ninst✝¹ : Algebra S S'\ninst✝ : IsScalarTower S S' R\nI : Ideal R\n⊢ LinearMap.range (cotangentToQuotientSquare I) =\n LinearMap.range (Li... | [
142,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_iterate | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.109928\nδ : Type ?u.109931\nσ : Type ?u.109934\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\nf : α → ℕ\ng : α → β\nh : α → β → β\nhf : Primrec f\nhg... | [
609,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | Measurable.apply_continuousLinearMap | [] | [
89,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.lists_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\n⊢ lists nil = ↑[[]]",
"tactic": "rw [nil, lists_coe, cyclicPermutations_nil]"
}
] | [
758,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_bounded_subset_le | [
{
"state_after": "α : Type u\ns : Set α\nc : Cardinal\n⊢ (#{ t // t ⊆ s ∧ (#↑t) ≤ c }) ≤ (#{ t // (#↑t) ≤ c })",
"state_before": "α : Type u\ns : Set α\nc : Cardinal\n⊢ (#{ t // t ⊆ s ∧ (#↑t) ≤ c }) ≤ max (#↑s) ℵ₀ ^ c",
"tactic": "refine' le_trans _ (mk_bounded_set_le s c)"
},
{
"state_after": "... | [
1143,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Monotone.compRel | [] | [
167,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Regular/Basic.lean | not_isRightRegular_zero_iff | [
{
"state_after": "R : Type u_1\ninst✝ : MulZeroClass R\na b : R\n⊢ (¬∃ x y, x ≠ y) ↔ ∀ (x y : R), x = y",
"state_before": "R : Type u_1\ninst✝ : MulZeroClass R\na b : R\n⊢ ¬IsRightRegular 0 ↔ Nontrivial R",
"tactic": "rw [nontrivial_iff, not_iff_comm, isRightRegular_zero_iff_subsingleton, subsingleton_i... | [
228,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.Fork.ι_ofι | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.cos_neg_iff_pi_div_two_lt_abs_toReal | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ cos θ < 0 ↔ π / 2 < abs (toReal θ)",
"tactic": "rw [← not_le, ← not_le, not_iff_not, cos_nonneg_iff_abs_toReal_le_pi_div_two]"
}
] | [
759,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.elim_nhds_subcover' | [] | [
204,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_empty | [] | [
138,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.sub_left | [] | [
191,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
21
] |
Mathlib/MeasureTheory/Measure/ProbabilityMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_eq_mass_mul | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : Nonempty Ω\nm0 : MeasurableSpace Ω\nμ : FiniteMeasure Ω\ninst✝ : TopologicalSpace Ω\nf : Ω →ᵇ ℝ≥0\n⊢ testAgainstNN (mass μ • ProbabilityMeasure.toFiniteMeasure (normalize μ)) f =\n mass μ * testAgainstNN (ProbabilityMeasure.toFiniteMeasure (normalize μ)) f",
"stat... | [
403,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Finite/Card.lean | Finite.card_le_of_injective' | [] | [
129,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_mono | [] | [
738,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.prod_eq_bot | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.188893\nι : Sort ?u.188896\nκ : ι → Sort ?u.188901\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns s₁ s₂ : LowerSet α\nt t₁ t₂ : LowerSet β\nx : α × β\n⊢ ↑(s ×ˢ t) = ↑⊥ ↔ ↑s = ↑⊥ ∨ ↑t = ↑⊥",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.188893... | [
1738,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1736,
1
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_eq_zero | [
{
"state_after": "n : ℕ\nh : sqrt n = 0\n⊢ 0 < 1",
"state_before": "n : ℕ\nh : sqrt n = 0\n⊢ sqrt n < 1",
"tactic": "rw [h]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : sqrt n = 0\n⊢ 0 < 1",
"tactic": "decide"
},
{
"state_after": "⊢ sqrt 0 = 0",
"state_before"... | [
118,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.snd_inv | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.zpowers_eq_closure | [
{
"state_after": "case h\nG : Type u_1\ninst✝² : Group G\nA : Type ?u.4059\ninst✝¹ : AddGroup A\nN : Type ?u.4065\ninst✝ : Group N\ng x✝ : G\n⊢ x✝ ∈ zpowers g ↔ x✝ ∈ closure {g}",
"state_before": "G : Type u_1\ninst✝² : Group G\nA : Type ?u.4059\ninst✝¹ : AddGroup A\nN : Type ?u.4065\ninst✝ : Group N\ng : G... | [
45,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.isOrtho_zero_left | [
{
"state_after": "R : Type u_2\nR₁ : Type u_1\nR₂ : Type u_5\nR₃ : Type ?u.6685\nM : Type ?u.6688\nM₁ : Type u_3\nM₂ : Type u_4\nMₗ₁ : Type ?u.6697\nMₗ₁' : Type ?u.6700\nMₗ₂ : Type ?u.6703\nMₗ₂' : Type ?u.6706\nK : Type ?u.6709\nK₁ : Type ?u.6712\nK₂ : Type ?u.6715\nV : Type ?u.6718\nV₁ : Type ?u.6721\nV₂ : Typ... | [
71,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_edist | [] | [
1187,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
11
] |
Mathlib/Order/Hom/Basic.lean | WithBot.toDualTopEquiv_symm_coe | [] | [
1254,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1252,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.neg_lt_of_tendsto_zero_of_pos | [
{
"state_after": "f : ℕ → ℝ\nhf : Tendsto f atTop (𝓝 0)\nr✝ : ℝ\nhr : 0 < r✝\nhg : Tendsto (fun x => -f x) atTop (𝓝 0)\n⊢ -ofSeq f < ↑r✝",
"state_before": "f : ℕ → ℝ\nhf : Tendsto f atTop (𝓝 0)\nr✝ : ℝ\nhr : 0 < r✝\nhg : Tendsto (fun x => -f x) atTop (𝓝 (-0))\n⊢ -ofSeq f < ↑r✝",
"tactic": "rw [neg_z... | [
209,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.strictAntiOn_arccos | [] | [
370,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Topology/SubsetProperties.lean | ClosedEmbedding.isCompact_preimage | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.93816\nπ : ι → Type ?u.93821\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t : Set α\nf : α → β\nhf : ClosedEmbedding f\nK : Set β\nhK : IsCompact (K ∩ range f)\n⊢ IsCompact (f ⁻¹' K)",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.9... | [
898,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
895,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.cancel_counitInv_right_assoc' | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ne : C ≌ D\nW X X' Y Y' Z : D\nf : W ⟶ X\ng : X ⟶ Y\nh : Y ⟶ Z\nf' : W ⟶ X'\ng' : X' ⟶ Y'\nh' : Y' ⟶ Z\n⊢ f ≫ g ≫ h ≫ (counitInv e).app Z = f' ≫ g' ≫ h' ≫ (counit... | [
428,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/LinearAlgebra/Prod.lean | Submodule.ker_inr | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.318044\nM₆ : Type ?u.318047\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid M₂\ninst✝¹ : Module R... | [
593,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/RingTheory/GradedAlgebra/Radical.lean | Ideal.IsHomogeneous.isPrime_iff | [] | [
155,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.single_dotProduct | [
{
"state_after": "l : Type ?u.160745\nm : Type u_1\nn : Type ?u.160751\no : Type ?u.160754\nm' : o → Type ?u.160759\nn' : o → Type ?u.160764\nR : Type ?u.160767\nS : Type ?u.160770\nα : Type v\nβ : Type w\nγ : Type ?u.160777\ninst✝³ : Fintype m\ninst✝² : Fintype n\ninst✝¹ : DecidableEq m\ninst✝ : NonUnitalNonAs... | [
833,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.numeratorHom_inj | [
{
"state_after": "R : Type u_1\ninst✝¹ : Ring R\nS : Submonoid R\ninst✝ : OreSet S\nhS : S ≤ R⁰\nr₁ r₂ : R\nh : ∃ u v, r₂ * ↑u = r₁ * v ∧ ↑1 * ↑u = ↑1 * v\n⊢ r₁ = r₂",
"state_before": "R : Type u_1\ninst✝¹ : Ring R\nS : Submonoid R\ninst✝ : OreSet S\nhS : S ≤ R⁰\nr₁ r₂ : R\nh : ↑numeratorHom r₁ = ↑numerator... | [
867,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.algebraMap_toProd | [] | [
406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | dist_mul_left | [] | [
360,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.testAgainstNN_mono | [
{
"state_after": "Ω : Type u_1\ninst✝⁵ : MeasurableSpace Ω\nR : Type ?u.49329\ninst✝⁴ : SMul R ℝ≥0\ninst✝³ : SMul R ℝ≥0∞\ninst✝² : IsScalarTower R ℝ≥0 ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : TopologicalSpace Ω\nμ : FiniteMeasure Ω\nf g : Ω →ᵇ ℝ≥0\nf_le_g : ↑f ≤ ↑g\n⊢ (∫⁻ (ω : Ω), ↑(↑f ω) ∂↑μ) ≤ ∫⁻ (ω ... | [
350,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_prod_of_pairwise_disjoint | [
{
"state_after": "case nil\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nl : List (Perm α)\nh✝ : List.Pairwise Disjoint l\nh : List.Pairwise Disjoint []\n⊢ support (List.prod []) = List.foldr (fun x x_1 => x ⊔ x_1) ⊥ (List.map support [])\n\ncase cons\nα : Type u_1\ninst✝¹ : DecidableE... | [
417,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Logic/Basic.lean | ExistsUnique.intro₂ | [
{
"state_after": "ι : Sort ?u.25148\nα✝ : Sort ?u.25153\nκ : ι → Sort ?u.25150\np✝ q✝ : α✝ → Prop\nα : Sort u_1\np : α → Sort u_2\ninst✝ : ∀ (x : α), Subsingleton (p x)\nq : (x : α) → p x → Prop\nw : α\nhp : p w\nhq : q w hp\nH : ∀ (y : α) (hy : p y), q y hy → y = w\n⊢ ∃! x, ∃ hx, q x hx",
"state_before": "... | [
942,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.exists_lipschitzOnWith | [] | [
2046,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2044,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.eq_empty_iff | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : Ico n m = []\n⊢ m - n = 0",
"tactic": "rw [← length, h, List.length]"
}
] | [
95,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | tangentCone_mono_nhds | [
{
"state_after": "case intro.intro.intro.intro\n𝕜 : Type u_2\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.28939\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type ?u.29029\ninst✝¹ : NormedAddCommGroup G\ninst✝ : Norme... | [
135,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.symm_mapsTo | [] | [
384,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.card_Ioi_eq_card_Ici_sub_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.116791\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : LocallyFiniteOrderTop α\na : α\n⊢ card (Ioi a) = card (Ici a) - 1",
"tactic": "rw [Ici_eq_cons_Ioi, card_cons, add_tsub_cancel_right]"
}
] | [
703,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearMap.detAux_def'' | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.143873\ninst✝¹¹ : CommRing R\nM : Type u_2\ninst✝¹⁰ : AddCommGroup M\ninst✝⁹ : Module R M\nM' : Type ?u.144464\ninst✝⁸ : AddCommGroup M'\ninst✝⁷ : Module R M'\nι : Type u_4\ninst✝⁶ : DecidableEq ι\ninst✝⁵ : Fintype ι\ne : Basis ι R M\nA : Type u_3\ni... | [
158,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_sub | [
{
"state_after": "case inl\nα : Type ?u.808531\nβ : Type ?u.808534\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nhq : 0 ≤ q\nh : p ≤ q\n⊢ ENNReal.ofReal (p - q) = ENNReal.ofReal p - ENNReal.ofReal q\n\ncase inr\nα : Type ?u.808531\nβ : Type ?u.808534\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nhq : 0 ≤ q\nh : q ≤ p\n⊢ ... | [
2134,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2129,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_id | [] | [
420,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.measure_lt_top_of_memℒp_indicator | [
{
"state_after": "α : Type u_2\nβ : Type ?u.1445144\nι : Type ?u.1445147\nE : Type u_1\nF : Type ?u.1445153\n𝕜 : Type ?u.1445156\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nμ : Measure α\np : ℝ≥0∞\nhp_pos : p ≠ 0\nhp_ne_top : p ≠ ⊤\nc : E\nhc : c ≠ 0\ns : Set α\nhs... | [
428,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isClosed_zeroLocus | [
{
"state_after": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns : Set R\n⊢ ∃ s_1, zeroLocus s = zeroLocus s_1",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ns : Set R\n⊢ IsClosed (zeroLocus s)",
"tactic": "rw [isClosed_iff_zeroLocus]"
},
{
... | [
440,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_inv_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.28599\nG : Type ?u.28602\ninst✝ : DivisionMonoid α\na b c : α\n⊢ a / b⁻¹ = a * b",
"tactic": "simp"
}
] | [
467,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Algebra/Group/Conj.lean | conj_inv | [] | [
102,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Submodule.map_mem_span_algebraMap_image | [
{
"state_after": "R : Type u\nS✝ : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝¹² : CommSemiring R\ninst✝¹¹ : Semiring S✝\ninst✝¹⁰ : AddCommMonoid A\ninst✝⁹ : Algebra R S✝\ninst✝⁸ : Module S✝ A\ninst✝⁷ : Module R A\ninst✝⁶ : IsScalarTower R S✝ A\nS : Type u_1\nT : Type u_2\ninst✝⁵ : CommSemiring S\ninst✝... | [
347,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.