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 | Finset.inter_left_idem | [] | [
1732,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1731,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Finset.lean | Set.Finite.lt_cInf_iff | [] | [
75,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.minimalPeriod_eq_zero_iff_nmem_periodicPts | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22504\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\n⊢ minimalPeriod f x = 0 ↔ ¬x ∈ periodicPts f",
"tactic": "rw [← minimalPeriod_pos_iff_mem_periodicPts, not_lt, nonpos_iff_eq_zero]"
}
] | [
320,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
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Mathlib/Analysis/Convex/Exposed.lean | isExposed_empty | [
{
"state_after": "case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : OrderedRing 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : TopologicalSpace E\ninst✝ : Module 𝕜 E\nl : E →L[𝕜] 𝕜\nA B C : Set E\nX : Finset E\nx : E\nx✝ : Set.Nonempty ∅\nw✝ : E\nhx : w✝ ∈ ∅\n⊢ False",
"state_before": "... | [
85,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousOn_iff'_right | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.199215\ninst✝¹ : UniformSpace α\ninst✝ : TopologicalSpace β\nf : β → α\ns : Set β\n⊢ ContinuousOn f s ↔ ∀ (b : β), b ∈ s → Tendsto (fun x => (f b, f x)) (𝓝[s] b) (𝓤 α)",
"tactic": "simp [Conti... | [
1951,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1949,
1
] |
Mathlib/CategoryTheory/Limits/Opposites.lean | CategoryTheory.Limits.pullbackIsoUnopPushout_inv_snd | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nJ : Type u₂\ninst✝² : Category J\nX✝ : Type v₂\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝¹ : HasPullback f g\ninst✝ : HasPushout f.op g.op\n⊢ (PushoutCocone.unop (colimit.cocone (span f.op g.op))).π.app WalkingCospan.right = pushou... | [
644,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.orderOf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ g : Perm α\nht : IsThreeCycle g\n⊢ _root_.orderOf g = 3",
"tactic": "rw [← lcm_cycleType, ht.cycleType, Multiset.lcm_singleton, normalize_eq]"
}
] | [
614,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Topology/Sheaves/PUnit.lean | TopCat.Presheaf.isSheaf_on_pUnit_of_isTerminal | [] | [
57,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | Antitone.ge_of_tendsto | [] | [
274,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_injective_image | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.388219\nδ : Type ?u.388222\nι : Type ?u.388225\nR : Type ?u.388228\nR' : Type ?u.388231\nm0 : MeasurableSpace α\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t : Set α\ninst✝² : MeasurableSpac... | [
2339,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2333,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.map_isPath_of_injective | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\nhinj : Injective ↑f\nhp : IsPath p\n⊢ IsPath (Walk.map f p)",
"tactic": "induction p with\n| nil... | [
1538,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1529,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_not_succ_of_ne_sup | [
{
"state_after": "α : Type ?u.283171\nβ : Type ?u.283174\nγ : Type ?u.283177\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\nhf : ∀ (i : ι), f i ≠ sup f\na : Ordinal\nhao : a < sup f\nhoa : sup f ≤ succ a\n⊢ False",
"state_before": "α : Type ?u.283171\nβ : Type ?u.283174\... | [
1289,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1285,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.ext | [] | [
93,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
92,
8
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.lt_succ_of_le | [] | [
213,
15
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
212,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Covby.succ_eq | [] | [
429,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.ext | [
{
"state_after": "case H\nF : PFunctor\nX : Type ?u.33413\nf : X → Obj F X\ninst✝ : Inhabited (M F)\nx y : M F\nH : ∀ (ps : Path F), iselect ps x = iselect ps y\n⊢ ∀ (i : ℕ), MIntl.approx x i = MIntl.approx y i",
"state_before": "F : PFunctor\nX : Type ?u.33413\nf : X → Obj F X\ninst✝ : Inhabited (M F)\nx y... | [
646,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Algebra/Order/Kleene.lean | kstar_mul_kstar | [] | [
267,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.mul_conj | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (z * ↑(starRingEnd ℂ) z).re = (↑(↑normSq z)).re ∧ (z * ↑(starRingEnd ℂ) z).im = (↑(↑normSq z)).im",
"tactic": "simp [normSq, mul_comm, sub_eq_neg_add, add_comm, ofReal']"
}
] | [
672,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
671,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_fun_injective | [] | [
161,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Int/GCD.lean | Int.pow_dvd_pow_iff | [
{
"state_after": "m n : ℤ\nk : ℕ\nk0 : 0 < k\nh : m ^ k ∣ n ^ k\n⊢ m ∣ n",
"state_before": "m n : ℤ\nk : ℕ\nk0 : 0 < k\n⊢ m ^ k ∣ n ^ k ↔ m ∣ n",
"tactic": "refine' ⟨fun h => _, fun h => pow_dvd_pow_of_dvd h _⟩"
},
{
"state_after": "no goals",
"state_before": "m n : ℤ\nk : ℕ\nk0 : 0 < k\nh :... | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.norm_zero_iff | [
{
"state_after": "case mp\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\n⊢ norm f = 0 → f ≈ 0\n\ncase mpr\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\n⊢ f ≈ 0 → norm f = 0",
"state_before": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\n⊢ norm f = 0 ↔ f ≈ 0",
"tactic": "constructor"
}... | [
137,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.valMinAbs_def_pos | [
{
"state_after": "case zero\ninst✝ : NeZero Nat.zero\nx : ZMod Nat.zero\n⊢ valMinAbs x = if val x ≤ Nat.zero / 2 then ↑(val x) else ↑(val x) - ↑Nat.zero\n\ncase succ\nn✝ : ℕ\ninst✝ : NeZero (Nat.succ n✝)\nx : ZMod (Nat.succ n✝)\n⊢ valMinAbs x = if val x ≤ Nat.succ n✝ / 2 then ↑(val x) else ↑(val x) - ↑(Nat.succ... | [
914,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.exchange | [
{
"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\nF G H I✝ : C ⥤ D\nI J K : D ⥤ E\nα : F ⟶ G\nβ : G ⟶ H\nγ : I ⟶ J\nδ : J ⟶ K\n⊢ (α ≫ β) ◫ (γ ≫ δ) = (α ◫ γ) ≫ β ◫ δ",
"tactic": "aesop_cat"
}
] | [
133,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mul_injective_of_disjoint | [
{
"state_after": "G : Type u_1\nG' : Type ?u.729648\ninst✝³ : Group G\ninst✝² : Group G'\nA : Type ?u.729657\ninst✝¹ : AddGroup A\nN : Type ?u.729663\ninst✝ : Group N\nH₁ H₂ : Subgroup G\nh : Disjoint H₁ H₂\nx y : { x // x ∈ H₁ } × { x // x ∈ H₂ }\nhxy : (fun g => ↑g.fst * ↑g.snd) x = (fun g => ↑g.fst * ↑g.snd)... | [
3667,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3661,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_clm_apply | [] | [
413,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nontrivial.nonempty | [] | [
2524,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2522,
11
] |
Mathlib/Order/MinMax.lean | min_max_distrib_right | [] | [
128,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.Hom.prev_eq | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC C₁ C₂ C₃ : HomologicalComplex V c\nf : Hom C₁ C₂\nj : ι\nw : ComplexShape.Rel c (ComplexShape.prev c j) j\n⊢ prev f j = (xPrevIso C₁ w).hom ≫ HomologicalComplex.Hom.f f (ComplexShape.prev c j) ≫ (x... | [
530,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.fst_add | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.range_coeSubmodule | [] | [
986,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/GroupTheory/SchurZassenhaus.lean | Subgroup.SchurZassenhausInduction.step0 | [
{
"state_after": "G : Type u\ninst✝² : Group G\ninst✝¹ : Fintype G\nh2 :\n ∀ (G' : Type u) [inst : Group G'] [inst_1 : Fintype G'],\n Fintype.card G' < Fintype.card G →\n ∀ {N' : Subgroup G'} [inst_2 : Normal N'],\n Nat.coprime (Fintype.card { x // x ∈ N' }) (index N') → ∃ H', IsComplement' N' H... | [
173,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
9
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_lt_of_mem_erase_min' | [] | [
1494,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1492,
1
] |
Mathlib/LinearAlgebra/Matrix/Orthogonal.lean | Matrix.HasOrthogonalRows.hasOrthogonalCols | [] | [
71,
4
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_toReal_le | [
{
"state_after": "case pos\nx : EReal\nh : x ≠ ⊥\nh' : x = ⊤\n⊢ ↑(toReal x) ≤ x\n\ncase neg\nx : EReal\nh : x ≠ ⊥\nh' : ¬x = ⊤\n⊢ ↑(toReal x) ≤ x",
"state_before": "x : EReal\nh : x ≠ ⊥\n⊢ ↑(toReal x) ≤ x",
"tactic": "by_cases h' : x = ⊤"
},
{
"state_after": "no goals",
"state_before": "case... | [
427,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_prod | [] | [
468,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
11
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.add_mem_iff_left | [] | [
660,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
11
] |
Mathlib/Order/BooleanAlgebra.lean | IsCompl.compl_eq_iff | [] | [
667,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.not_eq_not | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ {a b : Bool}, ¬a = !b ↔ a = b",
"tactic": "decide"
}
] | [
211,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/Separation.lean | Inducing.embedding | [] | [
204,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
11
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.coe_ne_one | [] | [
62,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/Order/Basic.lean | isOpen_gt' | [] | [
908,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropOn_of_mem_groupoid | [] | [
539,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.limsup_le_of_le | [] | [
443,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Quot.lean | Trunc.induction_on | [] | [
500,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
11
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_le_of_le | [
{
"state_after": "case inl\nn m l : ℕ\nhnl : n ≤ l\nhlm : l ≤ m\n⊢ filter (fun x => decide (l ≤ x)) (Ico n m) = Ico l m\n\ncase inr\nn m l : ℕ\nhnl : n ≤ l\nhml : m ≤ l\n⊢ filter (fun x => decide (l ≤ x)) (Ico n m) = Ico l m",
"state_before": "n m l : ℕ\nhnl : n ≤ l\n⊢ filter (fun x => decide (l ≤ x)) (Ico ... | [
205,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Analysis/Calculus/Dslope.lean | continuousWithinAt_dslope_of_ne | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\na b : 𝕜\ns : Set 𝕜\nh : b ≠ a\nhc : ContinuousWithinAt f s b\n⊢ ContinuousWithinAt (dslope f a) s b",
"state_before": "𝕜 : Type u_1\nE : Type u_2\ninst✝... | [
114,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Height.lean | Set.exists_chain_of_le_chainHeight | [
{
"state_after": "case inl\nα : Type u_1\nβ : Type ?u.3758\ninst✝¹ : LT α\ninst✝ : LT β\ns t : Set α\nl : List α\na : α\nn : ℕ\nhn : ↑n ≤ chainHeight s\nha : (⨆ (l : ↑(subchain s)), ↑(length ↑l)) = ⊤\n⊢ ∃ l, l ∈ subchain s ∧ length l = n\n\ncase inr\nα : Type u_1\nβ : Type ?u.3758\ninst✝¹ : LT α\ninst✝ : LT β\n... | [
109,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/CategoryTheory/Groupoid/FreeGroupoid.lean | CategoryTheory.Groupoid.Free.lift_unique | [
{
"state_after": "case hΦ\nV : Type u\ninst✝¹ : Quiver V\nV' : Type u'\ninst✝ : Groupoid V'\nφ✝ φ : V ⥤q V'\nΦ : FreeGroupoid V ⥤ V'\nhΦ : of V ⋙q Φ.toPrefunctor = φ\n⊢ Quotient.functor redStep ⋙ Φ = Paths.lift (Quiver.Symmetrify.lift φ)",
"state_before": "V : Type u\ninst✝¹ : Quiver V\nV' : Type u'\ninst✝ ... | [
188,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_right_of_le' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.153094\nι' : Type ?u.153097\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.153106\ninst✝ : OrderedAddCommGroup β\nl : Filter α\nf g : α → β\nC : β\nhf : Tendsto f l atTop\nhg : ∀ᶠ (x : α) in l, C ≤ g x\n⊢ ∀ᶠ (x : α) in l, (fun x => -g x) x ≤ -C",
"tact... | [
791,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_lt_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.284872\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\nn : σ\nf : MvPolynomial σ R\nd : ℕ\nh : 0 < d\n⊢ degreeOf n f < d ↔ ∀ (m : σ →₀ ℕ), m ∈ support f → ↑m n < d",
"tact... | [
507,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.enum_nil | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_iSup_nat' | [] | [
843,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
11
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_one | [] | [
299,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Order/Monotone/Basic.lean | MonotoneOn.dual | [] | [
230,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.cancel_coe | [] | [
1080,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
] |
Mathlib/GroupTheory/Perm/Fin.lean | Equiv.Perm.decomposeFin_symm_apply_zero | [
{
"state_after": "no goals",
"state_before": "n : ℕ\np : Fin (n + 1)\ne : Perm (Fin n)\n⊢ ↑(↑decomposeFin.symm (p, e)) 0 = p",
"tactic": "simp [Equiv.Perm.decomposeFin]"
}
] | [
45,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ico | [] | [
250,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_dvd_prod_of_dvd | [
{
"state_after": "case h₁\nι : Type ?u.85910\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.85919\ninst✝ : CommMonoid β\nS : Multiset α\ng1 g2 : α → β\nh : ∀ (a : α), a ∈ S → g1 a ∣ g2 a\n⊢ prod (map g1 0) ∣ prod (map g2 0)\n\ncase h₂\nι : Type ?u.85910\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.85919\ninst✝ : CommMono... | [
257,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Logic/Denumerable.lean | Nat.Subtype.succ_le_of_lt | [
{
"state_after": "α : Type ?u.43600\nβ : Type ?u.43603\ns : Set ℕ\ninst✝¹ : Infinite ↑s\ninst✝ : DecidablePred fun x => x ∈ s\nx y : ↑s\nh : y < x\nhx : ∃ m, ↑y + m + 1 ∈ s\nk : ℕ\nhk : ↑x = ↑y + k + 1\nthis : Nat.find hx ≤ k\n⊢ ↑y + Nat.find hx + 1 ≤ ↑y + k + 1",
"state_before": "α : Type ?u.43600\nβ : Typ... | [
251,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_fmod_right | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ fmod (a * b) a = 0",
"tactic": "rw [Int.mul_comm, mul_fmod_left]"
}
] | [
468,
35
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
467,
9
] |
Mathlib/Data/Nat/Sqrt.lean | Nat.sqrt_le_add | [
{
"state_after": "n : ℕ\n⊢ n ≤ succ (sqrt n) * sqrt n + sqrt n",
"state_before": "n : ℕ\n⊢ n ≤ sqrt n * sqrt n + sqrt n + sqrt n",
"tactic": "rw [← succ_mul]"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ n ≤ succ (sqrt n) * sqrt n + sqrt n",
"tactic": "exact le_of_lt_succ (l... | [
84,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.prod_set' | [
{
"state_after": "n : ℕ\nα : Type u_1\nβ : Type ?u.63254\nγ : Type ?u.63257\ninst✝ : CommGroup α\nv : Vector α n\ni : Fin n\na : α\n⊢ (List.prod (toList v) * if hn : ↑i < List.length (toList v) then (List.nthLe (toList v) (↑i) hn)⁻¹ * a else 1) =\n List.prod (toList v) * (get v i)⁻¹ * a",
"state_before":... | [
623,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | one_lt_div' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ 1 < a / b ↔ b < a",
"tactic": "rw [← mul_lt_mul_iff_right b, one_mul, div_eq_mul_inv, inv_mul_cancel_right]"
}
] | [
891,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.norm_comp_le_of_le' | [
{
"state_after": "V : Type ?u.470292\nV₁ : Type u_3\nV₂ : Type u_1\nV₃ : Type u_2\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g✝ : NormedAddGroupHom V₁ V₂\ng : NormedAddGroupHom V₂ V₃\nC₁ C₂ C₃ : ℝ\nh : C₃ = C₂ ... | [
670,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Algebra/Lie/SkewAdjoint.lean | mem_skewAdjointMatricesLieSubalgebra | [] | [
128,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/RingTheory/PowerBasis.lean | PowerBasis.dim_le_natDegree_of_root | [
{
"state_after": "R : Type ?u.115843\nS : Type u_2\nT : Type ?u.115849\ninst✝⁸ : CommRing R\ninst✝⁷ : Ring S\ninst✝⁶ : Algebra R S\nA : Type u_1\nB : Type ?u.116155\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : IsDomain B\ninst✝² : Algebra A B\nK : Type ?u.116577\ninst✝¹ : Field K\ninst✝ : Algebra A S\npb... | [
182,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Raised.add_left | [
{
"state_after": "case inl\nα : Type ?u.244533\nk m : ℕ\n⊢ Raised (k + m) (k + m)\n\ncase inr\nα : Type ?u.244533\nk n : ℕ\n⊢ Raised (k + n) (k + (n + 1))",
"state_before": "α : Type ?u.244533\nk n m : ℕ\nH : Raised n m\n⊢ Raised (k + n) (k + m)",
"tactic": "rcases H with (rfl | rfl)"
},
{
"stat... | [
803,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.coe_ringEquiv' | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.srange_top_iff_surjective | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN✝ : Type ?u.61232\nP : Type ?u.61235\nσ : Type ?u.61238\ninst✝³ : Mul M\ninst✝² : Mul N✝\ninst✝¹ : Mul P\nS : Subsemigroup M\nN : Type u_1\ninst✝ : Mul N\nf : M →ₙ* N\n⊢ ↑(srange f) = ↑⊤ ↔ Set.range ↑f = Set.univ",
"tactic": "rw [coe_srange, c... | [
785,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/Complex/Schwarz.lean | Complex.affine_of_mapsTo_ball_of_exists_norm_dslope_eq_div' | [] | [
140,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_atBot_curry | [] | [
1496,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1494,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_injective | [
{
"state_after": "θ ψ : Angle\nh : toReal θ = toReal ψ\n⊢ θ = ψ",
"state_before": "⊢ Function.Injective toReal",
"tactic": "intro θ ψ h"
},
{
"state_after": "case h\nψ : Angle\nx✝ : ℝ\nh : toReal ↑x✝ = toReal ψ\n⊢ ↑x✝ = ψ",
"state_before": "θ ψ : Angle\nh : toReal θ = toReal ψ\n⊢ θ = ψ",
... | [
545,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Topology/StoneCech.lean | denseRange_pure | [] | [
131,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Std/Data/AssocList.lean | Std.AssocList.toList_toAssocList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nl : AssocList α β\n⊢ List.toAssocList (toList l) = l",
"tactic": "induction l <;> simp [*]"
}
] | [
238,
27
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
237,
9
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.IsEquivalent.mul | [] | [
287,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | HasStrictDerivAt.hasDerivAt | [] | [
304,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic'_zero | [
{
"state_after": "no goals",
"state_before": "R✝ : Type ?u.32552\ninst✝³ : CommRing R✝\ninst✝² : IsDomain R✝\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\n⊢ cyclotomic' 0 R = 1",
"tactic": "simp only [cyclotomic', Finset.prod_empty, primitiveRoots_zero]"
}
] | [
78,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Data/Int/Lemmas.lean | Int.subNatNat_self | [
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ subNatNat (succ m) (succ m) = 0",
"tactic": "rw [subNatNat_of_sub_eq_zero (Nat.sub_self ..), Nat.sub_self, ofNat_zero]"
}
] | [
293,
91
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
291,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.ofDigits_digits_append_digits | [
{
"state_after": "no goals",
"state_before": "n✝ b m n : ℕ\n⊢ ofDigits b (digits b n ++ digits b m) = n + b ^ List.length (digits b n) * m",
"tactic": "rw [ofDigits_append, ofDigits_digits, ofDigits_digits]"
}
] | [
429,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.mul_transvection_apply_same | [
{
"state_after": "no goals",
"state_before": "n : Type u_1\np : Type ?u.14412\nR : Type u₂\n𝕜 : Type ?u.14417\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ni j : n\ninst✝ : Fintype n\na : n\nc : R\nM : Matrix n n R\n⊢ (M ⬝ transvection i j c) a j = M a j + c * M a... | [
131,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.add_mem_Icc_iff_right | [] | [
85,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Std/Data/Int/Lemmas.lean | Int.zero_lt_one | [] | [
654,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
654,
11
] |
Mathlib/Data/Fintype/Basic.lean | Finset.compl_eq_univ_iff | [] | [
198,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.maximalSubfieldWithHom_is_maximal | [] | [
290,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.equivFunOnFintype_single | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝¹ : (i : ι) → Zero (β i)\ns : Finset ι\nx✝ : (i : ↑↑s) → β ↑i\ni✝ : ι\ninst✝ : Fintype ι\ni : ι\nm : β i\nx : ι\n⊢ ↑equivFunOnFintype (single i m) x = Pi.single i m x",
"state_befo... | [
731,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | SymmetricRel.inter | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.17571\nU V : Set (α × α)\nhU : SymmetricRel U\nhV : SymmetricRel V\n⊢ SymmetricRel (U ∩ V)",
"tactic": "rw [SymmetricRel, preimage_inter, hU.eq, hV.eq]"
}
] | [
240,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.ext | [
{
"state_after": "case mk\nα : Type u_1\nE : Type u_2\nF : Type ?u.358556\nG : Type ?u.358559\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\ng : { x // x ∈ Lp E p }\nval✝ : α →ₘ[μ] E\nproperty✝ : val✝ ∈ Lp ... | [
166,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_eq_expSeries | [
{
"state_after": "no goals",
"state_before": "𝕂 : Type u_2\n𝕂' : Type u_3\n𝔸 : Type u_1\ninst✝⁶ : Field 𝕂\ninst✝⁵ : Field 𝕂'\ninst✝⁴ : Ring 𝔸\ninst✝³ : Algebra 𝕂 𝔸\ninst✝² : Algebra 𝕂' 𝔸\ninst✝¹ : TopologicalSpace 𝔸\ninst✝ : TopologicalRing 𝔸\nn : ℕ\nx : 𝔸\n⊢ (↑(expSeries 𝕂 𝔸 n) fun x_1 => x)... | [
655,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.addEquivBoundedOfCompact_apply | [] | [
97,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/RingTheory/MvPolynomial/Basic.lean | MvPolynomial.mem_restrictTotalDegree | [
{
"state_after": "σ : Type u\nR : Type v\ninst✝ : CommRing R\np✝ m : ℕ\np : MvPolynomial σ R\n⊢ p ∈ restrictTotalDegree σ R m ↔ ∀ (b : σ →₀ ℕ), b ∈ support p → (Finsupp.sum b fun x e => e) ≤ m",
"state_before": "σ : Type u\nR : Type v\ninst✝ : CommRing R\np✝ m : ℕ\np : MvPolynomial σ R\n⊢ p ∈ restrictTotalD... | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/PNat/Basic.lean | PNat.mod_add_div' | [
{
"state_after": "m k : ℕ+\n⊢ ↑(mod m k) + ↑k * div m k = ↑m",
"state_before": "m k : ℕ+\n⊢ ↑(mod m k) + div m k * ↑k = ↑m",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m k : ℕ+\n⊢ ↑(mod m k) + ↑k * div m k = ↑m",
"tactic": "exact mod_add_div _ _"
}
] | [
371,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.abs_exp_mul_exp_add_exp_neg_le_of_abs_im_le | [
{
"state_after": "a b : ℝ\nha : a ≤ 0\nz : ℂ\nhz : Abs.abs z.im ≤ b\nhb : b ≤ π / 2\n⊢ a * ((Real.exp z.re + Real.exp (-z.re)) * Real.cos (Abs.abs z.im)) ≤ a * (Real.exp (Abs.abs z.re) * Real.cos b)",
"state_before": "a b : ℝ\nha : a ≤ 0\nz : ℂ\nhz : Abs.abs z.im ≤ b\nhb : b ≤ π / 2\n⊢ ↑abs (exp (↑a * (exp ... | [
1419,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.closure_cycle_adjacent_swap | [
{
"state_after": "ι : Type ?u.2796652\nα : Type u_1\nβ : Type ?u.2796658\ninst✝² : DecidableEq α\ninst✝¹ : Finite β\ninst✝ : Fintype α\nσ : Perm α\nh1 : IsCycle σ\nh2 : support σ = ⊤\nx : α\nH : Subgroup (Perm α) := closure {σ, swap x (↑σ x)}\n⊢ closure {σ, swap x (↑σ x)} = ⊤",
"state_before": "ι : Type ?u.... | [
1665,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1618,
1
] |
Mathlib/RingTheory/Adjoin/FG.lean | Subalgebra.fg_of_submodule_fg | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁴ : CommSemiring R\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\nh : Submodule.FG ⊤\ns : Finset A\nhs : span R ↑s = ⊤\n⊢ ↑s ⊆ ↑(↑toSubmodule (Algebra.adjoin R ↑s))",
"state_before": "R : Type u\nA : Type v\nB ... | [
130,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/FieldTheory/Subfield.lean | SubfieldClass.coe_rat_mem | [
{
"state_after": "no goals",
"state_before": "K : Type u\nL : Type v\nM : Type w\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Field M\nS : Type u_1\ninst✝ : SetLike S K\nh : SubfieldClass S K\ns : S\nx : ℚ\n⊢ ↑x ∈ s",
"tactic": "simpa only [Rat.cast_def] using div_mem (coe_int_mem s x.num) (coe_nat_mem... | [
95,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Computability/Halting.lean | Nat.Partrec'.part_iff | [] | [
416,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | PowerSeries.coe_zero | [] | [
189,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.tan_arcsin | [
{
"state_after": "x : ℝ\n⊢ sin (arcsin x) / sqrt (1 - x ^ 2) = x / sqrt (1 - x ^ 2)",
"state_before": "x : ℝ\n⊢ tan (arcsin x) = x / sqrt (1 - x ^ 2)",
"tactic": "rw [tan_eq_sin_div_cos, cos_arcsin]"
},
{
"state_after": "case pos\nx : ℝ\nhx₁ : -1 ≤ x\n⊢ sin (arcsin x) / sqrt (1 - x ^ 2) = x / sq... | [
332,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_le_mul_left | [] | [
213,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.inv_apply | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
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