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/Algebra/Regular/Basic.lean | IsUnit.isRegular | [
{
"state_after": "case intro\nR : Type u_1\ninst✝ : Monoid R\nb : R\na : Rˣ\n⊢ IsRegular ↑a",
"state_before": "R : Type u_1\ninst✝ : Monoid R\na b : R\nua : IsUnit a\n⊢ IsRegular a",
"tactic": "rcases ua with ⟨a, rfl⟩"
},
{
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"state_before": "case intro\nR : Type u_1... | [
331,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.hyperfilter_le_cofinite | [] | [
480,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Function.Injective.hasSum_range_iff | [] | [
225,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | innerSL_apply | [] | [
1782,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1781,
1
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Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nM : Type u_2\nM₂ : Type ?u.110628\nM₃ : Type ?u.110631\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : AddCommGroup M₂\ninst✝³ : AddCommGroup M₃\ninst✝² : Module R M\ninst✝¹ : Module R M₂\ninst✝ : Module R M₃\nf : M →ₗ[R] M₂\np p' : Submodule R... | [
142,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_le_pow_card | [
{
"state_after": "case refine'_1\nι : Type u_1\nα : Type ?u.33275\nβ : Type ?u.33278\nM : Type ?u.33281\nN : Type u_2\nG : Type ?u.33287\nk : Type ?u.33290\nR : Type ?u.33293\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf✝ g : ι → N\ns✝ t s : Finset ι\nf : ι → N\nn : N\nh : ∀ (x : ι), x ∈ s → f x ≤ n\n⊢... | [
220,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pell_val | [] | [
128,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | parallelogram_law_with_nnnorm | [] | [
1130,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1128,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.symm_dual_comp | [] | [
1510,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1507,
1
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Mathlib/Data/Sym/Basic.lean | Sym.attach_cons | [] | [
459,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
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Mathlib/LinearAlgebra/Matrix/DotProduct.lean | Matrix.dotProduct_eq_iff | [] | [
65,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
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Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_summable' | [] | [
429,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/RingTheory/WittVector/WittPolynomial.lean | wittPolynomial_zMod_self | [
{
"state_after": "p : ℕ\nR : Type ?u.148919\ninst✝² : CommRing R\ninst✝¹ : DecidableEq R\nS : Type ?u.148934\ninst✝ : CommRing S\nn : ℕ\n⊢ ∑ x in range (n + 1 + 1), ↑C (↑p ^ x) * X x ^ p ^ (n + 1 - x) =\n ↑(expand p) (∑ x in range (n + 1), ↑C (↑p ^ x) * X x ^ p ^ (n - x))",
"state_before": "p : ℕ\nR : Ty... | [
170,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Sum/Order.lean | WithBot.orderIsoPUnitSumLex_symm_inl | [] | [
761,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Mul.lean | HasFDerivWithinAt.clm_apply | [] | [
125,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.den_eq_one_iff | [] | [
521,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
1
] |
Mathlib/Topology/Algebra/Order/UpperLower.lean | IsUpperSet.interior | [
{
"state_after": "α : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : Preorder α\ninst✝ : HasUpperLowerClosure α\ns : Set α\nh : IsUpperSet s\n⊢ IsLowerSet (closure (sᶜ))",
"state_before": "α : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : Preorder α\ninst✝ : HasUpperLowerClosure α\ns : Set α\nh : IsUpper... | [
106,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
11
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.add_im | [] | [
899,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
16
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_comm | [] | [
1156,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mul_subset_iff | [] | [
436,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Order/Closure.lean | LowerAdjoint.mem_iff | [
{
"state_after": "α : Type u_2\nι : Sort ?u.24409\nκ : ι → Sort ?u.24414\nβ : Type u_1\ninst✝ : SetLike α β\nl : LowerAdjoint SetLike.coe\ns : Set β\nx : β\n⊢ toFun l {x} ≤ toFun l s ↔ ∀ (S : α), toFun l s ≤ S → toFun l {x} ≤ S",
"state_before": "α : Type u_2\nι : Sort ?u.24409\nκ : ι → Sort ?u.24414\nβ : T... | [
494,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.ne_rat | [] | [
163,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/RingTheory/LaurentSeries.lean | LaurentSeries.powerSeriesPart_zero | [
{
"state_after": "case h\nR : Type u\ninst✝ : Semiring R\nn✝ : ℕ\n⊢ ↑(PowerSeries.coeff R n✝) (powerSeriesPart 0) = ↑(PowerSeries.coeff R n✝) 0",
"state_before": "R : Type u\ninst✝ : Semiring R\n⊢ powerSeriesPart 0 = 0",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case h... | [
78,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae' | [
{
"state_after": "ι : Type u_2\n𝕜 : Type ?u.242824\nE : Type u_1\nF : Type ?u.242830\nA✝ : Type ?u.242833\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : CompleteSpace E\ninst✝² : NormedSpace ℝ E\nf : ℝ → E\na b : ℝ\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\nμ : MeasureTheory.Measure ℝ\nu v ua va ub ... | [
288,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.WellFounded.finite_of_independent | [] | [
325,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | one_le_bit1 | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.130379\ninst✝ : LinearOrderedSemiring α\na b c d : α\n⊢ 1 ≤ bit1 a ↔ 0 ≤ a",
"tactic": "rw [bit1, le_add_iff_nonneg_left, bit0, ← two_mul, zero_le_mul_left (zero_lt_two : 0 < (2 : α))]"
}
] | [
910,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.RightSplit.shortExact | [] | [
79,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Std/Control/ForInStep/Lemmas.lean | ForInStep.done_bindList | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝ : Monad m\nf : α → β → m (ForInStep β)\na : β\nl : List α\n⊢ bindList f l (done a) = pure (done a)",
"tactic": "cases l <;> simp"
}
] | [
29,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
27,
9
] |
Mathlib/Algebra/Hom/Group.lean | MulHom.mul_comp | [] | [
1467,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1466,
1
] |
Mathlib/Data/Nat/Lattice.lean | Set.biUnion_lt_succ' | [] | [
210,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.pow_eq_top | [] | [
631,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_equiv_lpPiLp_symm | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | Metric.preimage_mul_right_ball | [
{
"state_after": "M : Type u\nG : Type v\nX : Type w\ninst✝⁵ : PseudoMetricSpace X\ninst✝⁴ : Group G\ninst✝³ : MulAction G X\ninst✝² : IsometricSMul G X\ninst✝¹ : PseudoMetricSpace G\ninst✝ : IsometricSMul Gᵐᵒᵖ G\na b : G\nr : ℝ\n⊢ (fun x => x * a) ⁻¹' ball b r = ball (b * a⁻¹) r",
"state_before": "M : Type... | [
479,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
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Mathlib/Algebra/Group/Defs.lean | mul_left_injective | [] | [
226,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | Commute.cast_nat_mul_right | [] | [
1089,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1088,
1
] |
Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.comp_eq | [
{
"state_after": "case w\nA B : GroupCat\nf : A ⟶ B\na : ↑A\n⊢ ↑(f ≫\n let_fun this := g;\n this)\n a =\n ↑(f ≫\n let_fun this := h;\n this)\n a",
"state_before": "A B : GroupCat\nf : A ⟶ B\n⊢ (f ≫\n let_fun this := g;\n this) =\n f ≫\n let_... | [
326,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.det_symm | [] | [
401,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.tendsto_nhds | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.423602\n𝕝 : Type ?u.423605\n𝕝₂ : Type ?u.423608\nE : Type u_2\nF : Type u_4\nG : Type ?u.423617\nι : Type u_3\nι' : Type ?u.423623\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ : TopologicalSpace E\np : Semino... | [
395,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPushout.inr_iso_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nW X Y Z : C\nh : X ⟶ Z\nk : Y ⟶ Z\nf : W ⟶ X\ng : W ⟶ Y\ncomm : f ≫ h = g ≫ k\ninst✝² : PreservesColimit (span f g) G\ninst✝¹ : HasPushout f g\ninst✝ : HasPushout (G.map f) (G.map g)\... | [
249,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Set/Sups.lean | Set.singleton_infs | [] | [
303,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/CategoryTheory/Closed/Cartesian.lean | CategoryTheory.CartesianClosed.uncurry_injective | [] | [
245,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_filter_le | [] | [
263,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_pow | [] | [
1803,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1802,
11
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.model_nonemptyTheory_iff | [
{
"state_after": "no goals",
"state_before": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.819644\nP : Type ?u.819647\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nT : Theory L\n⊢ M ⊨ nonemptyTheory L ↔ Nonempty M",
"tactic": "simp only ... | [
1069,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
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Mathlib/Algebra/Order/Group/Abs.lean | abs_add | [] | [
273,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Data/TypeVec.lean | TypeVec.const_iff_true | [
{
"state_after": "case fz\nn : ℕ\np : Prop\nn✝ : ℕ\nα : TypeVec (succ n✝)\nx : α Fin2.fz\n⊢ ofRepeat (TypeVec.const p α Fin2.fz x) ↔ p\n\ncase fs\nn : ℕ\np : Prop\nn✝ : ℕ\na✝ : Fin2 n✝\na_ih✝ : ∀ {α : TypeVec n✝} {x : α a✝}, ofRepeat (TypeVec.const p α a✝ x) ↔ p\nα : TypeVec (succ n✝)\nx : α (Fin2.fs a✝)\n⊢ ofR... | [
507,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
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] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.map_isGreatest | [] | [
1202,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1201,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.eq_cons_iff | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\na : α\nv : Vector α (Nat.succ n)\nv' : Vector α n\nh : head v = a ∧ tail v = v'\n⊢ head v ::ᵥ tail v = a ::ᵥ v'",
"tactic": "rw [h.1, h.2]"
}
] | [
67,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Order/Basic.lean | eq_of_forall_ge_iff | [] | [
553,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | exposedPoints_subset | [] | [
213,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_diagonal | [] | [
110,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_univ_pi | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.112247\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\ni : ι\nf : (i : ι) → α i\n⊢ f ∈ pi univ t ↔ ∀ (i : ι), f i ∈ t i",
"tactic": "simp"
}
] | [
648,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_subset_ite | [] | [
1823,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1822,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_div_cancel_of_mod_eq_zero | [
{
"state_after": "a b : Int\nH : mod a b = 0\nthis : mod a b + b * div a b = a\n⊢ b * div a b = a",
"state_before": "a b : Int\nH : mod a b = 0\n⊢ b * div a b = a",
"tactic": "have := mod_add_div a b"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nH : mod a b = 0\nthis : mod a b... | [
580,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
579,
1
] |
Mathlib/Logic/Basic.lean | ite_eq_iff | [
{
"state_after": "α : Sort u_1\nβ : Sort ?u.33143\nσ : α → Sort ?u.33139\nf : α → β\nP Q : Prop\ninst✝¹ : Decidable P\ninst✝ : Decidable Q\na b c : α\nA : P → α\nB : ¬P → α\n⊢ ((∃ h, a = c) ∨ ∃ h, b = c) ↔ P ∧ a = c ∨ ¬P ∧ b = c",
"state_before": "α : Sort u_1\nβ : Sort ?u.33143\nσ : α → Sort ?u.33139\nf : ... | [
1132,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Topology/Basic.lean | interior_mem_nhds | [] | [
1215,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/Order/Lattice.lean | Antitone.map_sup | [] | [
1202,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | ContinuousLinearEquiv.integral_comp_comm | [] | [
1144,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1143,
1
] |
Mathlib/Order/Filter/NAry.lean | Filter.mem_map₂_iff | [] | [
60,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.eq_mul_inv_iff_mul_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c u : αˣ\na b : α\nh : a = b * ↑c⁻¹\n⊢ a * ↑c = b",
"tactic": "rw [h, inv_mul_cancel_right]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b✝ c u : αˣ\na b : α\nh : a * ↑c = ... | [
323,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean | CategoryTheory.Free.lift_map_single | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁴ : CommRing R\nC : Type u\ninst✝³ : Category C\nD : Type u\ninst✝² : Category D\ninst✝¹ : Preadditive D\ninst✝ : Linear R D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\nr : R\n⊢ (lift R F).map (single f r) = r • F.map f",
"tactic": "simp"
}
] | [
375,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.max_map | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_eq_one | [] | [
183,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | ContinuousOn.div' | [] | [
1141,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Algebra/BigOperators/Fin.lean | Fin.prod_univ_six | [
{
"state_after": "α : Type ?u.25201\nβ : Type u_1\ninst✝ : CommMonoid β\nf : Fin 6 → β\n⊢ f (↑castSucc 0) * f (↑castSucc 1) * f (↑castSucc 2) * f (↑castSucc 3) * f (↑castSucc 4) * f (last 5) =\n f 0 * f 1 * f 2 * f 3 * f 4 * f 5",
"state_before": "α : Type ?u.25201\nβ : Type u_1\ninst✝ : CommMonoid β\nf ... | [
143,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/FunLike/Equiv.lean | EquivLike.comp_bijective | [] | [
229,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | AddLECancellable.add_tsub_assoc_of_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝⁵ : AddCommSemigroup α\ninst✝⁴ : PartialOrder α\ninst✝³ : ExistsAddOfLE α\ninst✝² : CovariantClass α α (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na✝ b c d : α\nhc : AddLECancellable c\nh : c ≤ b\na : α\n... | [
92,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
11
] |
Std/Data/Array/Lemmas.lean | Array.get_eq_getElem | [] | [
40,
83
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
9
] |
Mathlib/CategoryTheory/Whiskering.lean | CategoryTheory.whiskerLeft_comp | [] | [
145,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_equivMapOfInjective_apply | [] | [
587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.lt_top_of_sum_ne_top | [] | [
1237,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/Data/Sign.lean | Int.sign_eq_sign | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.128001\nn : ℤ\n⊢ sign n = ↑(↑SignType.sign n)",
"tactic": "obtain (n | _) | _ := n <;> simp [sign, Int.sign_neg, negSucc_lt_zero]"
}
] | [
486,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
485,
1
] |
Mathlib/CategoryTheory/PUnit.lean | CategoryTheory.Functor.pUnit_ext' | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nF G : C ⥤ Discrete PUnit\nX : C\n⊢ F.obj X = G.obj X",
"tactic": "simp only [eq_iff_true_of_subsingleton]"
}
] | [
52,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.trans | [] | [
67,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
11
] |
Mathlib/LinearAlgebra/Dual.lean | Submodule.le_dualAnnihilator_iff_le_dualCoannihilator | [] | [
848,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | fderivWithin_eventually_congr_set' | [] | [
816,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Std/Logic.lean | exists_apply_eq_apply | [] | [
485,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
485,
9
] |
Mathlib/GroupTheory/OrderOfElement.lean | zpow_eq_mod_orderOf | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Group G\ninst✝ : AddGroup A\ni : ℤ\n⊢ x ^ i = ?m.909316",
"tactic": "rw [← Int.emod_add_ediv i (orderOf x)]"
},
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y ... | [
579,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.totallyBounded_iff | [] | [
764,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.rnDeriv_smul | [
{
"state_after": "α : Type u_1\nβ : Type ?u.647949\nm : MeasurableSpace α\nμ✝ ν : Measure α\ns✝ t s : SignedMeasure α\nμ : Measure α\ninst✝ : HaveLebesgueDecomposition s μ\nr : ℝ\n⊢ withDensityᵥ μ (rnDeriv (r • s) μ) = withDensityᵥ μ (r • rnDeriv s μ)",
"state_before": "α : Type u_1\nβ : Type ?u.647949\nm :... | [
1164,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.subset_pointwise_smul_iff | [] | [
136,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_mk | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.cos_two_mul | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑(cos (2 * x)) = ↑(2 * cos x ^ 2 - 1)",
"tactic": "simp [cos_two_mul]"
}
] | [
1283,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
8
] |
Mathlib/MeasureTheory/Measure/Regular.lean | IsOpen.measure_eq_iSup_isClosed | [] | [
572,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.prod_isUnit | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.48568\nα : Type ?u.48571\nM : Type u_1\nN : Type ?u.48577\nP : Type ?u.48580\nM₀ : Type ?u.48583\nG : Type ?u.48586\nR : Type ?u.48589\ninst✝² : Monoid M\ninst✝¹ : Monoid N\ninst✝ : Monoid P\nl l₁ l₂ : List M\na : M\nx✝ : ∀ (m : M), m ∈ [] → IsUnit m... | [
149,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.hasSum_repr | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.790578\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G ... | [
475,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
11
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_add | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.13316\nα : Type u_1\nβ : Type ?u.13322\nγ : Type ?u.13325\ninst✝ : CommMonoid α\ns✝ t✝ : Multiset α\na : α\nm : Multiset ι\nf g : ι → α\ns t : Multiset α\nl₁ l₂ : List α\n⊢ prod (Quotient.mk (List.isSetoid α) l₁ + Quotient.mk (List.isSetoid α) l₂) =\... | [
119,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/List/Chain.lean | List.chain'_cons | [] | [
204,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_mul | [] | [
1237,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.sub_conj | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.2979461\ninst✝ : IsROrC K\nz : K\n⊢ z - ↑(starRingEnd K) z = ↑(↑re z) + ↑(↑im z) * I - (↑(↑re z) - ↑(↑im z) * I)",
"tactic": "rw [re_add_im, ← conj_eq_re_sub_im]"
},
{
"state_after": "no goals",
"state_before": "K : Type... | [
385,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.simple_of_cosimple | [
{
"state_after": "case mp\nC : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX : C\nh : ∀ {Z : C} (f : X ⟶ Z) [inst : Epi f], IsIso f ↔ f ≠ 0\nY : C\nf : Y ⟶ X\nI : Mono f\n⊢ IsIso f → f ≠ 0\n\ncase mpr\nC : Type u\ninst✝¹ : Category C\ninst✝ : Abelian C\nX : C\nh : ∀ {Z : C} (f : X ⟶ Z) [inst : Epi f], IsIso... | [
163,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/Basic.lean | Prod.le_def | [] | [
1193,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Data/List/Sort.lean | List.sublist_of_subperm_of_sorted | [
{
"state_after": "α : Type uu\nr : α → α → Prop\na : α\nl : List α\ninst✝ : IsAntisymm α r\nl₁ l₂ : List α\np : l₁ <+~ l₂\ns₁ : Sorted r l₁\ns₂ : Sorted r l₂\nw✝ : List α\nh : w✝ ~ l₁\nh' : w✝ <+ l₂\n⊢ l₁ <+ l₂",
"state_before": "α : Type uu\nr : α → α → Prop\na : α\nl : List α\ninst✝ : IsAntisymm α r\nl₁ l... | [
105,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Algebra/Algebra/Bilinear.lean | LinearMap.mulRight_toAddMonoidHom | [] | [
70,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Heyting/Hom.lean | CoheytingHom.coe_id | [] | [
431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.coe_Iic | [] | [
430,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | NNReal.pow_arith_mean_le_arith_mean_pow | [
{
"state_after": "no goals",
"state_before": "ι : Type u\ns : Finset ι\nw z : ι → ℝ≥0\nhw' : ∑ i in s, w i = 1\nn : ℕ\n⊢ (∑ i in s, w i * z i) ^ n ≤ ∑ i in s, w i * z i ^ n",
"tactic": "exact_mod_cast\n Real.pow_arith_mean_le_arith_mean_pow s _ _ (fun i _ => (w i).coe_nonneg)\n (by exact_mod_cast hw... | [
127,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Algebra/Hom/Group.lean | invMonoidHom_apply | [] | [
989,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
] |
Mathlib/LinearAlgebra/Matrix/SpecialLinearGroup.lean | Matrix.SpecialLinearGroup.toLin'_symm_to_linearMap | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Order/Hom/Lattice.lean | LatticeHom.toFun_eq_coe | [] | [
1054,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1054,
1
] |
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