file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.nonsing_inv_apply_not_isUnit | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.99734\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B : Matrix n n α\nh : ¬IsUnit (det A)\n⊢ A⁻¹ = 0",
"tactic": "rw [inv_def, Ring.inverse_non_unit _ h, zero_smul]"
}
] | [
261,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.of_add_of_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.23713\nm : MeasurableSpace α\nM : Type u_2\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\nv : VectorMeasure α M\nf : ℕ → Set α\nA B : Set α\nhA : MeasurableSet A\nhB : MeasurableSet B\nh : A ⊆ B\n⊢ ↑v A + ↑v ... | [
196,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_coe | [] | [
136,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
11
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_eq_one_iff | [] | [
1539,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.ofComapInfPrincipal_mem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.55399\nm : α → β\ns : Set α\ng : Ultrafilter β\nh : m '' s ∈ g\nf : Filter α := Filter.comap m ↑g ⊓ 𝓟 s\n⊢ s ∈ ofComapInfPrincipal h",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.55399\nm : α → β\ns : Set α\ng : Ultrafilter β\nh : m '' s ∈ g\n⊢... | [
532,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.measure_eq_iSup | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np q : Set α → Prop\nU : Set α\nε : ℝ≥0∞\nH : InnerRegular μ p q\nhU : q U\nr : ℝ≥0∞\nhr : r < ↑↑μ U\n⊢ r < ⨆ (K : Set α) (_ : K ⊆ U) (_ : p K), ↑↑μ K",
"state_before": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np q : Set α → Pro... | [
160,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_pos_iff_nonempty_of_isMulLeftInvariant | [] | [
573,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.epi_iff_cokernel_π_eq_zero | [] | [
292,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_emptyCollection | [] | [
1981,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1980,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mulPosMono_iff_mulPosStrictMono | [] | [
1000,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
999,
1
] |
Mathlib/CategoryTheory/Abelian/Images.lean | CategoryTheory.Abelian.coimage.fac | [] | [
92,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
11
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.induction_linear | [] | [
1117,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1115,
1
] |
Mathlib/Data/Set/Image.lean | Set.union_preimage_subset | [] | [
543,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_pos_right | [
{
"state_after": "a b : Int\nh : 0 < b\nthis : a + 0 < a + b\n⊢ a < a + b",
"state_before": "a b : Int\nh : 0 < b\n⊢ a < a + b",
"tactic": "have : a + 0 < a + b := Int.add_lt_add_left h a"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : 0 < b\nthis : a + 0 < a + b\n⊢ a < a + ... | [
813,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
811,
11
] |
Mathlib/Data/List/Basic.lean | List.foldr_fixed | [] | [
2436,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2435,
1
] |
Mathlib/Topology/Order/Basic.lean | mem_nhdsWithin_Ioi_iff_exists_Ioo_subset' | [] | [
1622,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1620,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Comp.lean | DifferentiableAt.comp | [] | [
132,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.infty_mem_opensOfCompl | [] | [
263,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsorBases.lean | AffineBasis.interior_convexHull | [
{
"state_after": "case inl\nι : Type u_1\nE : Type u_2\ninst✝² : Finite ι\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nb : AffineBasis ι ℝ E\nh✝ : Subsingleton ι\n⊢ interior (↑(convexHull ℝ).toOrderHom (range ↑b)) = {x | ∀ (i : ι), 0 < ↑(coord b i) x}\n\ncase inr\nι : Type u_1\nE : Type u_2\ninst✝² ... | [
83,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_eq_iff | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.57635\nα : Type u_1\nβ : Type ?u.57641\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na : α\nn : ℕ\nhn : n ≠ 0\n⊢ ⌈a⌉₊ = n ↔ ↑(n - 1) < a ∧ a ≤ ↑n",
"tactic": "rw [← ceil_le, ← not_le, ← ceil_le, not_le,\n tsub_lt_iff_right (Nat.add... | [
364,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.not_continuous_cofiniteTopology_of_symm | [
{
"state_after": "X : Type u_1\ninst✝² : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\ninst✝¹ : Infinite X\ninst✝ : DiscreteTopology X\ninhabited_h : Inhabited X\n⊢ ¬Continuous ↑CofiniteTopology.of.symm",
"state_before": "X : Type u_1\ninst✝² : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nins... | [
492,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1023730\nγ : Type ?u.1023733\nδ : Type ?u.1023736\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁴ : MeasurableSpace δ\ninst✝³ : NormedAddCommGroup β\ninst✝² : NormedAddCommGroup γ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf :... | [
896,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
881,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_iff_le_pred | [] | [
790,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_insert | [] | [
320,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_comp_eq | [] | [
216,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/AlgebraicTopology/FundamentalGroupoid/Basic.lean | Path.Homotopy.transAssocReparamAux_one | [
{
"state_after": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ (if 1 ≤ 4⁻¹ then 2 else if 1 ≤ 2⁻¹ then 1 + 4⁻¹ else 2⁻¹ * (1 + 1)) = 1",
"state_before": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx₀ x₁ : X\n⊢ transAssocR... | [
228,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.mk_le_mk | [] | [
445,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbit_eq_iff | [] | [
252,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.erase_zero | [] | [
777,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
776,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_erase_eq_ite | [] | [
162,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_ne_zero | [] | [
356,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/List/Basic.lean | List.foldl_fixed' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.230724\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β → α\na : α\nhf : ∀ (b : β), f a b = a\nb : β\nl : List β\n⊢ foldl f a (b :: l) = a",
"tactic": "rw [foldl_cons, hf b, foldl_fixed' hf l]"
}
] | [
2421,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2419,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.toString_extract | [
{
"state_after": "b e : Pos\nx✝ : Substring\nh₁✝ : Valid x✝\nh₂ : Valid { str := toString x✝, startPos := b, stopPos := e }\nl m r : List Char\nh₁ : ValidFor l m r x✝\n⊢ toString (Substring.extract x✝ b e) = String.extract (toString x✝) b e",
"state_before": "b e : Pos\nx✝ : Substring\nh₁ : Valid x✝\nh₂ : V... | [
1051,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1044,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.coeToSet_coeToSubmodule | [] | [
193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_mul_aleph0 | [] | [
1637,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.Homotopic.pi | [] | [
396,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
11
] |
Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.ext | [] | [
698,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_funUnique_symm | [] | [
2446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2445,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_and' | [] | [
1336,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.continuousOn_extend | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_2\nM : Type u_1\nH : Type u_4\nE' : Type ?u.135524\nM' : Type ?u.135527\nH' : Type ?u.135530\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\nf f' : LocalHomeomorp... | [
829,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
826,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | Matrix.toBilin'_apply' | [
{
"state_after": "R : Type ?u.258308\nM✝ : Type ?u.258311\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M✝\ninst✝¹⁶ : Module R M✝\nR₁ : Type ?u.258347\nM₁ : Type ?u.258350\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type u_2\nM₂ : Type ?u.258962\ninst✝¹² : CommSemiring R₂\ninst✝... | [
181,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_le | [] | [
476,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Topology/Algebra/Order/Field.lean | Filter.Tendsto.atTop_mul | [
{
"state_after": "𝕜 : Type u_1\nα : Type u_2\ninst✝² : LinearOrderedField 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l atTop\nhg : Tendsto g l (𝓝 C)\n⊢ (fun x => f x * (C / 2)) ≤ᶠ[l] fun x => f x * g x",
"state_before": "𝕜 : ... | [
68,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.card_le_card_of_forall_subsingleton' | [] | [
129,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_zero | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.monomial_mem_lifts_and_degree_eq | [
{
"state_after": "case pos\nR : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring S\nf : R →+* S\ns : S\nn : ℕ\nhl : ↑(monomial n) s ∈ lifts f\nhzero : s = 0\n⊢ ∃ q, map f q = ↑(monomial n) s ∧ degree q = degree (↑(monomial n) s)\n\ncase neg\nR : Type u\ninst✝¹ : Semiring R\nS : Type v\ninst✝ : Semiring... | [
165,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Memℒp.toLp_add | [] | [
141,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | measurableSet_iSup_of_mem_piiUnionInter | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nι : Type u_2\nm : ι → MeasurableSpace α\nS : Set ι\npt : Finset ι\nhpt : ↑pt ⊆ S\nft : ι → Set α\nht_m : ∀ (x : ι), x ∈ pt → ft x ∈ (fun n => {s | MeasurableSet s}) x\n⊢ MeasurableSet (⋂ (x : ι) (_ : x ∈ pt), ft x)",
"state_before": "α : Type u_1... | [
513,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.pow_pred_clog_lt_self | [
{
"state_after": "b : ℕ\nhb : 1 < b\nx : ℕ\nhx : 1 < x\n⊢ pred (clog b x) < clog b x",
"state_before": "b : ℕ\nhb : 1 < b\nx : ℕ\nhx : 1 < x\n⊢ b ^ pred (clog b x) < x",
"tactic": "rw [← not_le, le_pow_iff_clog_le hb, not_le]"
},
{
"state_after": "no goals",
"state_before": "b : ℕ\nhb : 1 < ... | [
326,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_bound | [
{
"state_after": "case inl\n𝕜 : Type ?u.342431\nE : Type u_1\nF : Type ?u.342437\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\na C x : ℝ\nn : ℕ\nhab : a ≤ a\nhf : ContDiffOn ℝ (↑n + 1) f (Icc a a)\nhx : x ∈ Icc a a\nhC : ∀ (y : ℝ), y ∈ Icc a a → ‖iteratedDerivWithin (n + 1) f (Icc a a) y‖... | [
369,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.uniformContinuous | [] | [
1153,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1150,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.bind_toFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.516416\ninst✝¹ : DecidableEq β\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : α → Finset β\ninst✝ : DecidableEq α\ns : Multiset α\nt : α → Multiset β\nx : β\n⊢ x ∈ toFinset (Multiset.bind s t) ↔ x ∈ Finset.biUnion (toFinset s) fun a => ... | [
3603,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3601,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | IsOpen.smul | [] | [
256,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_eq_top_of_nonneg | [
{
"state_after": "x : ℝ≥0∞\ny : ℝ\nhy0 : 0 ≤ y\n⊢ x = 0 ∧ y < 0 ∨ x = ⊤ ∧ 0 < y → x = ⊤",
"state_before": "x : ℝ≥0∞\ny : ℝ\nhy0 : 0 ≤ y\n⊢ x ^ y = ⊤ → x = ⊤",
"tactic": "rw [ENNReal.rpow_eq_top_iff]"
},
{
"state_after": "case inl\nx : ℝ≥0∞\ny : ℝ\nhy0 : 0 ≤ y\nh : x = 0 ∧ y < 0\n⊢ x = ⊤\n\ncase ... | [
419,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_inter_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.182312\ninst✝ : SemilatticeSup α\na b c : α\n⊢ Ico a b ∩ Ici c = Ico (a ⊔ c) b",
"tactic": "rw [← Ici_inter_Iio, ← Ici_inter_Iio, ← Ici_inter_Ici, inter_right_comm]"
}
] | [
1747,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1746,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.cardDistinctFactors_one | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.569000\n⊢ ↑ω 1 = 0",
"tactic": "simp [cardDistinctFactors]"
}
] | [
914,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
914,
1
] |
Mathlib/Order/BoundedOrder.lean | OrderDual.toDual_top | [] | [
310,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.mem_roots_sub_C' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np✝ q p : R[X]\na x : R\n⊢ x ∈ roots (p - ↑C a) ↔ p ≠ ↑C a ∧ eval x p = a",
"tactic": "rw [mem_roots', IsRoot.def, sub_ne_zero, eval_sub, sub_eq_zero, eval_C]"
}
] | [
637,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiable_fst | [] | [
187,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_empty | [] | [
99,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.image2_vsub | [] | [
601,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ne_zero_of_coeff_ne_zero | [] | [
131,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt | [
{
"state_after": "case hle\nι : Type ?u.20158965\n𝕜 : Type ?u.20158968\nE : Type ?u.20158971\nF : Type ?u.20158974\nA : Type ?u.20158977\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝ g✝ : ℝ → ℝ\na✝ b✝ : ℝ\nμ : MeasureTheory.Measure ℝ\nf g : ℝ → ℝ\na b : ℝ\nhab : a < b\nh... | [
1353,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_div' | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\np q : K[X]\nhq : q ≠ 0\n⊢ num (↑(algebraMap K[X] (RatFunc K)) p / ↑(algebraMap K[X] (RatFunc K)) q) =\n ↑C (leadingCoeff (q / gcd p q))⁻¹ * (p / gcd p q)",
"tactic": "rw [num, numDenom_div _ hq]"
}
] | [
1150,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1147,
9
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | UniformCauchySeqOnFilter.mono_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\np'' : Filter α\nhf : UniformCauchySeqOnFilter F p p'\nhp : p'' ≤ p'\nu : Set (β × β)\nhu : u ∈ 𝓤 β\nth... | [
487,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.HasImageMap.mk | [] | [
722,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | LipschitzWith.lipschitzWith_compLp | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.2832703\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : MeasureTheory.Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\ng✝ : E → F\nc : ℝ≥0\ninst✝ : Fac... | [
931,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Topology/Constructions.lean | isOpen_sum_iff | [] | [
893,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
892,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_empty_type | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.1411198\nR : Type ?u.1411201\nK : Type u_3\nA : Type u_2\nA' : Type ?u.1411210\nA'' : Type ?u.1411213\nV : Type u\nV' : Type ?u.1411218\nx : ι → A\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing A'\ninst✝⁷ : CommRing A''\ninst✝⁶ : Algebra R A\ninst✝⁵ : ... | [
570,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.essentiallySmallSelf | [] | [
87,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.factorial_mul_pow_le_factorial | [
{
"state_after": "no goals",
"state_before": "m✝ n m : ℕ\n⊢ m ! * succ m ^ 0 ≤ (m + 0)!",
"tactic": "simp"
},
{
"state_after": "m✝ n✝ m n : ℕ\n⊢ m ! * succ m ^ n * succ m ≤ (m + n)! * (m + n + 1)",
"state_before": "m✝ n✝ m n : ℕ\n⊢ m ! * succ m ^ (n + 1) ≤ (m + (n + 1))!",
"tactic": "rw ... | [
103,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Computability/Reduce.lean | equivalence_of_oneOneEquiv | [] | [
201,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Order/Antisymmetrization.lean | OrderIso.dualAntisymmetrization_apply | [] | [
264,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.eval₂Hom_eq_constantCoeff_of_vars | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.482825\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np✝ q : MvPolynomial σ R\ninst✝ : CommSemiring S\nf : R →+* S\ng : σ → S\np : MvPolynomial σ R\nhp : ∀ (i : σ), i ∈ vars p → g i = 0\n⊢ ↑(eval₂Hom f g) (∑ v in support p, ↑(mono... | [
833,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_bot | [] | [
190,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.one_le_cosh | [
{
"state_after": "no goals",
"state_before": "x✝ y z x : ℝ\n⊢ abs 0 ≤ abs x",
"tactic": "simp only [_root_.abs_zero, _root_.abs_nonneg]"
}
] | [
741,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_sub_Ioi | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\nthis : ∀ (a_1 : Set α), ((fun x => a + x) ∘ fun x => -x) '' a_1 = (fun x => a + x) '' ((fun x => -x) '' a_1)\n⊢ (fun x => a - x) '' Ioi b = Iio (a - b)",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun ... | [
335,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.gc_map_comap | [] | [
662,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/Analysis/MeanInequalities.lean | Real.rpow_sum_le_const_mul_sum_rpow | [
{
"state_after": "ι : Type u\ns : Finset ι\nf g : ι → ℝ\np q : ℝ\nhp : 1 ≤ p\nthis :\n ↑((∑ i in s, (fun i => { val := abs (f i), property := (_ : 0 ≤ abs (f i)) }) i) ^ p) ≤\n ↑(↑(card s) ^ (p - 1) * ∑ i in s, (fun i => { val := abs (f i), property := (_ : 0 ≤ abs (f i)) }) i ^ p)\n⊢ (∑ i in s, abs (f i)) ... | [
575,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_injective | [
{
"state_after": "α : Type u\nβ : Type v\nf : α → β\nh : Injective (image f)\nx x' : α\nhx : f x = f x'\n⊢ x = x'",
"state_before": "α : Type u\nβ : Type v\nf : α → β\n⊢ Injective (image f) ↔ Injective f",
"tactic": "refine' ⟨fun h x x' hx => _, Injective.image_injective⟩"
},
{
"state_after": "α... | [
1559,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_apply_self | [] | [
1037,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Convex.centerMass_mem | [
{
"state_after": "case empty\nR : Type u_1\nE : Type u_2\nF : Type ?u.81064\nι : Type u_3\nι' : Type ?u.81070\nα : Type ?u.81073\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ninst✝¹ : Module R α\n... | [
176,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | Monotone.covariant_of_const | [] | [
262,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.sum_elim | [] | [
871,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Data/PFun.lean | PFun.core_inter | [] | [
484,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_C_mul_eq_of_mul_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\nai : R\nau : ai * a = 1\n⊢ natDegree p = natDegree (1 * p)",
"tactic": "nth_rw 1 [← one_mul p]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\nS... | [
120,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/Maps.lean | QuotientMap.isOpen_preimage | [] | [
326,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
11
] |
Mathlib/Algebra/Module/Equiv.lean | AddEquiv.toIntLinearEquiv_refl | [] | [
875,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
1
] |
Mathlib/Topology/Algebra/Module/LocallyConvex.lean | locallyConvexSpace_iff_exists_convex_subset_zero | [] | [
103,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_eq_coe | [] | [
711,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Data/Complex/Exponential.lean | abv_sum_le_sum_abv | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\ninst✝² : LinearOrderedField α\nabv : β → α\ninst✝¹ : Semiring β\ninst✝ : IsAbsoluteValue abv\nγ : Type u_1\nf : γ → β\ns : Finset γ\nthis : DecidableEq γ\n⊢ abv (∑ k in ∅, f k) ≤ ∑ k in ∅, abv (f k)",
"tactic": "simp [abv_zero abv... | [
233,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/ContinuousFunction/Basic.lean | ContinuousMap.liftCover_coe' | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.64319\nδ : Type ?u.64322\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf g : C(α, β)\nι : Type ?u.64355\nS : ι → Set α\nφ : (i : ι) → C(↑(S i), β)\nhφ :\n ∀ (i j : ι) (x : α) (hxi : x... | [
444,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant | [
{
"state_after": "G : Type u_1\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableMul₂ G\nμ ν : Measure G\ninst✝³ : SigmaFinite ν\ninst✝² : SigmaFinite μ\ns : Set G\ninst✝¹ : MeasurableInv G\ninst✝ : IsMulRightInvariant μ\n⊢ QuasiMeasurePreserving Inv.inv",
"state_before": "G : Type u_1\ninst... | [
445,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | map_extChartAt_symm_nhdsWithin_range | [] | [
1200,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1198,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | LinearOrderedField.smul_Icc | [
{
"state_after": "case h\nα : Type ?u.54531\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\nx : K\n⊢ x ∈ r • Icc a b ↔ x ∈ Icc (r • a) (r • b)",
"state_before": "α : Type ?u.54531\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\n⊢ r • Icc a b = Icc (r • a) (r • b)",
... | [
213,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.le_maximalIdeal | [
{
"state_after": "case intro.intro\nR : Type u\nS : Type v\nT : Type w\nK : Type u'\ninst✝¹ : CommSemiring R\ninst✝ : LocalRing R\nJ : Ideal R\nhJ : J ≠ ⊤\nM : Ideal R\nhM1 : Ideal.IsMaximal M\nhM2 : J ≤ M\n⊢ J ≤ maximalIdeal R",
"state_before": "R : Type u\nS : Type v\nT : Type w\nK : Type u'\ninst✝¹ : Com... | [
141,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.map_bot | [] | [
534,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/Logic/Basic.lean | exists_true_left | [] | [
908,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
9
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.coeNat_injective | [] | [
85,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.π_app_right | [] | [
535,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
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