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/BigOperators/Basic.lean | Finset.prod_range_succ | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.432982\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : CommMonoid β\nf : ℕ → β\nn : ℕ\n⊢ ∏ x in range (n + 1), f x = (∏ x in range n, f x) * f n",
"tactic": "simp only [mul_comm, prod_range_succ_comm]"
}
] | [
1220,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/Basic.lean | MulEquiv.inv_symm | [] | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.EventuallyEq.prod_mk | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.185063\nι : Sort x\nl : Filter α\nf f' : α → β\nhf : f =ᶠ[l] f'\ng g' : α → γ\nhg : g =ᶠ[l] g'\nx✝ : α\na✝¹ : g x✝ = g' x✝\na✝ : f x✝ = f' x✝\n⊢ (fun x => (f x, g x)) x✝ = (fun x => (f' x, g' x)) x✝",
"state_before": "α : Type u\nβ : Type v\n... | [
1503,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1498,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.root_left_of_root_gcd | [
{
"state_after": "case intro\nR : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : Field R\np✝ q : R[X]\ninst✝ : CommSemiring k\nϕ : R →+* k\nf g : R[X]\nα : k\nhα : eval₂ ϕ α (EuclideanDomain.gcd f g) = 0\np : R[X]\nhp : f = EuclideanDomain.gcd f g * p\n⊢ eval₂ ϕ α f = 0",
"state_before... | [
340,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.ne_not | [] | [
220,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/RingTheory/Nilpotent.lean | isRadical_iff_pow_one_lt | [] | [
131,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_lift'_same_eq_lift' | [] | [
370,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.mapQ_id | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.284528\nM : Type ?u.284531\nr : R\nx y : M\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\np p' : Submodule R M\nR₂ : Type ?u.285544\nM₂ : Type ?u.285547\ninst✝² : Ring R₂\ninst✝¹ : AddCommGroup M₂\ninst✝ : Module R₂ M₂\nτ₁₂ : R →+* R... | [
445,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Finmap.lean | Finmap.Disjoint.symm_iff | [] | [
664,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Subtype.lean | Subtype.ext_iff_val | [] | [
94,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.85521\ninst✝¹ : DecidableEq β\nf✝ g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\ninst✝ : DecidableEq α\nf : α → β\ns₁ s₂ : Finset α\nx✝ : β\n⊢ x✝ ∈ image f (s₁ ∪ s₂) ↔ x✝ ∈ image f s₁ ∪ image f s₂",
"tactic": "... | [
477,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.continuous_setToFun | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1555022\nG : Type ?u.1555025\n𝕜 : Type ?u.1555028\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ℝ F'\ninst... | [
1514,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1512,
1
] |
Mathlib/Topology/Algebra/UniformRing.lean | UniformSpace.ring_sep_quot | [
{
"state_after": "α✝ : Type ?u.323008\nα : Type u\nr : CommRing α\ninst✝² : UniformSpace α\ninst✝¹ : UniformAddGroup α\ninst✝ : TopologicalRing α\n⊢ Quotient (Submodule.quotientRel (Ideal.closure ⊥)) = (α ⧸ Ideal.closure ⊥)",
"state_before": "α✝ : Type ?u.323008\nα : Type u\nr : CommRing α\ninst✝² : Uniform... | [
251,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/LinearAlgebra/Ray.lean | sameRay_neg_smul_left_iff | [] | [
569,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.AEStronglyMeasurable.fst | [] | [
190,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_mul_le_sum_mul_comp_perm | [] | [
405,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.fg_iff_monoid_fg | [] | [
324,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Data/ENat/Basic.lean | ENat.coe_one | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_eq_tsum_rpow | [
{
"state_after": "α : Type u_1\nE : α → Type u_2\np q : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < ENNReal.toReal p\nf : { x // x ∈ lp E p }\n⊢ (if hp : p = 0 then\n Eq.rec (motive := fun x x_1 => { x_2 // x_2 ∈ lp E x } → ℝ)\n (fun f => ↑(Finset.card (Set.Finite.toFinset (_ : Set.Fi... | [
413,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | summable_of_absolute_convergence_real | [
{
"state_after": "case refine'_1\nα : Type ?u.192\nβ : Type ?u.195\nι : Type ?u.198\nf : ℕ → ℝ\nr : ℝ\nhr : Tendsto (fun n => ∑ i in Finset.range n, abs (f i)) atTop (𝓝 r)\n⊢ ∀ (i : ℕ), 0 ≤ ‖f i‖\n\ncase refine'_2\nα : Type ?u.192\nβ : Type ?u.195\nι : Type ?u.198\nf : ℕ → ℝ\nr : ℝ\nhr : Tendsto (fun n => ∑ i ... | [
43,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
src/lean/Init/Data/Array/DecidableEq.lean | Array.isEqv_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : Array α\n⊢ (isEqv a a fun x y => decide (x = y)) = true",
"tactic": "simp [isEqv, isEqvAux_self]"
}
] | [
42,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
41,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.restrict_eq_domRestrict_codRestrict | [] | [
255,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.ker_liftQ | [] | [
473,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.PositiveCompacts.carrier_eq_coe | [] | [
361,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast_map | [
{
"state_after": "case nil\nι : Type ?u.138776\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → β\nl : List α\nhl✝ : l ≠ []\nhl : [] ≠ []\n⊢ getLast (map f []) (_ : ¬map f [] = []) = f (getLast [] hl)\n\ncase cons\nι : Type ?u.138776\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂... | [
1875,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1869,
1
] |
Mathlib/Algebra/Order/Archimedean.lean | le_of_forall_lt_rat_imp_le | [] | [
293,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.sub_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\nx✝ : a₁ ≡ b₁ [PMOD p]\nm : ℤ\nhm : b₁ - a₁ = m • p\n⊢ (∃ b, b₁ - b₂ - (a₁ - a₂) = ↑(Equiv.subLeft m).symm.symm b • p) ↔ a₂ ≡ b₂ [PMOD p]",
"tactic": "simp [sub_sub_sub_comm, hm, sub... | [
204,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
11
] |
Mathlib/Data/Nat/Log.lean | Nat.log_one_left | [] | [
82,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.conj_I | [
{
"state_after": "no goals",
"state_before": "⊢ (↑(starRingEnd ℂ) I).re = (-I).re ∧ (↑(starRingEnd ℂ) I).im = (-I).im",
"tactic": "simp"
}
] | [
522,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.quasiMeasurePreserving_mul_left | [
{
"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\ng : G\nthis : QuasiMeasurePreserving fun h => h * g⁻¹\n⊢ QuasiMeasurePrese... | [
511,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesAt.neg | [] | [
567,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Std/Data/List/Init/Lemmas.lean | List.any_nil | [] | [
34,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
34,
9
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.maximalSubfieldWithHom_eq_top | [
{
"state_after": "k : Type u\ninst✝⁶ : Field k\nK : Type u\nL : Type v\nM : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : Field M\ninst✝¹ : Algebra K M\ninst✝ : IsAlgClosed M\nhL : Algebra.IsAlgebraic K L\nE₁ E₂ E₃ : SubfieldWithHom K L M\n⊢ ⊤ ≤ (maximalSubfieldWithHom K L M).carrie... | [
337,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.ofDual_sup' | [] | [
1070,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1068,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.not_lt_zero | [] | [
409,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
11
] |
Mathlib/Data/Nat/Interval.lean | Nat.Ico_zero_eq_range | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Ico 0 = range",
"tactic": "rw [← bot_eq_zero, ← Iio_eq_Ico, Iio_eq_range]"
}
] | [
89,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.chaar_mem_clPrehaar | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nV : OpenNhdsOf 1\nthis :\n Classical.choose (_ : Set.Nonempty (haarProduct ↑K₀ ∩ ⋂ (V : OpenNhdsOf 1), clPrehaar (↑K₀) V)) ∈\n ⋂ (V : OpenNhdsOf 1), clPrehaar (↑K₀) V\n⊢ chaar ... | [
423,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/List/Rdrop.lean | List.rdropWhile_concat | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\n⊢ reverse\n (match p x with\n | true => dropWhile p (reverse l)\n | false => x :: reverse l) =\n if p x = true then reverse (dropWhile p (reverse l)) else l ++ [x]",
"state_before": "α : Type u_1\np : α → Bool\nl : Lis... | [
110,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.think_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nc : Computation α\nf : α → Computation β\n⊢ destruct (bind (think c) f) = Sum.inr (bind c f)",
"tactic": "simp [bind, Bind.f]"
}
] | [
744,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
743,
1
] |
Mathlib/Algebra/Module/Basic.lean | AddMonoid.End.nat_cast_def | [] | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.numeratorHom_apply | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Equiv.realize_boundedFormula | [
{
"state_after": "case falsum\nL : Language\nL' : Language\nM : Type w\nN : Type u_1\nP : Type ?u.650244\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\ng : M ≃[L] N\nv : α → M\nxs✝ : Fin n → M\nn✝ : ℕ\nxs : Fin n✝ → M\n⊢ BoundedFormula.Real... | [
967,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
950,
1
] |
Mathlib/Algebra/RingQuot.lean | RingQuot.liftAlgHom_unique | [
{
"state_after": "case w.H\nR : Type u₁\ninst✝⁶ : Semiring R\nS : Type u₂\ninst✝⁵ : CommSemiring S\nA : Type u₃\ninst✝⁴ : Semiring A\ninst✝³ : Algebra S A\nr : R → R → Prop\nT : Type u₄\ninst✝² : Semiring T\nB : Type u₄\ninst✝¹ : Semiring B\ninst✝ : Algebra S B\nf : A →ₐ[S] B\ns : A → A → Prop\nw : ∀ ⦃x y : A⦄,... | [
677,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.mul_left | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nht : IsUpperSet t\n⊢ IsUpperSet (⋃ (a : α) (_ : a ∈ s), a • t)",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nht : IsUpperSet t\n⊢ IsUpperSet (s * t)",
"tactic": "rw [← smul_eq_mul, ← Set.iU... | [
70,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sSup_eq_bsup | [
{
"state_after": "case e_a\nα : Type ?u.307782\nβ : Type ?u.307785\nγ : Type ?u.307788\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\n⊢ brange o f = range (familyOfBFamily o f)",
"state_before": "α : Type ?u.307782\nβ : Type ?u.307785\nγ : Type ?u.30... | [
1459,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1456,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.mem_support | [] | [
202,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.nonempty_def | [] | [
750,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Topology/Order/Basic.lean | continuousWithinAt_Ico_iff_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderClosedTopology α\na✝ b✝ : α\ninst✝ : TopologicalSpace γ\na b : α\nf : α → γ\nh : a < b\n⊢ ContinuousWithinAt f (Ico a b) b ↔ ContinuousWithinAt f (Iio b) b",
... | [
506,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Topology/Algebra/UniformField.lean | UniformSpace.Completion.mul_hatInv_cancel | [
{
"state_after": "K : Type u_1\ninst✝⁴ : Field K\ninst✝³ : UniformSpace K\ninst✝² : TopologicalDivisionRing K\ninst✝¹ : CompletableTopField K\ninst✝ : UniformAddGroup K\nx : hat K\nx_ne : x ≠ 0\nthis : T1Space (hat K)\n⊢ x * hatInv x = 1",
"state_before": "K : Type u_1\ninst✝⁴ : Field K\ninst✝³ : UniformSpa... | [
157,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wSameSide_iff_exists_right | [
{
"state_after": "R : Type u_1\nV : Type u_2\nV' : Type ?u.242614\nP : Type u_3\nP' : Type ?u.242620\ninst✝⁶ : LinearOrderedField R\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P'\ns : AffineSubspace R P\nx y p₂ : P\n... | [
460,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Analysis/Convex/Basic.lean | Monotone.convex_le | [] | [
381,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_left_of_ge | [] | [
785,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.bounds_bddBelow | [] | [
157,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isBoundedUnder_le_sup | [] | [
291,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.AEEqFun.integrable_iff_mem_L1 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1265765\nδ : Type ?u.1265768\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α →ₘ[μ] β\n⊢ Integrable f ↔ f ∈ Lp β 1",
"tactic": "rw ... | [
1238,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1237,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | abs_real_inner_div_norm_mul_norm_eq_one_iff | [] | [
1650,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1648,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.get_append_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ni : Nat\nas bs : List α\nh : i < length as\nh' : i < length (as ++ bs)\n⊢ get (as ++ bs) { val := i, isLt := h' } = get as { val := i, isLt := h }",
"tactic": "induction as generalizing i with\n| nil => trivial\n| cons a as ih =>\n cases i wit... | [
100,
25
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
94,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_map_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.29641\nf : α → β\np : Pmf α\nb : β\n⊢ b ∈ support (map f p) ↔ ∃ a, a ∈ support p ∧ f a = b",
"tactic": "simp"
}
] | [
61,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.degree_le | [
{
"state_after": "ι : Sort ?u.200951\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\nG' : Subgraph G\nv : V\ninst✝¹ : Fintype ↑(neighborSet G' v)\ninst✝ : Fintype ↑(SimpleGraph.neighborSet G v)\n⊢ degree G' v ≤ Fintype.card ↑(SimpleGraph.neighborSet G v)",
"state_before": "ι : Sort ... | [
810,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_self'' | [] | [
398,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Tactic/Abel.lean | Mathlib.Tactic.Abel.term_add_term | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommMonoid α\nn₁ : ℕ\nx a₁ : α\nn₂ : ℕ\na₂ : α\nn' : ℕ\na' : α\nh₁ : n₁ + n₂ = n'\nh₂ : a₁ + a₂ = a'\n⊢ term n₁ x a₁ + term n₂ x a₂ = term n' x a'",
"tactic": "simp [h₁.symm, h₂.symm, term, add_nsmul, add_assoc, add_left_comm]"
}
] | [
144,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.coe_restrictScalars | [] | [
700,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.erase_single | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.165062\nγ : Type ?u.165065\nι : Type ?u.165068\nM : Type u_2\nM' : Type ?u.165074\nN : Type ?u.165077\nP : Type ?u.165080\nG : Type ?u.165083\nH : Type ?u.165086\nR : Type ?u.165089\nS : Type ?u.165092\ninst✝ : Zero M\na : α\nb : M\ns : α\n⊢ ↑(erase a (single ... | [
658,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | EMetric.measure_ball_pos | [] | [
203,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.mem_thickening_iff | [
{
"state_after": "ι : Sort ?u.94466\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\nδ : ℝ\ns : Set α\nx✝ : α\nX : Type u\ninst✝ : PseudoMetricSpace X\nE : Set X\nx : X\nkey_iff : ∀ (z : X), edist x z < ENNReal.ofReal δ ↔ dist x z < δ\n⊢ x ∈ thickening δ E ↔ ∃ z, z ∈ E ∧ dist x z < δ",
"state_before"... | [
980,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.div_coe | [
{
"state_after": "m k : ℕ+\n⊢ (modDivAux k (↑m % ↑k) (↑m / ↑k)).snd = if ↑m % ↑k = 0 then pred (↑m / ↑k) else ↑m / ↑k",
"state_before": "m k : ℕ+\n⊢ div m k = if ↑m % ↑k = 0 then pred (↑m / ↑k) else ↑m / ↑k",
"tactic": "dsimp [div, modDiv]"
},
{
"state_after": "no goals",
"state_before": "m ... | [
274,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.ne_zero | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.2164084\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_3\ndec_ι : DecidableEq ι\nv : ι → E\nhv : Orthonormal 𝕜 v\ni : ... | [
975,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_neg | [] | [
148,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/CategoryTheory/Limits/Lattice.lean | CategoryTheory.Limits.CompleteLattice.colimit_eq_iSup | [] | [
231,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.abs_edgeDensity_sub_edgeDensity_le_two_mul_sub_sq | [
{
"state_after": "𝕜 : Type u_3\nι : Type ?u.39508\nκ : Type ?u.39511\nα : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrderedField 𝕜\nr : α → β → Prop\ninst✝ : (a : α) → DecidablePred (r a)\ns s₁ s₂ : Finset α\nt t₁ t₂ : Finset β\na : α\nb : β\nδ : 𝕜\nhs : s₂ ⊆ s₁\nht : t₂ ⊆ t₁\nhδ₀ : 0 ≤ δ\nhδ₁ : δ < 1\nhs₂ : (1... | [
245,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Computability/Ackermann.lean | ack_mono_right | [] | [
151,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.not_le_of_lt | [] | [
380,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
380,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.sum_mem | [] | [
170,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.coe_toOrthonormalBasis | [] | [
525,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.toRingHom_toRatAlgHom | [] | [
533,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
531,
1
] |
Mathlib/CategoryTheory/Limits/ConcreteCategory.lean | CategoryTheory.Limits.Concrete.limit_ext | [] | [
60,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Set.Finite.toFinset_vsub | [] | [
2271,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2269,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | Real.contDiffAt_rpow_const | [] | [
394,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_eq_neg_floor | [
{
"state_after": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\np : α\nhp : 0 < p\na b : α\n⊢ b - -⌊(a + p - b) / p⌋ • p ∈ Set.Ioc a (a + p)",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\np : α\nhp : 0 < p\na b : α\n⊢ toIocDiv hp a b = -⌊(a + p - b) ... | [
1011,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_sum | [] | [
234,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isPrimitiveClassified_of_coprime_of_odd_of_pos | [
{
"state_after": "case pos\nx y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhyo : y % 2 = 1\nhzpos : 0 < z\nh0 : x = 0\n⊢ IsPrimitiveClassified h\n\ncase neg\nx y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhyo : y % 2 = 1\nhzpos : 0 < z\nh0 : ¬x = 0\n⊢ IsPrimitiveClassified h",
... | [
560,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Std/Data/Array/Lemmas.lean | Array.get?_set_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\ni : Fin (size a)\nj : Nat\nv : α\nh : i.val ≠ j\n⊢ (set a i v)[j]? = a[j]?",
"tactic": "by_cases j < a.size <;> simp [getElem?_pos, getElem?_neg, *]"
}
] | [
100,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
98,
9
] |
Mathlib/Order/Hom/Lattice.lean | SupBotHom.copy_eq | [] | [
761,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.matches'_map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.138072\ndec : DecidableEq α\na✝ b : α\nf : α → β\na : α\n⊢ ↑(Language.map f) (matches' (char a)) = matches' (map f (char a))",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.138072\ndec : DecidableEq α\na✝ b : α\nf : α → β\na : α\n⊢ matches... | [
461,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Certificate.of_combineHyps | [
{
"state_after": "no goals",
"state_before": "ctx : Context\nc : PolyCnstr\ncs : Certificate\nh : PolyCnstr.denote ctx (combineHyps c cs) → False\n⊢ PolyCnstr.denote ctx c → denote ctx cs",
"tactic": "match cs with\n| [] => simp [combineHyps, denote] at *; exact h\n| (k, c')::cs =>\n intro h₁ h₂\n hav... | [
680,
20
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
671,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_eq_iInter_cthickening' | [
{
"state_after": "case pos\nι : Sort ?u.143633\nα : Type u\nβ : Type v\ninst✝ : PseudoEMetricSpace α\nδ ε : ℝ\ns✝ t : Set α\nx : α\nE : Set α\ns : Set ℝ\nhs : ∀ (ε : ℝ), 0 < ε → Set.Nonempty (s ∩ Ioc 0 ε)\nhs₀ : s ⊆ Ioi 0\n⊢ closure E = ⋂ (δ : ℝ) (_ : δ ∈ s), cthickening δ E\n\ncase neg\nι : Sort ?u.143633\nα :... | [
1356,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1346,
1
] |
Mathlib/RingTheory/Valuation/Basic.lean | AddValuation.IsEquiv.trans | [] | [
838,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Algebra/Associated.lean | eq_of_prime_pow_eq' | [
{
"state_after": "α : Type ?u.254209\nβ : Type ?u.254212\nγ : Type ?u.254215\nδ : Type ?u.254218\nR : Type u_1\ninst✝¹ : CancelCommMonoidWithZero R\ninst✝ : Unique Rˣ\np₁ p₂ : R\nk₁ k₂ : ℕ\nhp₁ : Prime p₁\nhp₂ : Prime p₂\nhk₁ : 0 < k₂\nh✝ : p₁ ^ k₁ = p₂ ^ k₂\nh : p₁ ^ k₁ ~ᵤ p₂ ^ k₂\n⊢ p₁ ~ᵤ p₂",
"state_befo... | [
725,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Order/WellFoundedSet.lean | Finset.isWf_sup | [] | [
577,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.mapRange_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.376063\nγ : Type ?u.376066\nι : Type ?u.376069\nM : Type u_2\nM' : Type ?u.376075\nN : Type u_1\nP : Type ?u.376081\nG : Type ?u.376084\nH : Type ?u.376087\nR : Type ?u.376090\nS : Type ?u.376093\ninst✝¹ : AddZeroClass M\ninst✝ : AddZer... | [
1172,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1169,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.isIso_left_of_isIso_biprod_map | [
{
"state_after": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasBinaryBiproducts C\nW X Y Z : C\nf : W ⟶ Y\ng : X ⟶ Z\ninst✝ : IsIso (biprod.map f g)\nt :\n (fun p => biprod.inl ≫ p ≫ biprod.fst) (biprod.map f g ≫ inv (biprod.map f g)) =\n (fun p => biprod.inl ≫ p ≫ biprod.fst) (... | [
1894,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1882,
1
] |
Mathlib/CategoryTheory/Preadditive/Schur.lean | CategoryTheory.mono_of_nonzero_from_simple | [] | [
41,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.isUnit_or_isUnit_one_sub_self | [] | [
173,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Order/WellFoundedSet.lean | WellFounded.isWf | [] | [
787,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
786,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Ultrafilter.le_cofinite_or_eq_pure | [] | [
333,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Set/Prod.lean | Set.Nonempty.prod | [] | [
311,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.range_add_one' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.55329\nβ : Type ?u.55332\nγ : Type ?u.55335\nn i j : ℕ\n⊢ (fun i => i + 1) i = (fun i => i + 1) j → i = j",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.55329\nβ : Type ?u.55332\nγ : Type ?u.55335\nn :... | [
299,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_neg_one | [
{
"state_after": "no goals",
"state_before": "⊢ arccos (-1) = π",
"tactic": "simp [arccos, add_halves]"
}
] | [
391,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_mul_bot_of_pos | [] | [
945,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
944,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.closure_univ | [] | [
1047,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1046,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.