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/Order/Filter/Basic.lean | Filter.map_comap_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.257261\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm✝ : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : Filter β\nm : α → β\nhf : range m ∈ f\n⊢ map m (comap m f) = f",
"tactic": "rw [map_comap, inf_eq_l... | [
2260,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2259,
1
] |
Std/Data/Int/DivMod.lean | Int.natAbs_div | [
{
"state_after": "a b : Int\nw✝¹ w✝ : Nat\n⊢ natAbs (div ↑w✝¹ ↑w✝) = Nat.div (natAbs ↑w✝¹) (natAbs ↑w✝)",
"state_before": "a b : Int\nw✝¹ w✝ : Nat\n⊢ natAbs (div (↑w✝¹) (-↑w✝)) = Nat.div (natAbs ↑w✝¹) (natAbs (-↑w✝))",
"tactic": "rw [Int.div_neg, natAbs_neg, natAbs_neg]"
},
{
"state_after": "no ... | [
563,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
558,
9
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_mulVec_const_apply_of_regular | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.66478\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Fintype V\ninst✝ : Semiring α\nd : ℕ\na : α\nhd : IsRegularOfDegree G d\nv : V\n⊢ mulVec (adjMatrix α G) (Function.const V a) v = ↑d * a",
"tactic": "simp... | [
261,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
src/lean/Init/Core.lean | decide_false_eq_false | [] | [
700,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
697,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.srange_snd | [] | [
919,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.Prepartition.mem_biUnionTagged | [] | [
140,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Data/List/Pairwise.lean | List.pairwise_pair | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9008\nR S T : α → α → Prop\na✝ : α\nl : List α\na b : α\n⊢ Pairwise R [a, b] ↔ R a b",
"tactic": "simp only [pairwise_cons, mem_singleton, forall_eq, forall_prop_of_false (not_mem_nil _),\n forall_true_iff, Pairwise.nil, and_true_i... | [
161,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.muld_val | [
{
"state_after": "no goals",
"state_before": "d x y : ℤ\n⊢ sqrtd * { re := x, im := y } = { re := d * y, im := x }",
"tactic": "simp [ext]"
}
] | [
326,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.symm_trans_self | [] | [
505,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.comap_fst_neBot_iff | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.265787\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : Filter α\nh✝ : IsEmpty β\n⊢ NeBot (comap Prod.fst f) ↔ NeBot f ∧ Nonempty β\n\ncase inr\nα : Type u\nβ : Type v\nγ : Type w\nδ... | [
2379,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2375,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_eq_prod_factorization | [
{
"state_after": "n : ℕ\nhn : n ≠ 0\n⊢ (Finsupp.prod (factorization n) fun p k => φ (p ^ k)) =\n Finsupp.prod (factorization n) fun p k => p ^ (k - 1) * (p - 1)",
"state_before": "n : ℕ\nhn : n ≠ 0\n⊢ φ n = Finsupp.prod (factorization n) fun p k => p ^ (k - 1) * (p - 1)",
"tactic": "rw [multiplicativ... | [
292,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocDiv_add_zsmul' | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\nm : ℤ\n⊢ b - (toIocDiv hp a b - m) • p ∈ Set.Ioc (a + m • p) (a + m • p + p)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : ... | [
259,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.map_dvd_map' | [
{
"state_after": "no goals",
"state_before": "R : 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✝ : Field k\nf : R →+* k\nx y : R[X]\nH : x = 0\n⊢ map f x ∣ map f y ↔ x ∣ y",
"tactic": "rw [H, Polynomial.map_zero, zero_dvd_iff, zero_dvd_iff, map_eq_zero]"
... | [
470,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.mem_roots_map | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝² : Field R\np q : R[X]\ninst✝¹ : CommRing k\ninst✝ : IsDomain k\nf : R →+* k\nx : k\nhp : p ≠ 0\n⊢ x ∈ roots (map f p) ↔ eval₂ f x p = 0",
"tactic": "rw [mem_roots (map_ne_zero hp), IsRoot... | [
365,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Data/List/Basic.lean | List.zipLeft_cons_cons | [] | [
4193,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4192,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | map_restrict_ae_le_map_indicator_ae | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.4605823\nδ : Type ?u.4605826\nι : Type ?u.4605829\nR : Type ?u.4605832\nR' : Type ?u.4605835\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ns t✝ : Set α\nf : α → β\ninst✝ : Zero β\nhs : MeasurableSet s\nt : Set β\n⊢ t ∈ Filter.map (indicator s... | [
4658,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4651,
1
] |
Mathlib/MeasureTheory/Integral/Layercake.lean | MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul | [
{
"state_after": "α : Type u_1\ninst✝¹ : MeasurableSpace α\nf : α → ℝ\ng : ℝ → ℝ\ns : Set α\nμ : Measure α\ninst✝ : SigmaFinite μ\nf_nn : 0 ≤ f\nf_mble : Measurable f\np : ℝ\np_pos : 0 < p\none_lt_p : -1 < p - 1\n⊢ (∫⁻ (ω : α), ENNReal.ofReal (f ω ^ p) ∂μ) =\n ENNReal.ofReal p * ∫⁻ (t : ℝ) in Ioi 0, ↑↑μ {a |... | [
259,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Topology/Order.lean | isOpen_induced | [] | [
871,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
870,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.isPwo_union | [] | [
441,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.support_monomial | [
{
"state_after": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\na : R\nH : a ≠ 0\n⊢ (match { toFinsupp := Finsupp.single n a } with\n | { toFinsupp := p } => p.support) =\n {n}",
"state_before": "R : Type u\na✝ b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\na : R\nH :... | [
836,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
835,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.eval₂_reverse_mul_pow | [] | [
354,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.isOrtho_sSup_left | [] | [
356,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_adjoin_left | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS T : Set E\n⊢ ↑(restrictScalars F (adjoin { x // x ∈ adjoin F S } T)) = ↑(adjoin F (S ∪ T))",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS T : Se... | [
392,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.dropn_tail | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nn : ℕ\n⊢ drop (tail s) n = drop s (1 + n)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\nn : ℕ\n⊢ drop (tail s) n = drop s (n + 1)",
"tactic": "rw [add_comm]"
},
{
"state_after": "α : Type u\nβ : Type v\nγ : Ty... | [
743,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_eq | [] | [
84,
52
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
84,
9
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | affineSpan_induction | [] | [
1184,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_def | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_add_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ cos (x + π / 2) = -sin x",
"tactic": "simp [cos_add]"
}
] | [
454,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.hsum_sub | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_2\nR✝ : Type ?u.2750260\ninst✝² : OrderedCancelAddCommMonoid Γ\ninst✝¹ : Semiring R✝\nα : Type u_3\nR : Type u_1\ninst✝ : Ring R\ns t : SummableFamily Γ R α\n⊢ hsum (s - t) = hsum s - hsum t",
"tactic": "rw [← lsum_apply, LinearMap.map_sub, lsum_a... | [
1651,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1649,
1
] |
Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.subsingleton_of_semisimple_lie_abelian | [
{
"state_after": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\ninst✝ : IsSemisimple R L\nh : ⊥ = ⊤\n⊢ Subsingleton L",
"state_before": "R : Type u\nL : Type v\ninst✝³ : CommRing R\ninst✝² : LieRing L\ninst✝¹ : LieAlgebra R L\ninst✝ : IsSemisimple R L\nh : IsLieAb... | [
100,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_op_C | [] | [
50,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Set/Prod.lean | Set.eval_image_pi_subset | [] | [
799,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_add | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\nx : S\n⊢ (sum (p + q) fun e a => ↑f a * x ^ e) = (sum p fun e a => ↑f a * x ^ e) + sum q fun e a => ↑f a * x ^ e",
"state_before": "R : Type u\nS : Type v\n... | [
95,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_sub_lt_descFactorial' | [
{
"state_after": "n : ℕ\nh : 0 + 2 ≤ n\n⊢ (n - (0 + 1)) * (n - (0 + 1)) < (n - 1) * n",
"state_before": "n : ℕ\nh : 0 + 2 ≤ n\n⊢ (n - (0 + 1)) ^ (0 + 2) < descFactorial n (0 + 2)",
"tactic": "rw [descFactorial_succ, pow_succ, pow_one, descFactorial_one]"
},
{
"state_after": "no goals",
"stat... | [
457,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | EMetric.eventually_nhds_zero_forall_closedBall_subset | [
{
"state_after": "ι : Type u_2\nX : Type u_1\ninst✝ : EMetricSpace X\nK U : ι → Set X\nhK : ∀ (i : ι), IsClosed (K i)\nhU : ∀ (i : ι), IsOpen (U i)\nhKU : ∀ (i : ι), K i ⊆ U i\nhfin : LocallyFinite K\nx : X\n⊢ ∀ (i : ι), x ∈ K i → ∀ᶠ (p : ℝ≥0∞ × X) in 𝓝 0 ×ˢ 𝓝 x, closedBall p.snd p.fst ⊆ U i",
"state_befo... | [
63,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.inner_weightedVSub | [
{
"state_after": "V : Type u_3\nP : Type u_4\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nι₁ : Type u_1\ns₁ : Finset ι₁\nw₁ : ι₁ → ℝ\np₁ : ι₁ → P\nh₁ : ∑ i in s₁, w₁ i = 0\nι₂ : Type u_2\ns₂ : Finset ι₂\nw₂ : ι₂ → ℝ\np₂ : ι₂ → P\nh₂ : ∑ i i... | [
93,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/MvPolynomial/PDeriv.lean | MvPolynomial.pderiv_X | [
{
"state_after": "no goals",
"state_before": "R : Type u\nσ : Type v\na a' a₁ a₂ : R\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\ninst✝ : DecidableEq σ\ni j : σ\n⊢ ↑(pderiv i) (X j) = Pi.single i 1 j",
"tactic": "rw [pderiv_def, mkDerivation_X]"
}
] | [
96,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.comap_incl_eq_top | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ :... | [
762,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | IsLocalization.Away.mul_invSelf | [
{
"state_after": "case h.e'_2.h.e'_5\nR : Type u_2\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_1\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type ?u.3731\ninst✝¹ : CommSemiring P\nx : R\ninst✝ : Away x S\n⊢ ↑(algebraMap R S) x = mk' S (↑{ val := x, property := (_ : x ∈ Submonoid.powers x) }) 1... | [
65,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/FieldTheory/Normal.lean | Normal.of_algEquiv | [
{
"state_after": "case intro\nF : Type u_1\nK : Type ?u.73378\ninst✝¹¹ : Field F\ninst✝¹⁰ : Field K\ninst✝⁹ : Algebra F K\nE : Type u_2\ninst✝⁸ : Field E\ninst✝⁷ : Algebra F E\ninst✝⁶ : Algebra K E\ninst✝⁵ : IsScalarTower F K E\nE' : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Algebra F E\ninst✝¹ : F... | [
150,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.cast_toNat_of_lt_aleph0 | [
{
"state_after": "no goals",
"state_before": "α β : Type u\nc : Cardinal\nh : c < ℵ₀\n⊢ ↑(↑toNat c) = c",
"tactic": "rw [toNat_apply_of_lt_aleph0 h, ← Classical.choose_spec (lt_aleph0.1 h)]"
}
] | [
1686,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1685,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.adjunction_counit_app_self | [
{
"state_after": "no goals",
"state_before": "X : TopCat\nU : Opens ↑X\n⊢ (map (inclusion U) ⋙ IsOpenMap.functor (_ : IsOpenMap ((forget TopCat).map (inclusion U)))).obj U =\n (𝟭 (Opens ↑X)).obj U",
"tactic": "simp"
}
] | [
352,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_prime_pow | [
{
"state_after": "case intro\np : ℕ\nhp : Prime p\nm : ℕ\nhn : 0 < succ m\n⊢ φ (p ^ succ m) = p ^ (succ m - 1) * (p - 1)",
"state_before": "p : ℕ\nhp : Prime p\nn : ℕ\nhn : 0 < n\n⊢ φ (p ^ n) = p ^ (n - 1) * (p - 1)",
"tactic": "rcases exists_eq_succ_of_ne_zero (pos_iff_ne_zero.1 hn) with ⟨m, rfl⟩"
},... | [
225,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Topology/Basic.lean | IsClosed.interior_union_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns✝ s₁ s₂ t✝ : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\ns t : Set α\nh : IsClosed t\n⊢ interior (s ∪ t) ⊆ interior s ∪ t",
"tactic": "simpa only [union_comm _ t] using h.interior_union_left"
}
] | [
1385,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1383,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.inclusion_mk | [] | [
1057,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1055,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_left | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np1 p2 : P\n⊢ InnerProductGeometry.angle (p1 -ᵥ p1) (p2 -ᵥ p1) = π / 2",
"state_before": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V... | [
147,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/Constructions.lean | ContinuousAt.snd | [] | [
384,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_injective | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.9713\nδ : Type ?u.9716\ninst✝ : MeasurableSpace α\ng : α →ₛ β\ntoFun✝ : α → β\nmeasurableSet_fiber'✝ : ∀ (x : β), MeasurableSet (toFun✝ ⁻¹' {x})\nfinite_range'✝ : Set.Finite (range toFun✝)\nH : ↑{ toFun := toFun✝, measurableSet_fiber' := measura... | [
72,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_prod | [] | [
1099,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Topology/Basic.lean | isOpen_sUnion | [] | [
130,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.ne_zero | [] | [
133,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_toSubmonoid | [] | [
445,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.Nonempty.ne_empty | [] | [
570,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | algebraicIndependent_equiv | [] | [
187,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.isRegular_of_isLeftRegular_det | [
{
"state_after": "case left\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nhA : IsLeftRegular (det A)\n⊢ IsLeftRegular A\n\ncase right\nm : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\n... | [
470,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Std/Data/List/Lemmas.lean | List.erase_cons_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\nh : b ≠ a\n⊢ List.erase (b :: l) a = b :: List.erase l a",
"tactic": "simp only [erase_cons, if_neg h]"
}
] | [
1040,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1039,
9
] |
Mathlib/Algebra/Hom/Units.lean | MonoidHom.coe_toHomUnits | [] | [
208,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Order/Atoms.lean | IsAtom.Iic | [] | [
71,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.dom_denumerable | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.19256\nβ✝ : Type ?u.19259\nσ : Type ?u.19262\ninst✝⁴ : Primcodable α✝\ninst✝³ : Primcodable β✝\ninst✝² : Primcodable σ\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Denumerable α\ninst✝ : Primcodable β\nf : α → β\nh : Primrec f\nn : ℕ\n⊢ Nat.pred (encode (O... | [
233,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | HasDerivAt.exp | [] | [
230,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.fst_swap | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.Colimit.ι_map_apply | [] | [
322,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
1
] |
Mathlib/Computability/PartrecCode.lean | Nat.Partrec.Code.rec_prim' | [
{
"state_after": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nc : α → Code\nhc : Primrec c\nz : α → σ\nhz : Primrec z\ns : α → σ\nhs : Primrec s\nl : α → σ\nhl : Primrec l\nr : α → σ\nhr : Primrec r\npr : α → Code × Code × σ × σ → σ\nhpr : Primrec₂ pr\nco : α → Code × Code × σ × σ... | [
385,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_conj_eq' | [] | [
767,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_lt_rpow_of_exponent_lt | [
{
"state_after": "x y z : ℝ\nhx : 1 < x\nhyz : y < z\n⊢ exp (log x * y) < exp (log x * z)",
"state_before": "x y z : ℝ\nhx : 1 < x\nhyz : y < z\n⊢ x ^ y < x ^ z",
"tactic": "repeat' rw [rpow_def_of_pos (lt_trans zero_lt_one hx)]"
},
{
"state_after": "x y z : ℝ\nhx : 1 < x\nhyz : y < z\n⊢ log x *... | [
472,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventuallyEq_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.183630\nι : Sort x\ns : Set α\nl : Filter α\n⊢ s =ᶠ[l] univ ↔ s ∈ l",
"tactic": "simp [eventuallyEq_set]"
}
] | [
1455,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1454,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.ofLe_apply | [] | [
629,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Topology/NhdsSet.lean | principal_le_nhdsSet | [] | [
83,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/Sign.lean | SignType.pos_iff | [
{
"state_after": "no goals",
"state_before": "a : SignType\n⊢ 0 < a ↔ a = 1",
"tactic": "cases a <;> decide"
}
] | [
196,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_subtype | [
{
"state_after": "no goals",
"state_before": "ι : Type u'\nι' : Type ?u.197690\nR : Type u_2\nK : Type ?u.197696\nM : Type u_1\nM' : Type ?u.197702\nM'' : Type ?u.197705\nV : Type u\nV' : Type ?u.197710\nv : ι → M\ninst✝⁶ : Semiring R\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : AddCommMonoid M'\ninst✝³ : AddCommMon... | [
384,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.trans_toLinearEquiv | [
{
"state_after": "case h\nR₁ : Type u_1\nR₂ : Type u_2\nR₃ : Type u_5\ninst✝²⁴ : Semiring R₁\ninst✝²³ : Semiring R₂\ninst✝²² : Semiring R₃\nσ₁₂ : R₁ →+* R₂\nσ₂₁ : R₂ →+* R₁\ninst✝²¹ : RingHomInvPair σ₁₂ σ₂₁\ninst✝²⁰ : RingHomInvPair σ₂₁ σ₁₂\nσ₂₃ : R₂ →+* R₃\nσ₃₂ : R₃ →+* R₂\ninst✝¹⁹ : RingHomInvPair σ₂₃ σ₃₂\nin... | [
1988,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1985,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.comp_apply | [] | [
718,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_add | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Odd (m + n) ↔ (Odd m ↔ Even n)",
"tactic": "rw [odd_iff_not_even, even_add, not_iff, odd_iff_not_even]"
}
] | [
176,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_univ | [] | [
1556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
1
] |
Mathlib/Data/Nat/Interval.lean | Finset.range_image_pred_top_sub | [
{
"state_after": "case zero\na b c : ℕ\n⊢ image (fun j => zero - 1 - j) (range zero) = range zero\n\ncase succ\na b c n✝ : ℕ\n⊢ image (fun j => succ n✝ - 1 - j) (range (succ n✝)) = range (succ n✝)",
"state_before": "a b c n : ℕ\n⊢ image (fun j => n - 1 - j) (range n) = range n",
"tactic": "cases n"
},... | [
332,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.rCond_of_bRiemann_eq_false | [
{
"state_after": "no goals",
"state_before": "ι✝ : Type ?u.29939\ninst✝ : Fintype ι✝\nI J : Box ι✝\nc c₁ c₂ : ℝ≥0\nr✝ r₁ r₂ : (ι✝ → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I\nl✝ l₁ l₂ : IntegrationParams\nι : Type u_1\nl : IntegrationParams\nhl : l.bRiemann = false\nr : (ι → ℝ) → ↑(Set.Ioi 0)\n⊢ RCo... | [
351,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.neg_bind | [] | [
256,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.or_and_distrib_left | [
{
"state_after": "no goals",
"state_before": "a b c : Bool\n⊢ (a || b && c) = ((a || b) && (a || c))",
"tactic": "cases a <;> simp"
}
] | [
191,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_add | [] | [
169,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.exists_measurable_superset₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.15260\nγ : Type ?u.15263\nδ : Type ?u.15266\nι : Type ?u.15269\ninst✝ : MeasurableSpace α\nμ✝ μ₁ μ₂ : Measure α\ns✝ s₁ s₂ t : Set α\nμ ν : Measure α\ns : Set α\n⊢ ∃ t, s ⊆ t ∧ MeasurableSet t ∧ ↑↑μ t = ↑↑μ s ∧ ↑↑ν t = ↑↑ν s",
"tacti... | [
224,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | ball_eq_of_symmetry | [
{
"state_after": "case h\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.55168\ninst✝ : UniformSpace α\nV : Set (β × β)\nhV : SymmetricRel V\nx y : β\n⊢ y ∈ ball x V ↔ y ∈ {y | (y, x) ∈ V}",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.55168\ninst✝ : Unif... | [
661,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Order/Antisymmetrization.lean | toAntisymmetrization_lt_toAntisymmetrization_iff | [] | [
191,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/Cover.lean | wcovby_iff_le_and_eq_or_eq | [] | [
167,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.separatingLeft_congr_iff | [
{
"state_after": "case h.e'_15\nR : Type u_1\nR₁ : Type ?u.510521\nR₂ : Type ?u.510524\nR₃ : Type ?u.510527\nM : Type ?u.510530\nM₁ : Type ?u.510533\nM₂ : Type ?u.510536\nMₗ₁ : Type u_4\nMₗ₁' : Type u_2\nMₗ₂ : Type u_5\nMₗ₂' : Type u_3\nK : Type ?u.510551\nK₁ : Type ?u.510554\nK₂ : Type ?u.510557\nV : Type ?u.5... | [
667,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
661,
1
] |
Mathlib/Analysis/Calculus/Taylor.lean | continuousOn_taylorWithinEval | [
{
"state_after": "𝕜 : Type ?u.239708\nE : Type u_1\nF : Type ?u.239714\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx : ℝ\nn : ℕ\ns : Set ℝ\nhs : UniqueDiffOn ℝ s\nhf : ContDiffOn ℝ (↑n) f s\n⊢ ContinuousOn (fun t => ∑ k in Finset.range (n + 1), ((↑k !)⁻¹ * (x - t) ^ k) • iteratedDerivWi... | [
139,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/PathConnected.lean | PathConnectedSpace.exists_path_through_family' | [
{
"state_after": "X : Type u_1\nY : Type ?u.698693\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx y z : X\nι : Type ?u.698708\nF : Set X\ninst✝ : PathConnectedSpace X\nn : ℕ\np : Fin (n + 1) → X\nthis : IsPathConnected univ\n⊢ ∃ γ t, ∀ (i : Fin (n + 1)), ↑γ (t i) = p i",
"state_before": "X : T... | [
1183,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | Differentiable.continuous | [] | [
747,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.empty | [] | [
102,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.dvd_prime | [
{
"state_after": "p m : ℕ+\npp : Prime p\n⊢ ↑m ∣ ↑p ↔ m = 1 ∨ m = p",
"state_before": "p m : ℕ+\npp : Prime p\n⊢ m ∣ p ↔ m = 1 ∨ m = p",
"tactic": "rw [PNat.dvd_iff]"
},
{
"state_after": "p m : ℕ+\npp : Prime p\n⊢ ↑m = 1 ∨ ↑m = ↑p ↔ m = 1 ∨ m = p",
"state_before": "p m : ℕ+\npp : Prime p\n⊢ ... | [
132,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.degreeOf_sub_lt | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommRing R\np q : MvPolynomial σ R\nx : σ\nf g : MvPolynomial σ R\nk : ℕ\nh : 0 < k\nhf : ∀ (m : σ →₀ ℕ), m ∈ support f → k ≤ ↑m x → coeff m f = coeff m g\nhg : ∀ (m : σ →₀ ℕ), m ∈ support g → k ≤ ↑m x → ... | [
194,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_one | [] | [
121,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/List/Chain.lean | List.chain_iff_pairwise | [] | [
129,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/List/Cycle.lean | List.next_ne_head_ne_getLast | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.59864\ninst✝ : DecidableEq α\nl : List α\nx : α\nh✝ : x ∈ l\ny : α\nh : x ∈ y :: l\nhy : x ≠ y\nhx : x ≠ getLast (y :: l) (_ : y :: l ≠ [])\n⊢ x ∈ l",
"tactic": "simpa [hy] using h"
},
{
"state_after": "case x_mem\nα : Type u_1\ninst✝ : D... | [
173,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Order/Category/NonemptyFinLinOrdCat.lean | NonemptyFinLinOrdCat.mono_iff_injective | [
{
"state_after": "A B : NonemptyFinLinOrdCat\nf : A ⟶ B\n⊢ Mono f → Function.Injective ↑f",
"state_before": "A B : NonemptyFinLinOrdCat\nf : A ⟶ B\n⊢ Mono f ↔ Function.Injective ↑f",
"tactic": "refine' ⟨_, ConcreteCategory.mono_of_injective f⟩"
},
{
"state_after": "A B : NonemptyFinLinOrdCat\nf ... | [
162,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Control/Bitraversable/Lemmas.lean | Bitraversable.tfst_tsnd | [
{
"state_after": "t : Type u → Type u → Type u\ninst✝⁵ : Bitraversable t\nβ : Type u\nF G : Type u → Type u\ninst✝⁴ : Applicative F\ninst✝³ : Applicative G\ninst✝² : IsLawfulBitraversable t\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα₀ α₁ β₀ β₁ : Type u\nf : α₀ → F α₁\nf' : β₀ → G β₁\nx : t α₀ ... | [
89,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.univ_pow | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.474133\nα : Type u_1\nβ : Type ?u.474139\nγ : Type ?u.474142\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq β\ninst✝¹ : Monoid α\ns t : Finset α\na : α\nm n : ℕ\ninst✝ : Fintype α\nhn : n ≠ 0\n⊢ ↑(univ ^ n) = ↑univ",
"tactic": "rw [coe_pow, coe_un... | [
954,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.to_map_ne_zero_of_mem_nonZeroDivisors | [] | [
105,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
11
] |
Mathlib/Order/PropInstances.lean | Prop.bot_eq_false | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_sub | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.967201\nm : Type u_1\nn : Type u_2\no : Type ?u.967210\nm' : o → Type ?u.967215\nn' : o → Type ?u.967220\nR : Type ?u.967223\nS : Type ?u.967226\nα : Type v\nβ : Type w\nγ : Type ?u.967233\ninst✝¹ : AddGroup α\ninst✝ : StarAddMonoid α\nM N : Matrix m... | [
2157,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2155,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_add_cosh | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ sinh x + cosh x = exp x",
"tactic": "rw [add_comm, cosh_add_sinh]"
}
] | [
732,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.