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/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_sup | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.282487\nβ : Type ?u.282490\nγ : Type ?u.282493\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nι : Type u\nf : ι → Ordinal\na : Ordinal\n⊢ a < sup f ↔ ∃ i, a < f i",
"tactic": "simpa only [not_forall, not_le] using not_congr (@sup_le_iff.{... | [
1277,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1276,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.mem_iff_infEdist_zero_of_closed | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.17353\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t : Set α\nΦ : α → β\nh : IsClosed s\n⊢ x ∈ s ↔ infEdist x s = 0",
"tactic": "rw [← mem_closure_iff_infEdist_zero, h.closure_eq]"
}
] | [
163,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.support_swap_mul_eq | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nx : α\nh : ↑f (↑f x) ≠ x\nhx : ↑f x = x\n⊢ support (swap x (↑f x) * f) = support f \\ {x}\n\ncase neg\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g f : Perm α\nx : α\nh : ↑f (↑f x) ≠ x\nhx : ¬↑... | [
495,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.div_dvd_of_dvd | [
{
"state_after": "case pos\nR : Type u\ninst✝ : EuclideanDomain R\np q : R\nhpq : q ∣ p\nhq : q = 0\n⊢ p / q ∣ p\n\ncase neg\nR : Type u\ninst✝ : EuclideanDomain R\np q : R\nhpq : q ∣ p\nhq : ¬q = 0\n⊢ p / q ∣ p",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\np q : R\nhpq : q ∣ p\n⊢ p / q ∣ p",
... | [
123,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.sinh_ofReal_re | [] | [
665,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_ite | [] | [
643,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tsum_eq_limsup_sum_nat | [] | [
858,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.mem_biInter | [] | [
860,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_singleton_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.266452\nγ : Type ?u.266455\ninst✝ : DecidableEq α\ns t u v : Finset α\na b : α\nha : ¬a ∈ s\n⊢ _root_.Disjoint {a} s",
"tactic": "simp [ha]"
}
] | [
2287,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2286,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.ext | [
{
"state_after": "case mk\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nn : ℕ\ns2 : Simplex k P n\npoints✝ : Fin (n + 1) → P\nIndependent✝ : AffineIndependent k points✝\nh : ∀ (i : Fin (n + 1)), points { points := points✝, Inde... | [
822,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Algebra/Associated.lean | associated_isUnit_mul_left_iff | [
{
"state_after": "α : Type ?u.166351\nβ✝ : Type ?u.166354\nγ : Type ?u.166357\nδ : Type ?u.166360\nβ : Type u_1\ninst✝ : CommMonoid β\nu a b : β\nhu : IsUnit u\n⊢ a * u ~ᵤ b ↔ a ~ᵤ b",
"state_before": "α : Type ?u.166351\nβ✝ : Type ?u.166354\nγ : Type ?u.166357\nδ : Type ?u.166360\nβ : Type u_1\ninst✝ : Com... | [
482,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.toSet_inj | [] | [
809,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.attachBound_apply_coe | [] | [
66,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
src/lean/Init/Core.lean | Iff.rfl | [] | [
664,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
663,
11
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_neg_iff | [] | [
1029,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | isOfFinOrder_one | [] | [
124,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_closure | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.54219\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx y : α\ns t u : Set α\nΦ : α → β\n⊢ hausdorffEdist (closure s) (closure t) = hausdorffEdist s t",
"tactic": "simp"
}
] | [
413,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/NumberTheory/Bernoulli.lean | sum_range_pow | [
{
"state_after": "A : Type ?u.791691\ninst✝¹ : CommRing A\ninst✝ : Algebra ℚ A\nn p : ℕ\nhne : ∀ (m : ℕ), ↑m ! ≠ 0\n⊢ ∑ k in range n, ↑k ^ p = ∑ i in range (p + 1), bernoulli i * ↑(Nat.choose (p + 1) i) * ↑n ^ (p + 1 - i) / (↑p + 1)",
"state_before": "A : Type ?u.791691\ninst✝¹ : CommRing A\ninst✝ : Algebra... | [
380,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/CategoryTheory/Localization/Predicate.lean | CategoryTheory.Functor.IsLocalization.for_id | [] | [
155,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioo_insert_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.94924\nα : Type u_1\ninst✝² : PartialOrder α\ninst✝¹ : LocallyFiniteOrder α\na b c : α\ninst✝ : DecidableEq α\nh : a < b\n⊢ insert b (Ioo a b) = Ioc a b",
"tactic": "rw [← coe_inj, coe_insert, coe_Ioo, coe_Ioc, Set.insert_eq, Set.union_comm, Set.... | [
581,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.add_mul_subset | [] | [
820,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.ext_iff_blocks | [
{
"state_after": "no goals",
"state_before": "l : Type u_4\nm : Type u_3\nn : Type u_2\no : Type u_1\np : Type ?u.5734\nq : Type ?u.5737\nm' : o → Type ?u.5742\nn' : o → Type ?u.5747\np' : o → Type ?u.5752\nR : Type ?u.5755\nS : Type ?u.5758\nα : Type u_5\nβ : Type ?u.5764\nA B : Matrix (n ⊕ o) (l ⊕ m) α\nx... | [
137,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/GroupTheory/GroupAction/Sum.lean | Sum.smul_inl | [] | [
48,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/Data/List/Nodup.lean | List.nodup_replicate | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr : α → α → Prop\na✝ b a : α\n⊢ Nodup (replicate 0 a) ↔ 0 ≤ 1",
"tactic": "simp [Nat.zero_le]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nl l₁ l₂ : List α\nr : α → α → Prop\n... | [
194,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | TopologicalGroup.exists_antitone_basis_nhds_one | [
{
"state_after": "case intro.mk\nα : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : TopologicalGroup G\nN : Subgroup G\nn : Subgroup.Normal N\ninst✝ : FirstCountableTopology G\nu : ℕ → Set G\nhu : HasBasis (𝓝 1) (fun x => True) u\nu_anti : Antitone u\n⊢ ∃ u,... | [
1036,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | mul_min_of_nonneg | [] | [
973,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Order/WithBot.lean | WithBot.coe_min | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.prod_eq' | [
{
"state_after": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\nM : Monoid α\nl₁ l₂ : List α\nh : l₁ ~ l₂\nhc : Pairwise Commute l₁\n⊢ ∀ (x : α), x ∈ l₁ → ∀ (y : α), y ∈ l₁ → ∀ (z : α), z * x * y = z * y * x",
"state_before": "α : Type uu\nβ : Type vv\nl₁✝ l₂✝ : List α\nM : Monoid α\nl₁ l₂ : List α\nh : l₁ ~ ... | [
575,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_ofMul | [] | [
2208,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2207,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_subset_image_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.82868\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt✝ : Finset β\na : α\nb c : β\nt : Finset α\nhf : Injective f\n⊢ ↑(image f s) ⊆ ↑(image f t) ↔ ↑s ⊆ ↑t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.82868\ninst✝ : DecidableEq β\nf... | [
457,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.log_opow | [
{
"state_after": "case h.e'_2\nb : Ordinal\nhb : 1 < b\nx : Ordinal\n⊢ log b (b ^ x) = log b (b ^ x * 1 + 0)",
"state_before": "b : Ordinal\nhb : 1 < b\nx : Ordinal\n⊢ log b (b ^ x) = x",
"tactic": "convert log_opow_mul_add hb zero_ne_one.symm hb (opow_pos x (zero_lt_one.trans hb))\n using 1"
},
{
... | [
428,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.insertNth_apply_same | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Fin (n + 1) → Type u\nβ : Type v\ni : Fin (n + 1)\nx : α i\np : (j : Fin n) → α (↑(succAbove i) j)\n⊢ insertNth i x p i = x",
"tactic": "simp [insertNth, succAboveCases]"
}
] | [
665,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
664,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.isPartitionTop | [] | [
730,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
729,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_eq_none | [] | [
134,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
134,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_vaddConst_symm | [] | [
711,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.pureMonoidHom_apply | [] | [
654,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | AddSubgroup.toIntSubmodule_symm | [] | [
400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Algebra/Module/BigOperators.lean | Multiset.sum_smul | [] | [
31,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_some | [] | [
3308,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3306,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | SubsemiringClass.coe_subtype | [] | [
106,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_coe_iff | [] | [
40,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | bit0_eq_zero | [] | [
81,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Topology/Order/Basic.lean | tendsto_nhds_top_mono | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝³ : TopologicalSpace β\ninst✝² : Preorder β\ninst✝¹ : OrderTop β\ninst✝ : OrderTopology β\nl : Filter α\nf g : α → β\nhg : f ≤ᶠ[l] g\nhf : ∀ (i : β), i < ⊤ → ∀ᶠ (a : α) in l, f a ∈ Ioi i\n⊢ ∀ (i : β), i < ⊤ → ∀ᶠ (a : α) in l, g a ∈ Ioi i",
"state_be... | [
1165,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1161,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | IsOpen.eq_empty_of_measure_zero | [] | [
84,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.smul_toNNReal | [
{
"state_after": "α : Type ?u.819259\nβ : Type ?u.819262\na✝ b✝ c d : ℝ≥0∞\nr p q a : ℝ≥0\nb : ℝ≥0∞\n⊢ ENNReal.toNNReal (↑a * b) = a * ENNReal.toNNReal b",
"state_before": "α : Type ?u.819259\nβ : Type ?u.819262\na✝ b✝ c d : ℝ≥0∞\nr p q a : ℝ≥0\nb : ℝ≥0∞\n⊢ ENNReal.toNNReal (a • b) = a * ENNReal.toNNReal b"... | [
2209,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2207,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.measure_union_add_inter₀ | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.17157\nα : Type u_1\nβ : Type ?u.17163\nγ : Type ?u.17166\nm0 : MeasurableSpace α\nμ : Measure α\ns✝ t s : Set α\nht : NullMeasurableSet t\n⊢ ↑↑μ (s ∪ t) + ↑↑μ (s ∩ t) = ↑↑μ s + ↑↑μ t",
"tactic": "rw [← measure_inter_add_diff₀ (s ∪ t) ht, union_i... | [
327,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_mul_X | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝² : Semiring R\np q r : R[X]\ninst✝¹ : Semiring S\nf : R →+* S\nx : S\ninst✝ : Semiring T\nk : ℕ\n⊢ Commute (↑f (coeff X k)) x",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝² ... | [
192,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/Atoms.lean | IsSimpleOrder.eq_bot_of_lt | [] | [
509,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.memℒp_one_iff_integrable | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.827340\nδ : Type ?u.827343\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → β\n⊢ Memℒp f 1 ↔ Integrable f",
"tactic": "simp_rw [I... | [
447,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.set_average_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.195874\nm0 : MeasurableSpace α\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : CompleteSpace F\nμ : Measure α\ns✝ : Set E... | [
116,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Group/Commute.lean | mul_inv_cancel_comm_assoc | [] | [
418,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_subset_singleton' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.136560\nγ : Type ?u.136563\nι : Type ?u.136566\nM : Type u_2\nM' : Type ?u.136572\nN : Type ?u.136575\nP : Type ?u.136578\nG : Type ?u.136581\nH : Type ?u.136584\nR : Type ?u.136587\nS : Type ?u.136590\ninst✝ : Zero M\na✝ a' : α\nb✝ : M... | [
499,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
src/lean/Init/SimpLemmas.lean | or_true | [] | [
88,
81
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
88,
9
] |
Mathlib/LinearAlgebra/DirectSum/Finsupp.lean | finsuppTensorFinsupp_apply | [
{
"state_after": "case h0\nR✝ : Type u\nM✝ : Type v\nN✝ : Type w\ninst✝⁹ : Ring R✝\ninst✝⁸ : AddCommGroup M✝\ninst✝⁷ : Module R✝ M✝\ninst✝⁶ : AddCommGroup N✝\ninst✝⁵ : Module R✝ N✝\nR : Type u_1\nM : Type u_2\nN : Type u_3\nι : Type u_4\nκ : Type u_5\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Modul... | [
78,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.coe_range | [] | [
654,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.pow_lt_ascFactorial' | [
{
"state_after": "n k : ℕ\n⊢ (n + 1) * (n + 1) ^ (k + 1) < (n + (k + 1) + 1) * ascFactorial n (k + 1)",
"state_before": "n k : ℕ\n⊢ (n + 1) ^ (k + 2) < ascFactorial n (k + 2)",
"tactic": "rw [pow_succ, ascFactorial, mul_comm]"
},
{
"state_after": "no goals",
"state_before": "n k : ℕ\n⊢ (n + ... | [
296,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Topology/Support.lean | range_eq_image_mulTSupport_or | [] | [
86,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Order/BoundedOrder.lean | not_bot_lt_iff | [] | [
386,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | differentiableAt_iff_restrictScalars | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝⁹ : NontriviallyNormedField 𝕜'\ninst✝⁸ : NormedAlgebra 𝕜 𝕜'\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : IsScalarTower 𝕜 𝕜' E\nF : Type u_3\ninst✝³ : ... | [
123,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.integrableOn_Ioi_deriv_of_nonpos' | [
{
"state_after": "E : Type ?u.164089\nf f' : ℝ → E\ng g' : ℝ → ℝ\na b l : ℝ\nm : E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhderiv : ∀ (x : ℝ), x ∈ Ici a → HasDerivAt g (g' x) x\ng'neg : ∀ (x : ℝ), x ∈ Ioi a → g' x ≤ 0\nhg : Tendsto g atTop (𝓝 l)\nx : ℝ\nhx : x ∈ Ici a... | [
773,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
770,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.hom_refl | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\n⊢ ConnectedComponent.map (InduceHom Hom.id (_ : Lᶜ ⊆ Lᶜ)) C = C",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\n⊢ hom (_ : L ⊆ L) C = C",
"tactic": "change C.map _ = C"
... | [
212,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.smul_mem_pointwise_smul_iff₀ | [] | [
531,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
1
] |
Mathlib/Algebra/Symmetrized.lean | SymAlg.sym_inv | [] | [
219,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/NumberTheory/Multiplicity.lean | multiplicity.pow_sub_pow_of_prime | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nn✝ : ℕ\ninst✝² : CommRing R\na b x✝ y✝ : R\np✝ : ℕ\ninst✝¹ : IsDomain R\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np : R\nhp : Prime p\nx y : R\nhxy : p ∣ x - y\nhx : ¬p ∣ x\nn : ℕ\nhn : ¬p ∣ ↑n\n⊢ multiplicity p (x ^ n - y ^ n) = multiplicity p (... | [
164,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Order.lean | continuous_iInf_rng | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.42166\nf : α → β\nι : Sort u_1\nt₁ : TopologicalSpace α\nt₂ : ι → TopologicalSpace β\n⊢ Continuous f ↔ ∀ (i : ι), Continuous f",
"tactic": "simp only [continuous_iff_coinduced_le, le_iInf_iff]"
}
] | [
805,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image_subset_image₂_right | [] | [
99,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.map_nil | [] | [
695,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
694,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_le_sub_left_of_le_add | [
{
"state_after": "a b c : Int\nh✝ : c ≤ a + b\nh : -a ≤ -c + b\n⊢ -a ≤ b - c",
"state_before": "a b c : Int\nh : c ≤ a + b\n⊢ -a ≤ b - c",
"tactic": "have h := Int.le_neg_add_of_add_le (Int.sub_left_le_of_le_add h)"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : c ≤ a + b... | [
1019,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1017,
11
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_sUnion_le | [
{
"state_after": "α✝ β α : Type u\nA : Set (Set α)\n⊢ (#↑(⋃ (i : ↑A), ↑i)) ≤ (#↑A) * ⨆ (s : ↑A), #↑↑s",
"state_before": "α✝ β α : Type u\nA : Set (Set α)\n⊢ (#↑(⋃₀ A)) ≤ (#↑A) * ⨆ (s : ↑A), #↑↑s",
"tactic": "rw [sUnion_eq_iUnion]"
},
{
"state_after": "no goals",
"state_before": "α✝ β α : Typ... | [
2053,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2051,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictMonoOn_univ | [] | [
404,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
9
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.Prepartition.IsPartition.biUnionTagged | [] | [
170,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.preimage_metric_closedBall | [
{
"state_after": "case h\nR : Type ?u.1012446\nR' : Type ?u.1012449\n𝕜 : Type u_2\n𝕜₂ : Type ?u.1012455\n𝕜₃ : Type ?u.1012458\n𝕝 : Type ?u.1012461\nE : Type u_1\nE₂ : Type ?u.1012467\nE₃ : Type ?u.1012470\nF : Type ?u.1012473\nG : Type ?u.1012476\nι : Type ?u.1012479\ninst✝⁶ : SeminormedRing 𝕜\ninst✝⁵ : Ad... | [
815,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Topology/Algebra/Order/Compact.lean | Continuous.exists_forall_ge_of_hasCompactMulSupport | [] | [
362,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Data/List/Sections.lean | List.mem_sections | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.11\nL : List (List α)\nf : List α\nh : f ∈ sections L\n⊢ Forall₂ (fun x x_1 => x ∈ x_1) f L\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.11\nL : List (List α)\nf : List α\nh : Forall₂ (fun x x_1 => x ∈ x_1) f L\n⊢ f ∈ sections L",
"state_before": "... | [
37,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.mem_roots' | [
{
"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 : R[X]\n⊢ a ∈ roots p ↔ p ≠ 0 ∧ IsRoot p a",
"tactic": "rw [← count_pos, count_roots p, rootMultiplicity_pos']"
}
] | [
577,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.vec3_dotProduct | [] | [
507,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.coe_disjoint | [] | [
2893,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2892,
1
] |
Mathlib/Data/Set/Intervals/Instances.lean | Set.Icc.coe_ne_zero | [] | [
86,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | Filter.Tendsto.const_smul | [] | [
84,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Data/MvPolynomial/Equiv.lean | MvPolynomial.eval_eq_eval_mv_eval' | [
{
"state_after": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type ?u.1054353\na a' a₁ a₂ : R\ne : ℕ\ns✝ : σ →₀ ℕ\ninst✝ : CommSemiring R\nn : ℕ\ns : Fin n → R\ny : R\nf : MvPolynomial (Fin (n + 1)) R\nφ : (MvPolynomial (Fin n) R)[X] →ₐ[R] R[X] :=\n let src := mapRingHom (eval s);\n {\n toRingHo... | [
413,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.comap_bot | [] | [
2806,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2805,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Eventually.mono | [] | [
1132,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/ModelTheory/Types.lean | FirstOrder.Language.Theory.exists_modelType_is_realized_in | [
{
"state_after": "case intro\nL : Language\nT : Theory L\nα : Type w\nM✝ : Type w'\ninst✝² : Structure L M✝\ninst✝¹ : Nonempty M✝\ninst✝ : M✝ ⊨ T\np : CompleteType T α\nM : ModelType ↑p\n⊢ ∃ M, p ∈ realizedTypes T (↑M) α",
"state_before": "L : Language\nT : Theory L\nα : Type w\nM : Type w'\ninst✝² : Struct... | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_disjUnion | [] | [
364,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_hom_add_index | [] | [
415,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_natAdd | [] | [
1398,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1397,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.prev_reverse_eq_next' | [] | [
856,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
8
] |
Mathlib/Data/List/Basic.lean | List.mem_pmap | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.328936\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\np : α → Prop\nf : (a : α) → p a → β\nl : List α\nH : ∀ (a : α), a ∈ l → p a\nb : β\n⊢ b ∈ pmap f l H ↔ ∃ a h, f a (_ : p a) = b",
"tactic": "simp only [pmap_eq_map_attach, me... | [
3143,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3141,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | subset_interior_smul | [] | [
1249,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1248,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.ofMultiset_apply_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.183679\nγ : Type ?u.183682\ns : Multiset α\nhs : s ≠ 0\na : α\nha : ¬a ∈ s\n⊢ ↑(ofMultiset s hs) a = 0",
"tactic": "simpa only [ofMultiset_apply, ENNReal.div_eq_zero_iff, Nat.cast_eq_zero, Multiset.count_eq_zero,\n ENNReal.nat_ne_t... | [
195,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.map_smul_of_tower | [] | [
423,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Order/Heyting/Regular.lean | Heyting.IsRegular.himp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : HeytingAlgebra α\na b : α\nha : IsRegular a\nhb : IsRegular b\n⊢ IsRegular (a ⇨ b)",
"tactic": "rw [IsRegular, compl_compl_himp_distrib, ha.eq, hb.eq]"
}
] | [
74,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | balanced_iUnion₂ | [] | [
196,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_right_Ico | [
{
"state_after": "ι : Type ?u.218659\nα : Type u_1\ninst✝² : OrderedCancelAddCommMonoid α\ninst✝¹ : ExistsAddOfLE α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ ↑(addRightEmbedding c) '' Set.Ico a b = Set.Ico (a + c) (b + c)",
"state_before": "ι : Type ?u.218659\nα : Type u_1\ninst✝² : OrderedCancelAddCommMo... | [
1065,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.mk'_eq_of_eq | [] | [
377,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.le_one | [] | [
252,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.Separable.isCoprime | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\nf g : R[X]\nh : Separable (f * g)\nthis : IsCoprime f (↑derivative (f * g))\n⊢ IsCoprime f g",
"state_before": "R : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\nf g : R[X]\nh : Separable (f * g... | [
112,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.Lifts.exists_lift_of_splits | [] | [
1143,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean | mulLeft_bijective₀ | [] | [
37,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.sub_sub_sub | [
{
"state_after": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b c d : X ⟶ Y\n⊢ prod.lift (prod.lift a b ≫ σ) (prod.lift c d ≫ σ) ≫ σ = a - b - (c - d)",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na b c d : X ⟶ Y\n⊢ a - c - (b ... | [
375,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.