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/Hom/Basic.lean | OrderIso.withBotCongr_symm | [] | [
1353,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | StrictAntiOn.inv | [] | [
1336,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.sum_comp | [] | [
194,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.isSatisfiable_directed_union_iff | [
{
"state_after": "L : Language\nT✝ : Theory L\nα : Type w\nn : ℕ\nT' : Theory L\nι : Type u_1\ninst✝ : Nonempty ι\nT : ι → Theory L\nh : Directed (fun x x_1 => x ⊆ x_1) T\nh' : ∀ (i : ι), IsSatisfiable (T i)\n⊢ IsSatisfiable (⋃ (i : ι), T i)",
"state_before": "L : Language\nT✝ : Theory L\nα : Type w\nn : ℕ\... | [
138,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.map_id_apply | [] | [
440,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/CategoryTheory/Opposites.lean | CategoryTheory.op_id | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.coe_castPred_le_self | [
{
"state_after": "case inl\nn m : ℕ\n⊢ ↑(castPred (last (n + 1))) ≤ ↑(last (n + 1))\n\ncase inr\nn m : ℕ\ni : Fin (n + 2)\nh : i < last (n + 1)\n⊢ ↑(castPred i) ≤ ↑i",
"state_before": "n m : ℕ\ni : Fin (n + 2)\n⊢ ↑(castPred i) ≤ ↑i",
"tactic": "rcases i.le_last.eq_or_lt with (rfl | h)"
},
{
"sta... | [
2467,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2462,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_mul_eq_smul | [] | [
599,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_self_eq_zero | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.1685745\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\nx : E\n⊢ inner x x = 0 ↔ x = 0",
"tacti... | [
614,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.mk_eq_monoidOf_mk' | [] | [
1655,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1654,
1
] |
Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat_.hom_ext | [] | [
124,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Nat/Totient.lean | Nat.totient_mul_of_prime_of_not_dvd | [
{
"state_after": "p n : ℕ\nhp : Prime p\nh : ¬p ∣ n\n⊢ coprime p n",
"state_before": "p n : ℕ\nhp : Prime p\nh : ¬p ∣ n\n⊢ φ (p * n) = (p - 1) * φ n",
"tactic": "rw [totient_mul _, totient_prime hp]"
},
{
"state_after": "no goals",
"state_before": "p n : ℕ\nhp : Prime p\nh : ¬p ∣ n\n⊢ coprim... | [
386,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.pos | [
{
"state_after": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\nh : Sized (node s l x r)\n⊢ 0 < size l + size r + 1",
"state_before": "α : Type u_1\ns : ℕ\nl : Ordnode α\nx : α\nr : Ordnode α\nh : Sized (node s l x r)\n⊢ 0 < s",
"tactic": "rw [h.1]"
},
{
"state_after": "no goals",
... | [
147,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.map_singletonSubgraph | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.208301\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nv : V\nx✝¹ x✝ : W\n⊢ ⊥ → ∃ x, ↑f x = x✝¹ ∧ ∃ x, ↑f x = x✝",
"state_before": "ι : Sort ?u.208301\nV : Type u\nW : Type v\nG : SimpleGraph V\nG' : SimpleGraph W\nf : G →g G'\nv : V... | [
867,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
] |
Mathlib/Topology/Instances/Rat.lean | Int.closedEmbedding_coe_rat | [
{
"state_after": "no goals",
"state_before": "⊢ Pairwise fun x y => 1 ≤ dist ↑x ↑y",
"tactic": "simpa using Int.pairwise_one_le_dist"
}
] | [
84,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_fintypeIoc | [
{
"state_after": "no goals",
"state_before": "n : ℕ\na b : Fin n\n⊢ Fintype.card ↑(Set.Ioc a b) = ↑b - ↑a",
"tactic": "rw [← card_Ioc, Fintype.card_ofFinset]"
}
] | [
113,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_le | [] | [
257,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.Integrable.integrableAtFilter | [] | [
398,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Data/List/NatAntidiagonal.lean | List.Nat.antidiagonal_succ | [
{
"state_after": "n : ℕ\n⊢ (0, n + 1) :: (succ 0, n + 1 - succ 0) :: map ((fun i => (i, n + 1 - i)) ∘ succ ∘ succ) (range n) =\n (0, n + 1) :: (succ 0, n) :: map (Prod.map succ id ∘ (fun i => (i, n - i)) ∘ succ) (range n)",
"state_before": "n : ℕ\n⊢ antidiagonal (n + 1) = (0, n + 1) :: map (Prod.map succ... | [
76,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_sub_const_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ (fun x => x - a) '' Ici b = Ici (b - a)",
"tactic": "simp [sub_eq_neg_add]"
}
] | [
374,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Data/List/Func.lean | List.Func.forall_val_of_forall_mem | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\na : α\nas✝ as1 as2 as3 : List α\ninst✝¹ : Inhabited α\ninst✝ : Inhabited β\nas : List α\np : α → Prop\nh1 : p default\nh2 : ∀ (x : α), x ∈ as → p x\nn : ℕ\n⊢ p (get n as)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nas✝ as1 as2 as3 : Lis... | [
225,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_nat_mul_two_pi_sub | [] | [
1193,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtr.congr | [] | [
625,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
8
] |
Mathlib/Algebra/Lie/Basic.lean | LieEquiv.symm_trans | [] | [
658,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/Algebra/Parity.lean | Even.isSquare_pow | [
{
"state_after": "case intro\nF : Type ?u.14072\nα : Type u_1\nβ : Type ?u.14078\nR : Type ?u.14081\ninst✝ : Monoid α\na✝ : α\nn : ℕ\na : α\n⊢ IsSquare (a ^ (n + n))",
"state_before": "F : Type ?u.14072\nα : Type u_1\nβ : Type ?u.14078\nR : Type ?u.14081\ninst✝ : Monoid α\nn : ℕ\na : α\n⊢ Even n → ∀ (a : α)... | [
119,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_triangle_left | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.4281\ninst✝ : PseudoEMetricSpace α\nx y z : α\n⊢ edist x y ≤ edist x z + edist z y",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.4281\ninst✝ : PseudoEMetricSpace α\nx y z : α\n⊢ edist x y ≤ edist z x + edist z y",
"tactic": "rw [edist_comm z... | [
101,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/RingTheory/Localization/Integral.lean | IsFractionRing.isAlgebraic_iff | [
{
"state_after": "case mp.intro.intro\nR : Type ?u.95350\ninst✝¹² : CommRing R\nM : Submonoid R\nS : Type ?u.95557\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Algebra R S\nP : Type ?u.95813\ninst✝⁹ : CommRing P\nA : Type u_1\nK : Type u_3\nC : Type u_2\ninst✝⁸ : CommRing A\ninst✝⁷ : IsDomain A\ninst✝⁶ : Field K\ninst✝⁵ : ... | [
165,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_union_compl_iff_inter_subset | [] | [
1767,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1766,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.sort_perm_toList | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3947\nr : α → α → Prop\ninst✝³ : DecidableRel r\ninst✝² : IsTrans α r\ninst✝¹ : IsAntisymm α r\ninst✝ : IsTotal α r\ns : Finset α\n⊢ ↑(sort r s) = ↑(toList s)",
"state_before": "α : Type u_1\nβ : Type ?u.3947\nr : α → α → Prop\ninst✝³ : DecidableRel r\ninst✝² : Is... | [
82,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.dist_conj_comm | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.548925\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz w : ℂ\n⊢ dist (↑(starRingEnd ℂ) z) w = dist z (↑(starRingEnd ℂ) w)",
"tactic": "rw [← dist_conj_conj, conj_conj]"
}
] | [
340,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderiv_const_add | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.289578\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
320,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.zsmul_mem | [] | [
244,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
11
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.mem_sup_right | [
{
"state_after": "M : Type u_1\nA : Type ?u.44116\nB : Type ?u.44119\ninst✝ : MulOneClass M\nS T : Submonoid M\n⊢ T ≤ S ⊔ T",
"state_before": "M : Type u_1\nA : Type ?u.44116\nB : Type ?u.44119\ninst✝ : MulOneClass M\nS T : Submonoid M\n⊢ ∀ {x : M}, x ∈ T → x ∈ S ⊔ T",
"tactic": "rw [←SetLike.le_def]"
... | [
246,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | Subgroup.Normal.conjAct | [] | [
390,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.separable_of_subsingleton | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Type v\ninst✝¹ : CommSemiring S\ninst✝ : Subsingleton R\nf : R[X]\n⊢ Separable f",
"tactic": "simp [Separable, IsCoprime]"
}
] | [
65,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.countable_closure_of_compact | [
{
"state_after": "case intro.intro.intro\nα : Type u\nβ : Type v\nX : Type ?u.313712\ninst✝¹ : PseudoEMetricSpace α\nγ : Type w\ninst✝ : EMetricSpace γ\ns : Set γ\nhs : IsCompact s\nt : Set γ\nhts : t ⊆ s\nhtc : Set.Countable t\nhsub : s ⊆ closure t\n⊢ ∃ t, t ⊆ s ∧ Set.Countable t ∧ s = closure t",
"state_b... | [
1122,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.fderivWithin'' | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\ninst✝³ : Normed... | [
997,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
980,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_map | [] | [
964,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Algebra/Group/Basic.lean | inv_mul_eq_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.31497\nG : Type ?u.31500\ninst✝ : DivisionCommMonoid α\na b c d : α\n⊢ a⁻¹ * b = b / a",
"tactic": "simp"
}
] | [
510,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.div_surjective | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.139727\ninst✝¹¹ : CommRing R\nM : Submonoid R\nS : Type ?u.139919\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nP : Type ?u.140156\ninst✝⁸ : CommRing P\nA : Type u_1\ninst✝⁷ : CommRing A\ninst✝⁶ : IsDomain A\nK : Type u_2\nB : Type ?u.140339\ninst✝⁵ :... | [
171,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.snd_neg | [] | [
239,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_bit0 | [
{
"state_after": "case mk\nn✝ m n val✝ : ℕ\nisLt✝ : val✝ < n\n⊢ ↑(bit0 { val := val✝, isLt := isLt✝ }) = bit0 ↑{ val := val✝, isLt := isLt✝ } % n",
"state_before": "n✝ m n : ℕ\nk : Fin n\n⊢ ↑(bit0 k) = bit0 ↑k % n",
"tactic": "cases k"
},
{
"state_after": "no goals",
"state_before": "case mk... | [
721,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
719,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsSeparable.union | [
{
"state_after": "case intro.intro\nα : Type u\nt : TopologicalSpace α\ns u : Set α\nhu : IsSeparable u\ncs : Set α\ncs_count : Set.Countable cs\nhcs : s ⊆ closure cs\n⊢ IsSeparable (s ∪ u)",
"state_before": "α : Type u\nt : TopologicalSpace α\ns u : Set α\nhs : IsSeparable s\nhu : IsSeparable u\n⊢ IsSepara... | [
397,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.pi_le_four | [
{
"state_after": "no goals",
"state_before": "⊢ 0 < 2",
"tactic": "norm_num"
},
{
"state_after": "no goals",
"state_before": "⊢ 2 = 4 / 2",
"tactic": "norm_num"
}
] | [
162,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.isHomogeneous_zero | [] | [
147,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_natCast | [] | [
696,
23
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695,
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | exists_between_of_forall_le | [] | [
646,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
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Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean | gramSchmidtNormed_unit_length' | [
{
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290,
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286,
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Mathlib/Topology/Constructions.lean | isClosed_sigma_iff | [
{
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1456,
67
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1455,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_setOf_frequently_eq_zero | [
{
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2943,
50
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2940,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_le_trim_iff | [
{
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1647,
70
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1645,
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Mathlib/Data/Vector/Basic.lean | Vector.removeNth_insertNth | [] | [
539,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
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Mathlib/Algebra/Order/Sub/Defs.lean | add_tsub_le_left | [] | [
105,
30
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Mathlib/Data/Set/Basic.lean | Set.compl_setOf | [] | [
1632,
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Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.eval_section_surjective_of_surjective | [
{
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag_map | [] | [
514,
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Mathlib/Data/Set/Prod.lean | Set.diag_image | [
{
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525,
35
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518,
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.cylinder_zero | [
{
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121,
87
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121,
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.basis_pair_right | [
{
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213,
33
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211,
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_mul_diff | [] | [
1046,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
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Mathlib/Order/Filter/Lift.lean | Filter.lift_map_le | [] | [
129,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/SetTheory/Ordinal/NaturalOps.lean | NatOrdinal.toOrdinal_toNatOrdinal | [] | [
90,
8
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Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_nonempty | [
{
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98,
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Mathlib/NumberTheory/Padics/PadicNumbers.lean | Padic.valuation_map_mul | [
{
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1102,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsOrthoᵢ.nondegenerate_of_not_isOrtho_basis_self | [] | [
836,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
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Mathlib/Algebra/Bounds.lean | subset_upperBounds_mul | [] | [
111,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
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Mathlib/Topology/Connected.lean | Embedding.isTotallyDisconnected | [] | [
1347,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
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Mathlib/Analysis/Convex/Function.lean | LinearOrder.strictConvexOn_of_lt | [
{
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453,
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441,
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Mathlib/Data/Multiset/Basic.lean | Multiset.empty_eq_zero | [] | [
106,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
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Mathlib/Data/Set/Image.lean | Set.nonempty_of_nonempty_preimage | [] | [
178,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
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Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.map_sup | [] | [
1010,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
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Mathlib/Data/Seq/Computation.lean | Computation.mem_map | [
{
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{
"state_after"... | [
892,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
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Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.ResidueField.map_id | [] | [
418,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.supp_eq_of_isUniform | [
{
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681,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
675,
1
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Mathlib/Topology/MetricSpace/Basic.lean | CauchySeq.bounded_range | [
{
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}
] | [
2439,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2438,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Real.differentiable_sin | [] | [
591,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | csSup_image2_eq_csSup_csInf | [] | [
1394,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
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Mathlib/Order/Monotone/Basic.lean | StrictAnti.le_iff_le | [] | [
811,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
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Mathlib/Topology/Bases.lean | TopologicalSpace.isSeparable_of_separableSpace_subtype | [
{
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444,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_add_Ici | [] | [
44,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
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Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.terminal.comp_from | [
{
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}
] | [
374,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
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Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_trans_trans_symm | [] | [
614,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_bit1 | [
{
"state_after": "no goals",
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}
] | [
527,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
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Mathlib/Order/Hom/Lattice.lean | SupHom.comp_assoc | [] | [
418,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_X | [] | [
444,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
1
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_of_isUnit | [] | [
171,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
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Mathlib/Data/Set/Basic.lean | Set.mem_inter | [] | [
899,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
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Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.map_sub_le | [
{
"state_after": "no goals",
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},
{
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127,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Algebra/Order/Floor.lean | Int.fract_lt_one | [] | [
883,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_monomial | [
{
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"tactic": "classical\n refine' Finset.sup_le fun t h... | [
103,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.biUnion_op_smul_finset | [] | [
1844,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1843,
1
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Mathlib/Algebra/Support.lean | Function.mulSupport_iSup | [
{
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190,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
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Std/Data/Int/DivMod.lean | Int.ofNat_dvd_left | [
{
"state_after": "no goals",
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"tactic": "rw [← natAbs_dvd_natAbs, natAbs_ofNat]"
}
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662,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
661,
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Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.nonarchimedean | [
{
"state_after": "case inr\np : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nthis : ∀ {q r : ℚ}, padicValRat p q ≤ padicValRat p r → padicNorm p (q + r) ≤ max (padicNorm p q) (padicNorm p r)\nhle : ¬padicValRat p q ≤ padicValRat p r\n⊢ padicNorm p (q + r) ≤ max (padicNorm p q) (padicNorm p r)\n\np : ℕ\nhp : Fact (Nat.P... | [
211,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
11
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_X_add_C | [] | [
111,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Data/Semiquot.lean | Semiquot.ext | [] | [
57,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsOrthoᵢ.not_isOrtho_basis_self_of_separatingLeft | [
{
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Mathlib/Logic/Basic.lean | Exists₂.imp | [] | [
639,
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.mul_toMatrix' | [
{
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Mathlib/GroupTheory/Subsemigroup/Centralizer.lean | Set.div_mem_centralizer₀ | [
{
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... | [
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