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/Data/Set/Basic.lean | Set.Subset.trans | [] | [
363,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/CategoryTheory/Simple.lean | CategoryTheory.kernel_zero_of_nonzero_from_simple | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : HasZeroMorphisms C\nX Y : C\ninst✝¹ : Simple X\nf : X ⟶ Y\ninst✝ : HasKernel f\nw : f ≠ 0\n⊢ kernel.ι f = 0",
"tactic": "classical\n by_contra h\n haveI := isIso_of_mono_of_nonzero h\n exact w (eq_zero_of_epi_kern... | [
93,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_mono | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX Y Z : C\nf✝ : X ⟶ Y\ninst✝¹ : HasImage f✝\nf : X ⟶ Y\ninst✝ : Mono f\n⊢ (imageSubobjectIso f ≪≫ imageMonoIsoSource f ≪≫ (underlyingIso f).symm).hom ≫ arrow (Subobject.mk f) =\n arrow (imageSubobject f)",
"tactic": "simp"... | [
431,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_le_pi_div_two_iff | [
{
"state_after": "case inl\nz : ℂ\nhre : 0 ≤ z.re\n⊢ arg z ≤ π / 2 ↔ 0 ≤ z.re ∨ z.im < 0\n\ncase inr\nz : ℂ\nhre : z.re < 0\n⊢ arg z ≤ π / 2 ↔ 0 ≤ z.re ∨ z.im < 0",
"state_before": "z : ℂ\n⊢ arg z ≤ π / 2 ↔ 0 ≤ z.re ∨ z.im < 0",
"tactic": "cases' le_or_lt 0 (re z) with hre hre"
},
{
"state_after... | [
341,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.prod_cyclotomic'_eq_X_pow_sub_one | [
{
"state_after": "K✝ : Type ?u.240784\ninst✝² : Field K✝\nK : Type u_1\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nζ : K\nn : ℕ\nhpos : 0 < n\nh : IsPrimitiveRoot ζ n\nhd : Set.PairwiseDisjoint ↑(Nat.divisors n) fun k => primitiveRoots k K\n⊢ ∏ i in Nat.divisors n, cyclotomic' i K = X ^ n - 1",
"state_before"... | [
177,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_subset_div_left | [] | [
690,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_omega | [] | [
865,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
864,
1
] |
Std/Data/String/Lemmas.lean | Substring.ValidFor.nextn | [
{
"state_after": "no goals",
"state_before": "l m₁ m₂ r : List Char\nx✝¹ : Substring\nx✝ : ValidFor l (m₁ ++ m₂) r x✝¹\n⊢ Substring.nextn x✝¹ 0 { byteIdx := utf8Len m₁ } = { byteIdx := utf8Len m₁ + utf8Len (List.take 0 m₂) }",
"tactic": "simp [Substring.nextn]"
},
{
"state_after": "l m₁ m₂ r : L... | [
866,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
856,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_id_mk' | [] | [
632,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiffOn_of_subsingleton | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹⁰ : NormedAddCommGroup D\ninst✝⁹ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nG : Type uG\ninst✝⁴ : Norme... | [
126,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | HasFDerivWithinAt.uniqueDiffWithinAt | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\ns : Set E\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivWithinAt f f' s x\nhs : UniqueDiffWithin... | [
506,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat_dvd_iff_le | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\na n : ℕ\nha : a ≠ 0\n⊢ p ^ n ∣ a ↔ n ≤ padicValNat p a",
"tactic": "rw [pow_dvd_iff_le_multiplicity, ← padicValNat_def' hp.out.ne_one ha.bot_lt, PartENat.coe_le_coe]"
}
] | [
465,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_le | [
{
"state_after": "no goals",
"state_before": "n m : Nat\n⊢ n - m ≤ n",
"tactic": "induction m with\n| zero => exact Nat.le_refl (n - 0)\n| succ m ih => apply Nat.le_trans (pred_le (n - m)) ih"
},
{
"state_after": "no goals",
"state_before": "case zero\nn : Nat\n⊢ n - zero ≤ n",
"tac... | [
234,
57
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
231,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_one_sub | [] | [
439,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.not_inseparable_infty_coe | [] | [
415,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.sum_apply' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nι : Type u_1\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ✝ : { x // x ∈ kernel α β }\ninst✝ : Countable ι\nκ : ι → { x // x ∈ kernel α β }\na : α\ns : Set β\nhs : MeasurableSet s\n⊢ ↑↑(↑(kernel.sum κ) a) s = ∑' (n : ι), ↑↑(↑(κ n... | [
234,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
src/lean/Init/SizeOf.lean | sizeOf_default | [] | [
47,
61
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
47,
9
] |
Mathlib/Data/Stream/Init.lean | Stream'.map_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\nf : α → β\ns : Stream' α\n⊢ map f s = f (head s) :: map f (tail s)",
"tactic": "rw [← Stream'.eta (map f s), tail_map, head_map]"
}
] | [
165,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.mem_Ici_iff | [] | [
1097,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1096,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.lieIdeal_oper_eq_linear_span' | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\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 : LieModule R L M\ninst✝³ : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
100,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Combinatorics/SimpleGraph/Acyclic.lean | SimpleGraph.IsAcyclic.path_unique | [
{
"state_after": "case mk\nV : Type u\nG✝ G : SimpleGraph V\nh : IsAcyclic G\nv w : V\nq : Path G v w\np : Walk G v w\nhp : Walk.IsPath p\n⊢ { val := p, property := hp } = q",
"state_before": "V : Type u\nG✝ G : SimpleGraph V\nh : IsAcyclic G\nv w : V\np q : Path G v w\n⊢ p = q",
"tactic": "obtain ⟨p, h... | [
113,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_lt_smul_of_neg | [
{
"state_after": "k : Type u_2\nM : Type u_1\nN : Type ?u.7657\ninst✝³ : OrderedRing k\ninst✝² : OrderedAddCommGroup M\ninst✝¹ : Module k M\ninst✝ : OrderedSMul k M\na b : M\nc : k\nh : a < b\nhc : c < 0\n⊢ -c • a < -c • b",
"state_before": "k : Type u_2\nM : Type u_1\nN : Type ?u.7657\ninst✝³ : OrderedRing... | [
58,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | RingHom.range_eq_map | [
{
"state_after": "case h\nR : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ng : S →+* T\nf✝ f : R →+* S\nx✝ : S\n⊢ x✝ ∈ range f ↔ x✝ ∈ Subring.map f ⊤",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ng : S →+* T\nf✝ ... | [
664,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
662,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.comp_inv_eq | [] | [
434,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_X_pow_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r : R[X]\nn : ℕ\n⊢ degree (X ^ n) ≤ ↑n",
"tactic": "simpa only [C_1, one_mul] using degree_C_mul_X_pow_le n (1 : R)"
}
] | [
472,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.absorbent_closedBall_zero | [] | [
991,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
11
] |
Mathlib/Algebra/Order/Group/Defs.lean | lt_inv_iff_mul_lt_one' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ b * a < b * b⁻¹ ↔ b * a < 1",
"tactic": "rw [mul_inv_self]"
}
] | [
194,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.concat_cons | [] | [
289,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.trim_smul | [] | [
1758,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1756,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.mk_add_moveRight_inr | [] | [
1548,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1545,
1
] |
Mathlib/Computability/Ackermann.lean | lt_ack_right | [] | [
200,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.ModEq.refl | [] | [
50,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
11
] |
Mathlib/Topology/ExtremallyDisconnected.lean | StoneCech.projective | [
{
"state_after": "X : Type u\ninst✝¹ : TopologicalSpace X\ninst✝ : DiscreteTopology X\nY Z : Type u\n_tsY : TopologicalSpace Y\n_tsZ : TopologicalSpace Z\n_csY : CompactSpace Y\n_t2Y : T2Space Y\n_csZ✝ : CompactSpace Z\n_csZ : T2Space Z\nf : StoneCech X → Z\ng : Y → Z\nhf : Continuous f\nhg : Continuous g\ng_su... | [
83,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_zero | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.871391\n𝕜 : Type ?u.871394\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\ninst✝⁶ : CompleteSpace E\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : SMulCommClass ℝ 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedS... | [
847,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.toList_eq_singleton_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.31600\nγ : Type ?u.31603\na : α\nm : Multiset α\n⊢ toList m = [a] ↔ m = {a}",
"tactic": "rw [← perm_singleton, ← coe_eq_coe, coe_toList, coe_singleton]"
}
] | [
483,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.surjOn_iUnion₂ | [] | [
1598,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1596,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_iff_exists_injOn | [] | [
61,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.support_neg | [] | [
88,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_cast_heq | [
{
"state_after": "α✝ : Type ?u.17749\nβ : Type ?u.17752\nγ : Type ?u.17755\nf : α✝ ↪ β\ns✝ : Finset α✝\nα : Type u_1\ns : Finset α\n⊢ HEq (map (Equiv.toEmbedding (Equiv.cast (_ : α = α))) s) s",
"state_before": "α✝ : Type ?u.17749\nβ✝ : Type ?u.17752\nγ : Type ?u.17755\nf : α✝ ↪ β✝\ns✝ : Finset α✝\nα β : Ty... | [
134,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_filter_of_mem | [] | [
1991,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1990,
1
] |
Mathlib/Data/Set/Basic.lean | Set.inter_diff_distrib_left | [] | [
1613,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1612,
1
] |
Mathlib/Data/Nat/Factorial/Basic.lean | Nat.descFactorial_eq_zero_iff_lt | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ descFactorial n 0 = 0 ↔ n < 0",
"tactic": "simp only [descFactorial_zero, Nat.one_ne_zero, Nat.not_lt_zero]"
},
{
"state_after": "n k : ℕ\n⊢ n ≤ k → n ≠ k → n ≤ k",
"state_before": "n k : ℕ\n⊢ descFactorial n (succ k) = 0 ↔ n < succ k",
... | [
402,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/List/Indexes.lean | List.foldlIdxSpec_cons | [] | [
262,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Std/Data/String/Lemmas.lean | String.revFind_of_valid | [
{
"state_after": "no goals",
"state_before": "p : Char → Bool\ns : String\n⊢ revFind s p =\n Option.map (fun x => { byteIdx := utf8Len x }) (List.tail? (List.dropWhile (fun x => !p x) (List.reverse s.data)))",
"tactic": "simpa using revFindAux_of_valid p s.1.reverse []"
}
] | [
353,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
351,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.one_minus_le_one | [
{
"state_after": "no goals",
"state_before": "x : ↑I\n⊢ 1 - ↑x ≤ 1",
"tactic": "simpa using x.2.1"
}
] | [
152,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Set/Countable.lean | Set.Countable.image | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nhs : Set.Countable s\nf : α → β\n⊢ Set.Countable (range fun x => f ↑x)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ns : Set α\nhs : Set.Countable s\nf : α → β\n⊢ Set.Countable (f '' s)",
"tactic": "rw [ima... | [
137,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | Basis.finite_index_of_rank_lt_aleph0 | [] | [
856,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
854,
1
] |
Std/Data/Array/Lemmas.lean | Array.get_set_eq | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.14725\na : Array α\ni : Fin (size a)\nv : α\n⊢ i.val < size (set a i v)",
"tactic": "simp [i.2]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\na : Array α\ni : Fin (size a)\nv : α\n⊢ (set a i v)[i.val] = v",
"tact... | [
89,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
87,
9
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_inj | [] | [
379,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.coe_true | [
{
"state_after": "no goals",
"state_before": "⊢ (true = true) = True",
"tactic": "simp"
}
] | [
115,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Combinatorics/SimpleGraph/Prod.lean | SimpleGraph.Preconnected.ofBoxProdLeft | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.82005\nG : SimpleGraph α\nH : SimpleGraph β\ninst✝ : Nonempty β\nh : Preconnected (G □ H)\n⊢ Preconnected G",
"tactic": "classical\nrintro a₁ a₂\nobtain ⟨w⟩ := h (a₁, Classical.arbitrary _) (a₂, Classical.arbitrary _)\... | [
186,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.mem_coeSubmodule | [] | [
106,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/Convex/Join.lean | convexJoin_empty_right | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.18687\n𝕜 : Type u_2\nE : Type u_1\ninst✝² : OrderedSemiring 𝕜\ninst✝¹ : AddCommMonoid E\ninst✝ : Module 𝕜 E\ns✝ t s₁ s₂ t₁ t₂ u : Set E\nx y : E\ns : Set E\n⊢ convexJoin 𝕜 s ∅ = ∅",
"tactic": "simp [convexJoin]"
}
] | [
66,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/List/Permutation.lean | List.permutationsAux2_fst | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nt : α\nts : List α\nr : List β\ny : α\nys : List α\nf : List α → β\n⊢ (permutationsAux2 t ts r (y :: ys) f).fst = y :: ys ++ ts",
"tactic": "simp [permutationsAux2, permutationsAux2_fst t _ _ ys]"
}
] | [
60,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean | Geometry.SimplicialComplex.faces_bot | [] | [
255,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.natDegree_list_prod_le | [
{
"state_after": "case nil\nR : Type u\nι : Type w\ns : Finset ι\nS : Type u_1\ninst✝ : Semiring S\n⊢ natDegree (List.prod []) ≤ List.sum (List.map natDegree [])\n\ncase cons\nR : Type u\nι : Type w\ns : Finset ι\nS : Type u_1\ninst✝ : Semiring S\nhd : S[X]\ntl : List S[X]\nIH : natDegree (List.prod tl) ≤ List.... | [
82,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.image₂_right | [
{
"state_after": "α : Type u_2\nα' : Type ?u.69695\nβ : Type u_1\nβ' : Type ?u.69701\nγ : Type ?u.69704\nγ' : Type ?u.69707\nδ : Type ?u.69710\nδ' : Type ?u.69713\nε : Type ?u.69716\nε' : Type ?u.69719\nζ : Type ?u.69722\nζ' : Type ?u.69725\nν : Type ?u.69728\ninst✝⁸ : DecidableEq α'\ninst✝⁷ : DecidableEq β'\ni... | [
368,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Algebra/GradedMonoid.lean | SetLike.coe_gMul | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_of_le | [] | [
558,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | hasStrictFDerivAt_euclidean | [
{
"state_after": "𝕜 : Type u_1\nι : Type u_3\nH : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup H\ninst✝¹ : NormedSpace 𝕜 H\ninst✝ : Fintype ι\nf : H → EuclideanSpace 𝕜 ι\nf' : H →L[𝕜] EuclideanSpace 𝕜 ι\nt : Set H\ny : H\n⊢ (∀ (i : ι),\n HasStrictFDerivAt (fun x => (↑(EuclideanSpace.equiv... | [
326,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | norm_toNNReal' | [] | [
900,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
899,
1
] |
Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_eq_true | [] | [
692,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.prod_lt_prod_of_nonempty' | [
{
"state_after": "case Hle\nι : Type u_1\nα : Type ?u.128549\nβ : Type ?u.128552\nM : Type u_2\nN : Type ?u.128558\nG : Type ?u.128561\nk : Type ?u.128564\nR : Type ?u.128567\ninst✝ : OrderedCancelCommMonoid M\nf g : ι → M\ns t : Finset ι\nhs : Finset.Nonempty s\nHlt : ∀ (i : ι), i ∈ s → f i < g i\n⊢ ∀ (i : ι),... | [
456,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.coeff_pow_of_natDegree_le | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\npn : natDegree p ≤ n\n⊢ coeff (p ^ Nat.zero) (n * Nat.zero) = coeff p n ^ Nat.zero\n\ncase succ\nR : Type u\nS : Type v\nι : Type w\na b : R\nm✝ n : ℕ\ninst✝ : Semiring R\np q r : R[X]\npn : natD... | [
184,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.ext | [] | [
1815,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1814,
1
] |
Mathlib/Analysis/Normed/Group/Quotient.lean | NormedAddGroupHom.isQuotientQuotient | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\nN : Type ?u.464490\ninst✝¹ : SeminormedAddCommGroup M\ninst✝ : SeminormedAddCommGroup N\nS : AddSubgroup M\nm : M\n⊢ ‖↑(AddSubgroup.normedMk S) m‖ = sInf ((fun m_1 => ‖m + m_1‖) '' ↑(ker (AddSubgroup.normedMk S)))",
"tactic": "simpa [S.ker_norm... | [
378,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.ae_eq_trim_iff | [] | [
1807,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1804,
1
] |
Mathlib/CategoryTheory/Sites/Canonical.lean | CategoryTheory.Sheaf.isSheaf_of_representable | [] | [
228,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.isGLB | [
{
"state_after": "α : Type u_3\nβ : Type ?u.1210770\nγ : Type ?u.1210773\nγ₂ : Type ?u.1210776\nδ : Type u_2\nι✝ : Sort y\ns t u : Set α\ninst✝¹³ : TopologicalSpace α\ninst✝¹² : MeasurableSpace α\ninst✝¹¹ : BorelSpace α\ninst✝¹⁰ : TopologicalSpace β\ninst✝⁹ : MeasurableSpace β\ninst✝⁸ : BorelSpace β\ninst✝⁷ : T... | [
1138,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1131,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.choose_mem | [] | [
3060,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3059,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.subtypeDomain_add | [] | [
510,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Order/Bounds/Basic.lean | OrderTop.upperBounds_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝³ : Preorder α\ninst✝² : Preorder β\ns t : Set α\na b : α\ninst✝¹ : PartialOrder γ\ninst✝ : OrderTop γ\n⊢ upperBounds univ = {⊤}",
"tactic": "rw [isGreatest_univ.upperBounds_eq, Ici_top]"
}
] | [
812,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.zpowers_one_eq_bot | [] | [
225,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝⁴ : DecidableEq ι\ninst✝³ : (i : ι) → DecidableEq (α i)\ninst✝² : (i : ι) → PartialOrder (α i)\ninst✝¹ : (i : ι) → Zero (α i)\ninst✝ : (i : ι) → LocallyFiniteOrder (α i)\nf g : Π₀ (i : ι), α i\n⊢ card (Ioc f g) = ∏ i in suppo... | [
190,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.of_smul_filter | [] | [
1221,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1220,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Bundle.Trivial.trivialization_source | [] | [
88,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.set_integral_restrict | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nι : Type ?u.1446410\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ : { x // x ∈ kernel α β }\ns t✝ : Set β\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf : β → E\na : α\nhs : Mea... | [
524,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_lf_of_equiv | [] | [
831,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.mem_factors_mul_left | [
{
"state_after": "case inl\np b : ℕ\nhb : b ≠ 0\nhpa : p ∈ factors 0\n⊢ p ∈ factors (0 * b)\n\ncase inr\np a b : ℕ\nhpa : p ∈ factors a\nhb : b ≠ 0\nha : a ≠ 0\n⊢ p ∈ factors (a * b)",
"state_before": "p a b : ℕ\nhpa : p ∈ factors a\nhb : b ≠ 0\n⊢ p ∈ factors (a * b)",
"tactic": "rcases eq_or_ne a 0 wit... | [
289,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.eventually_lift'_iff | [] | [
270,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eq_zero_on_quadrant_I | [] | [
438,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.pow_subset_pow | [
{
"state_after": "F : Type ?u.52486\nα : Type u_1\nβ : Type ?u.52492\nγ : Type ?u.52495\ninst✝ : Monoid α\ns t : Set α\na : α\nm n : ℕ\nhst : s ⊆ t\n⊢ 1 ⊆ t ^ 0",
"state_before": "F : Type ?u.52486\nα : Type u_1\nβ : Type ?u.52492\nγ : Type ?u.52495\ninst✝ : Monoid α\ns t : Set α\na : α\nm n : ℕ\nhst : s ⊆ ... | [
960,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Analysis/LocallyConvex/AbsConvex.lean | AbsConvexOpenSets.coe_balanced | [] | [
119,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.hasPullback_assoc_symm | [] | [
2381,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2380,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.nextCoeffUp_C_eq_zero | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\nc : R\n⊢ (if natTrailingDegree (↑C c) = 0 then 0 else coeff (↑C c) (natTrailingDegree (↑C c) + 1)) = 0",
"state_before": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Semiring R\nc : R\n⊢ nextCoeffUp (↑C c) = 0",
"tacti... | [
490,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.disjoint_iff_right | [] | [
735,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.isLocalization_of_base_ringEquiv | [
{
"state_after": "R : Type u_1\ninst✝⁴ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝³ : CommSemiring S\ninst✝² : Algebra R S\nP : Type u_3\ninst✝¹ : CommSemiring P\ninst✝ : IsLocalization M S\nh : R ≃+* P\nthis : Algebra P S := RingHom.toAlgebra (RingHom.comp (algebraMap R S) (RingEquiv.toRingHom (Ring... | [
801,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Std/Data/List/Lemmas.lean | List.drop_suffix | [] | [
1719,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1718,
1
] |
Mathlib/RingTheory/Ideal/LocalRing.lean | LocalRing.maximalIdeal_eq_bot | [] | [
534,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
1
] |
Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.leftAdjointUniq_trans_app | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF F' F'' : C ⥤ D\nG : D ⥤ C\nadj1 : F ⊣ G\nadj2 : F' ⊣ G\nadj3 : F'' ⊣ G\nx : C\n⊢ (leftAdjointUniq adj1 adj2).hom.app x ≫ (leftAdjointUniq adj2 adj3).hom.app x =\n ((leftAdjointUniq adj1 adj2).hom ≫ (leftAdjointUniq adj2 ad... | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | LinearMap.toBilinAux_eq | [] | [
504,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.natAdd_natAdd | [] | [
1448,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1446,
1
] |
Mathlib/Algebra/Star/Pointwise.lean | Set.star_univ | [] | [
49,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.dense_induction | [
{
"state_after": "M : Type u_1\nN : Type ?u.25831\nA : Type ?u.25834\ninst✝¹ : MulOneClass M\ns✝ : Set M\ninst✝ : AddZeroClass A\nt : Set A\nS : Submonoid M\np : M → Prop\nx : M\ns : Set M\nhs : closure s = ⊤\nHs : ∀ (x : M), x ∈ s → p x\nH1 : p 1\nHmul : ∀ (x y : M), p x → p y → p (x * y)\nthis : ∀ (x : M), x ... | [
491,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.cons_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.78559\nn' : Type ?u.78562\no' : Type ?u.78565\ninst✝ : Zero α\nv : Fin n → α\nx : α\nh : vecCons x v = 0\n⊢ v = 0",
"tactic": "convert congr_arg vecTail h"
},
{
"state_after": "no goals",
"state_before": "α : T... | [
559,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Sheaf.existsUnique_gluing' | [
{
"state_after": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : ConcreteCategory C\ninst✝² : HasLimits C\ninst✝¹ : ReflectsIsomorphisms ConcreteCategory.forget\ninst✝ : PreservesLimits ConcreteCategory.forget\nX : TopCat\nF : Sheaf C X\nι : Type v\nU : ι → Opens ↑X\nV : Opens ↑X\niUV : (i : ι) → U i ⟶ V\nhcover : V... | [
270,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Data/List/Basic.lean | List.append_concat | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.25691\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ : List α\na : α\nl₁ l₂ : List α\n⊢ l₁ ++ concat l₂ a = concat (l₁ ++ l₂) a",
"tactic": "simp"
}
] | [
579,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.det_eq_neg_det_of_opposite_orientation | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nne : Nonempty ι\ne f : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\nh : Basis.orientation (OrthonormalBasis.toBasis e) ≠ Basis.orientation (OrthonormalBasis.t... | [
99,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Int/ModEq.lean | Int.exists_unique_equiv | [
{
"state_after": "m n a✝ b✝ c d a b : ℤ\nhb : 0 < b\nthis : a % b < abs b\n⊢ a % b < b",
"state_before": "m n a✝ b✝ c d a b : ℤ\nhb : 0 < b\n⊢ a % b < b",
"tactic": "have : a % b < |b| := emod_lt _ (ne_of_gt hb)"
},
{
"state_after": "no goals",
"state_before": "m n a✝ b✝ c d a b : ℤ\nhb : 0 ... | [
311,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.not_countable_real | [
{
"state_after": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\n⊢ ℵ₀ < 𝔠",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\n⊢ ¬Set.Countable Set.univ",
"tactic": "rw [← le_aleph0_iff_set_countable, not_le, mk_univ_real]"
},
{
"state_after": "no goals",
"state_before": "c : ℝ\nf g : ℕ → Bool\nn : ℕ\n⊢ ℵ₀ < 𝔠... | [
223,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.