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/PNat/Basic.lean | PNat.mul_div_exact | [
{
"state_after": "case a\nm k : ℕ+\nh : k ∣ m\n⊢ ↑(k * divExact m k) = ↑m",
"state_before": "m k : ℕ+\nh : k ∣ m\n⊢ k * divExact m k = m",
"tactic": "apply PNat.eq"
},
{
"state_after": "case a\nm k : ℕ+\nh : k ∣ m\n⊢ ↑k * ↑(divExact m k) = ↑m",
"state_before": "case a\nm k : ℕ+\nh : k ∣ m\n⊢... | [
435,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Konig.lean | TopCat.partialSections.directed | [
{
"state_after": "J✝ : Type v\ninst✝¹ : SmallCategory J✝\nJ : Type u\ninst✝ : SmallCategory J\nF : J ⥤ TopCat\nA B : TopCat.FiniteDiagram J\n⊢ ∃ z,\n (fun G => partialSections F G.snd) A ⊇ (fun G => partialSections F G.snd) z ∧\n (fun G => partialSections F G.snd) B ⊇ (fun G => partialSections F G.snd) ... | [
131,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_one | [] | [
479,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
478,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_filter_ne_one | [] | [
769,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | isPiSystem_Ico_mem | [] | [
200,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Topology/Order/Basic.lean | exists_Ico_subset_of_mem_nhds' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na : α\ns : Set α\nhs : s ∈ 𝓝 a\nu : α\nhu : a < u\n⊢ ∃ u', u' ∈ Ioc a u ∧ Ico a u' ⊆ s",
"tactic": "simpa only [OrderDual.exists, exists_prop, ... | [
1238,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.id_comp | [] | [
228,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.mono_left | [] | [
2922,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2920,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_self_homothety | [] | [
162,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.I_to_real | [] | [
854,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Topology/ContinuousOn.lean | mem_nhdsWithin_subtype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.302592\nγ : Type ?u.302595\nδ : Type ?u.302598\ninst✝ : TopologicalSpace α\ns : Set α\na : { x // x ∈ s }\nt u : Set { x // x ∈ s }\n⊢ t ∈ 𝓝[u] a ↔ t ∈ comap Subtype.val (𝓝[Subtype.val '' u] ↑a)",
"tactic": "rw [nhdsWithin, nhds_s... | [
488,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Topology/Inseparable.lean | Specializes.prod | [] | [
212,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_zero | [
{
"state_after": "case mp\n𝕜 : Type u\ninst✝⁸ : NontriviallyNormedField 𝕜\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 : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nX : Type uX\ninst✝¹ : ... | [
981,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
969,
1
] |
Mathlib/Analysis/Complex/Basic.lean | IsROrC.normSq_to_complex | [] | [
477,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.measurePreserving_swap | [] | [
518,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Data/List/MinMax.lean | List.argmax_concat | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder β\ninst✝ : DecidableRel fun x x_1 => x < x_1\nf✝ : α → β\nl✝ : List α\no : Option α\na✝ m : α\nf : α → β\na : α\nl : List α\n⊢ foldl (argAux fun b c => f c < f b) none (l ++ [a]) =\n Option.casesOn (foldl (argAux fun b c => f c < f b) none l) (s... | [
143,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/LinearAlgebra/Ray.lean | SameRay.trans | [
{
"state_after": "case inl\nR : Type u_1\ninst✝⁵ : StrictOrderedCommSemiring R\nM : Type u_2\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nN : Type ?u.13611\ninst✝² : AddCommMonoid N\ninst✝¹ : Module R N\nι : Type ?u.13693\ninst✝ : DecidableEq ι\ny z : M\nhyz : SameRay R y z\nhxy : SameRay R 0 y\nhy : y = 0 →... | [
117,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.of_mul_left | [] | [
386,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | nndist_right_midpoint | [] | [
212,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nf✝ : R[X]\nN : ℕ\nf : R[X]\n⊢ reflect N f = 0 ↔ f = 0",
"tactic": "rw [ofFinsupp_eq_zero, reflect, embDomain_eq_zero, ofFinsupp_eq_zero]"
}
] | [
131,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.unit_left | [] | [
201,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.ofReal_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.814833\nβ : Type ?u.814836\na b c d : ℝ≥0∞\nr p✝ q✝ : ℝ≥0\np q : ℝ\nhq : 0 ≤ q\n⊢ ENNReal.ofReal (p * q) = ENNReal.ofReal p * ENNReal.ofReal q",
"tactic": "rw [mul_comm, ofReal_mul hq, mul_comm]"
}
] | [
2174,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2172,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_int_mul_iff | [
{
"state_after": "no goals",
"state_before": "q : ℚ\nm : ℤ\nn : ℕ\nx : ℝ\n⊢ Irrational (↑m * x) ↔ m ≠ 0 ∧ Irrational x",
"tactic": "rw [← cast_coe_int, irrational_rat_mul_iff, Int.cast_ne_zero]"
}
] | [
614,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
src/lean/Init/Prelude.lean | Eq.symm | [] | [
311,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
310,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_add_two_add_one | [
{
"state_after": "no goals",
"state_before": "n✝ b n : ℕ\n⊢ digits (b + 2) (n + 1) = (n + 1) % (b + 2) :: digits (b + 2) ((n + 1) / (b + 2))",
"tactic": "simp [digits, digitsAux_def]"
}
] | [
121,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasStrictFDerivAt_exp_smul_const' | [] | [
405,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Data/List/Intervals.lean | List.Ico.filter_le_of_top_le | [
{
"state_after": "n m l : ℕ\nhml : m ≤ l\nk : ℕ\nhk : k ∈ Ico n m\n⊢ ¬l ≤ k",
"state_before": "n m l : ℕ\nhml : m ≤ l\nk : ℕ\nhk : k ∈ Ico n m\n⊢ ¬decide (l ≤ k) = true",
"tactic": "rw [decide_eq_true_eq]"
},
{
"state_after": "no goals",
"state_before": "n m l : ℕ\nhml : m ≤ l\nk : ℕ\nhk : k... | [
197,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/List/Basic.lean | List.getLastI_eq_getLast? | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.38004\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\ninst✝ : Inhabited α\n⊢ getLastI [] = Option.iget (getLast? [])",
"tactic": "simp [getLastI, Inhabited.default]"
},
{
"state_after": "no goals",
"state_before": "ι ... | [
830,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/CategoryTheory/Sites/CompatiblePlus.lean | CategoryTheory.GrothendieckTopology.plusCompIso_whiskerLeft | [
{
"state_after": "case w.h\nC : Type u\ninst✝¹² : Category C\nJ : GrothendieckTopology C\nD : Type w₁\ninst✝¹¹ : Category D\nE : Type w₂\ninst✝¹⁰ : Category E\nF✝ : D ⥤ E\ninst✝⁹ : ∀ (α β : Type (max v u)) (fst snd : β → α), HasLimitsOfShape (WalkingMulticospan fst snd) D\ninst✝⁸ : ∀ (α β : Type (max v u)) (fst... | [
156,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Algebra/Associated.lean | Associates.mk_dvd_mk | [] | [
948,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
947,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.inf_objs_exists | [
{
"state_after": "case empty\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsCofiltered C\n⊢ ∃ S, ∀ {X : C}, X ∈ ∅ → _root_.Nonempty (S ⟶ X)\n\ncase insert\nC : Type u\ninst✝¹ : Category C\ninst✝ : IsCofiltered C\nX : C\nO' : Finset C\nnm : ¬X ∈ O'\nh : ∃ S, ∀ {X : C}, X ∈ O' → _root_.Nonempty (S ⟶ X)\n⊢ ∃ S, ∀ {X_... | [
631,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_mono_left | [] | [
237,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsWf.min_le | [] | [
643,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | Algebra.ofId_apply | [] | [
562,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_one | [] | [
150,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nth_zip | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Std/Data/List/Lemmas.lean | List.length_tail | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ length (tail l) = length l - 1",
"tactic": "cases l <;> rfl"
}
] | [
865,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
865,
9
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.prod_pprod | [] | [
898,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Order/Bounds/Basic.lean | subset_upperBounds_lowerBounds | [] | [
262,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.mem_mk | [] | [
61,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.isNormal_iff_strictMono_limit | [] | [
428,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.sub_toProd | [] | [
233,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.toBasis_orthonormalBasisOneI | [] | [
644,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
642,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.set_eventuallyLE_iff_inf_principal_le | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.209114\nι : Sort x\ns t : Set α\nl : Filter α\n⊢ t ∈ l ⊓ 𝓟 s ↔ l ⊓ 𝓟 s ≤ l ⊓ 𝓟 t",
"tactic": "simp only [le_inf_iff, inf_le_left, true_and_iff, le_principal_iff]"
}
] | [
1744,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1741,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_def | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.278467\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝¹ : CommSemiring R\np✝ q : MvPolynomial σ R\ninst✝ : DecidableEq σ\nn : σ\np : MvPolynomial σ R\n⊢ Multiset.count n (degrees p) = Multiset.count n (degrees p)",
"state_before": "R : Type u\nS... | [
493,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Mathlib/CategoryTheory/Abelian/Basic.lean | CategoryTheory.Abelian.monoLift_comp | [] | [
502,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.add_nat | [] | [
259,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Ici_eq_integral_Ioi' | [] | [
642,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_bot | [] | [
1023,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1022,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.Lex.mono_right | [] | [
524,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictAnti_comp_ofDual_iff | [] | [
187,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.last_sub | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ni : Fin (n + 1)\n⊢ ↑(last n - i) = ↑(↑rev i)",
"tactic": "rw [coe_sub_iff_le.2 i.le_last, val_last, val_rev, Nat.succ_sub_succ_eq_sub]"
}
] | [
2009,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2008,
1
] |
Mathlib/Topology/SubsetProperties.lean | IsCompact.compl_mem_cocompact | [] | [
538,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
537,
1
] |
Mathlib/Computability/Ackermann.lean | add_lt_ack | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ 0 + n < ack 0 n",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "m : ℕ\n⊢ m + 1 + 0 < ack (m + 1) 0",
"tactic": "simpa using add_lt_ack m 1"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ m... | [
188,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_add | [] | [
193,
25
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
192,
11
] |
Mathlib/GroupTheory/Coset.lean | Subgroup.card_eq_card_quotient_mul_card_subgroup | [
{
"state_after": "α : Type u_1\ninst✝³ : Group α\ns✝ t : Subgroup α\ninst✝² : Fintype α\ns : Subgroup α\ninst✝¹ : Fintype { x // x ∈ s }\ninst✝ : DecidablePred fun a => a ∈ s\n⊢ Fintype.card α = Fintype.card ((α ⧸ s) × { x // x ∈ s })",
"state_before": "α : Type u_1\ninst✝³ : Group α\ns✝ t : Subgroup α\nins... | [
785,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_zero | [] | [
626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean | Euclidean.isOpen_ball | [] | [
78,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Localization.one_rel | [] | [
420,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.biUnion_subset_biUnion_of_subset_left | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.518185\ninst✝ : DecidableEq β\ns s₁ s₂ : Finset α\nt✝ t₁ t₂ t : α → Finset β\nh : s₁ ⊆ s₂\nx : β\n⊢ x ∈ Finset.biUnion s₁ t → x ∈ Finset.biUnion s₂ t",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.518185\ninst✝ : DecidableEq β\ns s₁ s₂ : ... | [
3616,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3612,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.size_push | [] | [
65,
24
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
64,
9
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_atBot | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∃ v, v ∈ atBot ∧ ∀ (y : ℝ), y ∈ v → HasDerivAt f (f' y) y\nhgg' : ∃ v, v ∈ atBot ∧ ∀ (y : ℝ), y ∈ v → HasDerivAt g (g' y) y\nhg' : ∃ v, v ∈ atBot ∧ ∀ (y : ℝ), y ∈ v → g' y ≠ 0\nhfbot : Tendsto f atBot (𝓝 0)\nhgbot : Tendsto g atBot... | [
375,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_nsmul | [] | [
1224,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1223,
1
] |
Mathlib/Topology/MetricSpace/Polish.lean | PolishSpace.IsClopenable.compl | [
{
"state_after": "case intro.intro.intro.intro\nα : Type u_1\nβ : Type ?u.67736\ninst✝ : TopologicalSpace α\ns : Set α\nt : TopologicalSpace α\nt_le : t ≤ inst✝\nt_polish : PolishSpace α\nh : IsClosed s\nh' : IsOpen s\n⊢ IsClopenable (sᶜ)",
"state_before": "α : Type u_1\nβ : Type ?u.67736\ninst✝ : Topologic... | [
403,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_congr_of_surjective | [] | [
444,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | IsCompact.isSeparable | [] | [
2247,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2245,
1
] |
Mathlib/CategoryTheory/Monoidal/Rigid/Basic.lean | CategoryTheory.tensorLeftHomEquiv_id_tensor_comp_evaluation | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCategory C\nY Z : C\ninst✝ : HasLeftDual Z\nf : Y ⟶ ᘁZ\n⊢ (λ_ Y).inv ≫ (η_ (ᘁZ) Z ⊗ 𝟙 Y) ≫ (α_ (ᘁZ) Z Y).hom ≫ (𝟙 ᘁZ ⊗ (𝟙 Z ⊗ f) ≫ ε_ (ᘁZ) Z) = f ≫ (ρ_ ᘁZ).inv",
"state_before": "C : Type u₁\ninst✝² : Category C\ninst✝¹ : MonoidalCatego... | [
516,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.coe_mk | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Order/RelClasses.lean | transitive_lt | [] | [
905,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Data/Sigma/Basic.lean | Sigma.forall | [] | [
92,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.mul_eq_one_iff | [
{
"state_after": "case refine'_1\nι : Type ?u.338842\nα : Type u_1\ninst✝ : OrderedCommGroup α\ns t : NonemptyInterval α\nh : s * t = 1\n⊢ ∃ a b, s = pure a ∧ t = pure b ∧ a * b = 1\n\ncase refine'_2\nι : Type ?u.338842\nα : Type u_1\ninst✝ : OrderedCommGroup α\ns t : NonemptyInterval α\n⊢ (∃ a b, s = pure a ∧ ... | [
540,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
11
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_div_gcd_div_gcd | [
{
"state_after": "no goals",
"state_before": "i j : ℤ\nH : 0 < gcd i j\n⊢ gcd (i / ↑(gcd i j)) (j / ↑(gcd i j)) = 1",
"tactic": "rw [gcd_div (gcd_dvd_left i j) (gcd_dvd_right i j), natAbs_ofNat, Nat.div_self H]"
}
] | [
334,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Algebra/GradedMonoid.lean | List.dProdIndex_cons | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.two_mul_sub_one_mem_iff | [
{
"state_after": "no goals",
"state_before": "t : ℝ\n⊢ 2 * t - 1 ∈ I ↔ t ∈ Icc (1 / 2) 1",
"tactic": "constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith"
}
] | [
178,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Std/Logic.lean | exists_eq_left' | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\np q : α → Prop\nb : Prop\na' : α\n⊢ (∃ a, a' = a ∧ p a) ↔ p a'",
"tactic": "simp [@eq_comm _ a']"
}
] | [
467,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
467,
9
] |
Mathlib/Order/Filter/AtTopBot.lean | Function.Injective.map_atTop_finset_prod_eq | [
{
"state_after": "ι : Type ?u.378253\nι' : Type ?u.378256\nα : Type u_1\nβ : Type u_3\nγ : Type u_2\ninst✝ : CommMonoid α\ng : γ → β\nhg : Injective g\nf : β → α\nhf : ∀ (x : β), ¬x ∈ Set.range g → f x = 1\nthis : DecidableEq β\n⊢ Filter.map (fun s => ∏ i in s, f (g i)) atTop = Filter.map (fun s => ∏ i in s, f ... | [
1972,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1957,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.toDual_inf | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Data/QPF/Multivariate/Basic.lean | MvQPF.suppPreservation_iff_isUniform | [
{
"state_after": "case mp\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\n⊢ SuppPreservation → IsUniform\n\ncase mpr\nn : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\nq : MvQPF F\n⊢ IsUniform → SuppPreservation",
"state_before": "n : ℕ\nF : TypeVec n → Type u_1\ninst✝ : MvFunctor F\... | [
267,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.add_toZNum | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.456739\nm n : Num\n⊢ toZNum (m + n) = toZNum m + toZNum n",
"tactic": "cases m <;> cases n <;> rfl"
}
] | [
800,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.mk_coe | [
{
"state_after": "case h\nR : Type u\nL₁ : Type v\nL₂ : Type w\nL₃ : Type w₁\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L₁\ninst✝⁴ : LieAlgebra R L₁\ninst✝³ : LieRing L₂\ninst✝² : LieAlgebra R L₂\ninst✝¹ : LieRing L₃\ninst✝ : LieAlgebra R L₃\nf : L₁ →ₗ⁅R⁆ L₂\nh₁ : ∀ (x y : L₁), ↑f (x + y) = ↑f x + ↑f y\nh₂ :\n ∀ (... | [
401,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_pow | [] | [
823,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
11
] |
Mathlib/LinearAlgebra/Matrix/IsDiag.lean | Matrix.isDiag_neg_iff | [] | [
92,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | MonoidHom.map_neg | [
{
"state_after": "no goals",
"state_before": "β : Type ?u.296855\nA : Type ?u.296858\nG : Type ?u.296861\nM : Type u_1\nR : Type u_2\ninst✝³ : Ring R\ninst✝² : Monoid M\ninst✝¹ : LinearOrder M\ninst✝ : CovariantClass M M (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\nf : R →* M\nx : R\n⊢ ↑f (-x) = ↑f x",
... | [
805,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/MeasureTheory/Measure/OpenPos.lean | EMetric.measure_closedBall_pos | [] | [
207,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_right_injective | [] | [
522,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.Measure.toSignedMeasure_eq_toSignedMeasure_iff | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.135386\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\nh : toSignedMeasure μ = toSignedMeasure ν\n⊢ μ = ν\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.135386\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝... | [
458,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Group.conjugates_subset_normal | [
{
"state_after": "G : Type u_1\nG' : Type ?u.435622\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.435631\ninst✝ : AddGroup A\ns : Set G\nN : Subgroup G\ntn : Subgroup.Normal N\na✝ : G\nh : a✝ ∈ N\na : G\nhc : a ∈ conjugatesOf a✝\n⊢ a ∈ ↑N",
"state_before": "G : Type u_1\nG' : Type ?u.435622\ninst✝² : Gr... | [
2430,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2426,
1
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.Functor.sum_map_inr | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.option_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.21098\nσ : Type ?u.21101\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nn : ℕ\n⊢ (Nat.casesOn (encode (decode n)) 0 fun n => Nat.succ (Nat.succ n)) = encode (Option.map some (decode n))",
"tactic": "cases @d... | [
246,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/GroupTheory/Perm/Option.lean | Equiv.Perm.decomposeOption_symm_sign | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ne : Perm α\n⊢ ↑sign (↑decomposeOption.symm (none, e)) = ↑sign e",
"tactic": "simp"
}
] | [
81,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Tactic/NormNum/Core.lean | Mathlib.Meta.NormNum.IsNat.to_raw_eq | [] | [
52,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | TopologicalSpace.Opens.localHomeomorphSubtypeCoe_coe | [] | [
1337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1336,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.prod_same_eq | [] | [
433,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Order/Lattice.lean | le_sup_left | [] | [
132,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Combinatorics/Pigeonhole.lean | Finset.exists_le_card_fiber_of_mul_le_card_of_maps_to | [] | [
289,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Order/Heyting/Basic.lean | sup_himp_self_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.72997\nα : Type u_1\nβ : Type ?u.73003\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c d a b : α\n⊢ a ⊔ b ⇨ b = a ⇨ b",
"tactic": "rw [sup_himp_distrib, himp_self, inf_top_eq]"
}
] | [
433,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.range_snd | [] | [
1285,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1284,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ring.not_isField_iff_exists_prime | [] | [
774,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Logic/Equiv/TransferInstance.lean | Equiv.mulEquiv_symm_apply | [
{
"state_after": "α : Type u\nβ : Type v\ne✝ e : α ≃ β\ninst✝ : Mul β\nb : β\n⊢ ↑(MulEquiv.symm (mulEquiv e)) b = ↑e.symm b",
"state_before": "α : Type u\nβ : Type v\ne✝ e : α ≃ β\ninst✝ : Mul β\nb : β\n⊢ ↑(MulEquiv.symm (mulEquiv e)) b = ↑e.symm b",
"tactic": "intros"
},
{
"state_after": "no go... | [
158,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
] |
Mathlib/Topology/Instances/Real.lean | Real.uniformContinuous_const_mul | [] | [
126,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
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