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/Computability/Primrec.lean | Primrec₂.left | [] | [
430,
7
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429,
1
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Mathlib/Data/List/Perm.lean | List.Perm.countp_eq | [
{
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474,
87
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472,
1
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Mathlib/Data/Real/Sqrt.lean | Real.sqrt_nonneg | [] | [
196,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
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Mathlib/Algebra/Module/Equiv.lean | LinearEquiv.map_add | [] | [
494,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
493,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_toIsometryEquiv | [] | [
451,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
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Mathlib/Order/CompleteLattice.lean | iInf_eq_of_forall_ge_of_forall_gt_exists_lt | [] | [
1115,
59
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1113,
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Mathlib/Data/Set/Finite.lean | Set.finite_univ_iff | [] | [
716,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
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Mathlib/Topology/Algebra/Monoid.lean | Submonoid.le_topologicalClosure | [] | [
445,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.le_sup_left | [
{
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... | [
474,
20
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470,
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Mathlib/Order/Cover.lean | Covby.eq_or_eq | [] | [
396,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange.addMonoidHom_toZeroHom | [] | [
234,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
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Mathlib/Analysis/Analytic/Basic.lean | analyticOn_const | [] | [
534,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
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Mathlib/Data/Set/Ncard.lean | Set.subset_iff_eq_of_ncard_le | [] | [
329,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
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Mathlib/Algebra/Order/Kleene.lean | kstar_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.48091\nι : Type ?u.48094\nπ : ι → Type ?u.48099\ninst✝ : KleeneAlgebra α\na b c : α\nh : a∗ = a\n⊢ a * a = a",
"tactic": "rw [← h, kstar_mul_kstar]"
}
] | [
273,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | Subalgebra.starClosure_le | [] | [
400,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
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src/lean/Init/Core.lean | Quotient.rel_of_eq | [] | [
1497,
38
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1496,
9
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.range_comp_of_range_eq_top | [
{
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1718,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Lipschitz.lean | Metric.Bounded.left_of_prod | [
{
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"tactic": "simpa only [fst_image_prod s ht] using (@LipschitzWith.prod_f... | [
480,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.homothety_mul | [] | [
822,
37
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820,
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Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_toAddSubmonoid | [] | [
154,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_filter_lt_of_lt_right | [] | [
351,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
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Std/Data/List/Lemmas.lean | List.not_mem_cons_of_ne_of_not_mem | [] | [
101,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
100,
1
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Mathlib/Analysis/NormedSpace/Star/Mul.lean | mul_flip_isometry | [] | [
73,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.index_union_le | [
{
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234,
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225,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.lmul'_comp_includeRight | [] | [
953,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
952,
1
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Std/Data/AssocList.lean | Std.AssocList.toList_eq_toListTR | [
{
"state_after": "case h.h.h\nα : Type u_2\nβ : Type u_1\nas : AssocList α β\n⊢ toList as = toListTR as",
"state_before": "⊢ @toList = @toListTR",
"tactic": "funext α β as"
},
{
"state_after": "case h.h.h\nα : Type u_2\nβ : Type u_1\nas : AssocList α β\n⊢ toList as = (List.foldl (fun d x => Arra... | [
69,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
67,
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Mathlib/Data/List/Basic.lean | List.enum_append | [
{
"state_after": "no goals",
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"tactic": "simp [enum, enumFrom_append]"
}
] | [
3905,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3904,
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Mathlib/Order/Hom/Lattice.lean | SupHom.coe_top | [] | [
495,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.algebraMap_eq | [] | [
1309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1307,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.map_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nf : α → β\nhf : LeftOrdContinuous f\ns : Set α\n⊢ f (sSup s) = ⨆ (x : α) (_ : x ∈ s), f x",
"tactic": "rw [hf.map_sSup', sSup_image]"
}
] | [
135,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Disjointed.lean | disjointed_subset | [] | [
167,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_of_subsingleton | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.1406680\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.140677... | [
1121,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
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Mathlib/LinearAlgebra/Matrix/Charpoly/Minpoly.lean | Matrix.minpoly_toLin | [] | [
50,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.Measure.measure_preimage_inv | [] | [
421,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
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Mathlib/Logic/Equiv/Basic.lean | Equiv.symm_trans_swap_trans | [
{
"state_after": "α : Sort u_2\ninst✝¹ : DecidableEq α\nβ : Sort u_1\ninst✝ : DecidableEq β\na b : α\ne : α ≃ β\nx : β\nthis : ∀ (a : (fun x => α) x), ↑e.symm x = a ↔ x = ↑e a\n⊢ ↑((e.symm.trans (swap a b)).trans e) x = ↑(swap (↑e a) (↑e b)) x",
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1608,
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Mathlib/FieldTheory/Adjoin.lean | PowerBasis.equivAdjoinSimple_gen | [] | [
1294,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1292,
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] |
Mathlib/Data/List/Basic.lean | List.scanr_nil | [] | [
2680,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2679,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | trop_iInf | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : ConditionallyCompleteLinearOrder R\ninst✝ : Fintype S\nf : S → WithTop R\n⊢ trop (⨅ (i : S), f i) = ∑ i : S, trop (f i)",
"tactic": "rw [iInf, ← Set.image_univ, ← coe_univ, trop_sInf_image]"
}
] | [
113,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_nnreal' | [
{
"state_after": "α : Type u_2\nβ : Type ?u.2014\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : PseudoMetrizableSpace β\ninst✝³ : MeasurableSpace β\ninst✝² : BorelSpace β\nι : Type u_1\nf : ι → α → ℝ≥0\ng : α → ℝ≥0\nu : Filter ι\ninst✝¹ : NeBot u\ninst✝ : IsCountablyGenerated u\nlim : Tendst... | [
58,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Init/Function.lean | Function.RightInverse.surjective | [] | [
111,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/GroupTheory/Subgroup/ZPowers.lean | Subgroup.range_zpowersHom | [] | [
49,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balanceL_eq_balance | [
{
"state_after": "case nil\nα : Type u_1\nl : Ordnode α\nx : α\nsl : Sized l\nsr : Sized nil\nH1 : size l = 0 → size nil ≤ 1\nH2 : 1 ≤ size l → 1 ≤ size nil → size nil ≤ delta * size l\n⊢ balanceL l x nil = balance l x nil\n\ncase node\nα : Type u_1\nl : Ordnode α\nx : α\nsl : Sized l\nrs : ℕ\nrl : Ordnode α\nr... | [
774,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | tendsto_of_no_upcrossings | [
{
"state_after": "case pos\nα : Type u\nβ : Type v\ninst✝³ : ConditionallyCompleteLinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : DenselyOrdered α\nf : Filter β\nu : β → α\ns : Set α\nhs : Dense s\nH : ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a < b → ¬((∃ᶠ (n : β) in f, u n < a) ∧ ∃ᶠ ... | [
253,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Analysis/Normed/Group/HomCompletion.lean | NormedAddCommGroup.denseRange_toCompl | [] | [
154,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | min_abs_abs_le_abs_min | [] | [
338,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Deprecated/Subfield.lean | Field.closure.isSubfield | [
{
"state_after": "F : Type u_1\ninst✝ : Field F\nS : Set F\nsrc✝ : IsSubmonoid (closure S) := isSubmonoid\na b : F\nha : a ∈ closure S\nhb : b ∈ closure S\n⊢ a + b ∈ closure S",
"state_before": "F : Type u_1\ninst✝ : Field F\nS : Set F\nsrc✝ : IsSubmonoid (closure S) := isSubmonoid\n⊢ ∀ {a b : F}, a ∈ closu... | [
125,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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] |
Mathlib/Topology/ContinuousOn.lean | ContinuousWithinAt.congr_mono | [] | [
974,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
1
] |
Mathlib/Computability/Partrec.lean | Computable.succ | [] | [
322,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalExtrOn.inter | [] | [
129,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.ofLE_mk_le_mk_of_comm | [
{
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339,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
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] |
Mathlib/Data/Fintype/Basic.lean | Finset.univ_unique | [] | [
123,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Algebra/Lie/Basic.lean | nsmul_lie | [] | [
193,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/Constructions.lean | embedding_inclusion | [] | [
1124,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.one_sub_X_sq_mul_U_eq_pol_in_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.37792\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nn : ℕ\n⊢ (1 - X ^ 2) * U R n = X * T R (n + 1) - T R (n + 2)",
"tactic": "rw [T_eq_X_mul_T_sub_pol_U, ← sub_add, sub_self, zero_add]"
}
] | [
158,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_reindex_apply | [
{
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432,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Data/Set/Function.lean | Monotone.restrict | [] | [
1328,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
11
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | isLUB_ciSup_set | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.31436\nι : Sort ?u.31439\ninst✝ : ConditionallyCompleteLattice α\ns✝ t : Set α\na b : α\nf : β → α\ns : Set β\nH : BddAbove (f '' s)\nHne : Set.Nonempty s\n⊢ IsLUB (f '' s) (sSup (f '' s))",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.31... | [
495,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_add_of_neg_add_le_right | [
{
"state_after": "a b c : Int\nh : a + -c ≤ b\n⊢ a ≤ b + c",
"state_before": "a b c : Int\nh : -c + a ≤ b\n⊢ a ≤ b + c",
"tactic": "rw [Int.add_comm] at h"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh : a + -c ≤ b\n⊢ a ≤ b + c",
"tactic": "exact Int.le_add_of_sub_right... | [
1008,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1006,
11
] |
Mathlib/Algebra/Hom/Group.lean | map_zpow' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.55822\nβ : Type ?u.55825\nM : Type ?u.55828\nN : Type ?u.55831\nP : Type ?u.55834\nG : Type u_1\nH : Type u_2\nF : Type u_3\ninst✝⁴ : MulOneClass M\ninst✝³ : MulOneClass N\ninst✝² : DivInvMonoid G\ninst✝¹ : DivInvMonoid H\ninst✝ : MonoidHomClass F G ... | [
459,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
src/lean/Init/Prelude.lean | eq_of_heq | [] | [
455,
22
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
451,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.toWithTop_top' | [
{
"state_after": "no goals",
"state_before": "h : Decidable ⊤.Dom\n⊢ toWithTop ⊤ = ⊤",
"tactic": "convert toWithTop_top"
}
] | [
559,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.isComplete_map_iff' | [] | [
259,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.le_rpow_of_log_le | [
{
"state_after": "case inl\nx y z : ℝ\nhx✝ : 0 ≤ x\nhy : 0 < y\nh : log x ≤ z * log y\nhx : 0 < x\n⊢ x ≤ y ^ z\n\ncase inr\ny z : ℝ\nhy : 0 < y\nhx : 0 ≤ 0\nh : log 0 ≤ z * log y\n⊢ 0 ≤ y ^ z",
"state_before": "x y z : ℝ\nhx : 0 ≤ x\nhy : 0 < y\nh : log x ≤ z * log y\n⊢ x ≤ y ^ z",
"tactic": "obtain hx ... | [
599,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.attach_zero | [] | [
1568,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.sInf_le | [] | [
1176,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1174,
11
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.strictMono_y | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : m < n + 1\nthis : yn a1 m ≤ yn a1 n\n⊢ yn a1 m < yn a1 (n + 1)",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : m < n + 1\n⊢ yn a1 m < yn a1 (n + 1)",
"tactic": "have : yn a1 m ≤ yn a1 n :=\n Or.elim (lt_or_eq_of_le <| Nat.le_of_succ_le_succ h) (fun h... | [
412,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.isIso_ι_of_isTerminal | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nJ : Type u\ninst✝¹ : Category J\nj : J\nI : IsTerminal j\nF : J ⥤ C\ninst✝ : HasColimit F\n⊢ colimit.ι F j ≫ colimit.desc F (coconeOfDiagramTerminal I F) = 𝟙 (F.obj j)",
"tactic": "simp"
},
{
"state_after": "case w\... | [
733,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
731,
1
] |
Mathlib/RingTheory/ClassGroup.lean | ClassGroup.mk_mk0 | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nK : Type u_2\nL : Type ?u.1219112\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : DecidableEq L\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : Algebra K L\ninst✝⁴ : FiniteDimensional K L\ninst✝³ : Algebra R L\nins... | [
268,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_one | [] | [
141,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
141,
9
] |
Mathlib/Order/WithBot.lean | WithBot.forall | [] | [
71,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
11
] |
Mathlib/Data/Int/Log.lean | Int.log_zero_right | [] | [
126,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.exists_mem_support_of_mem_support_prod | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nl : List (Perm α)\nx : α\nhx : ∀ (f : Perm α), f ∈ l → ¬x ∈ support f\n⊢ ¬x ∈ support (List.prod l)",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nl : List (Perm α)\nx : α\nhx ... | [
346,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.coe_toEquiv_symm | [] | [
1222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.gcd_dvd | [
{
"state_after": "case pos\nx y z : ℤ\nh : PythagoreanTriple x y z\nh0 : Int.gcd x y = 0\n⊢ ↑(Int.gcd x y) ∣ z\n\ncase neg\nx y z : ℤ\nh : PythagoreanTriple x y z\nh0 : ¬Int.gcd x y = 0\n⊢ ↑(Int.gcd x y) ∣ z",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\n⊢ ↑(Int.gcd x y) ∣ z",
"tactic": "by_... | [
182,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Order/SupIndep.lean | Finset.supIndep_iff_pairwiseDisjoint | [] | [
152,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Analysis/Calculus/LHopital.lean | HasDerivAt.lhopital_zero_atBot_on_Iio | [
{
"state_after": "a b : ℝ\nhab : a < b\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ (x : ℝ), x ∈ Iio a → HasDerivAt f (f' x) x\nhgg' : ∀ (x : ℝ), x ∈ Iio a → HasDerivAt g (g' x) x\nhg' : ∀ (x : ℝ), x ∈ Iio a → g' x ≠ 0\nhfbot : Tendsto f atBot (𝓝 0)\nhgbot : Tendsto g atBot (𝓝 0)\nhdiv : Tendsto (fun x => f' x ... | [
203,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/MvPolynomial/CommRing.lean | MvPolynomial.C_sub | [] | [
66,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.min'_singleton | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.336329\nα : Type u_1\nβ : Type ?u.336335\nγ : Type ?u.336338\nι : Type ?u.336341\nκ : Type ?u.336344\ninst✝ : LinearOrder α\ns : Finset α\nH : Finset.Nonempty s\nx a : α\n⊢ min' {a} (_ : Finset.Nonempty {a}) = a",
"tactic": "simp [min']"
}
] | [
1347,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1347,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_one | [
{
"state_after": "no goals",
"state_before": "⊢ 0 < 1",
"tactic": "norm_num"
}
] | [
51,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/CategoryTheory/Monoidal/Preadditive.lean | CategoryTheory.leftDistributor_rightDistributor_assoc | [
{
"state_after": "case w.w\nC : Type u_2\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\ninst✝³ : MonoidalCategory C\ninst✝² : MonoidalPreadditive C\ninst✝¹ : HasFiniteBiproducts C\nJ : Type\ninst✝ : Fintype J\nX Y : C\nf : J → C\nj✝ : J\n⊢ ((leftDistributor X f ⊗ asIso (𝟙 Y)) ≪≫ rightDistributor Y fun j => X ⊗ ... | [
238,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.le_inter_add_diff | [
{
"state_after": "case h.e'_3.h.e'_3\nα : Type u_1\nβ : Type ?u.18650\nR : Type ?u.18653\nR' : Type ?u.18656\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\nt s : Set α\n⊢ t = t ∩ s ∪ t \\ s",
"state_before": "α : Type u_1\nβ : Type ?u.18650\nR : Type ?u.18653\nR' : Type ?u.18656\nms : Set (OuterMeasure ... | [
223,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_ite_zero_one | [
{
"state_after": "case inl\nF✝ : Type ?u.81005\nα : Type u_2\nβ : Type u_3\nγ : Type ?u.81014\nx✝¹ : NonAssocSemiring α\nx✝ : NonAssocSemiring β\nf✝ : α →+* β\nx y : α\nF : Type u_1\ninst✝¹ : RingHomClass F α β\nf : F\np : Prop\ninst✝ : Decidable p\nh : p\n⊢ ↑f (if p then 0 else 1) = 0\n\ncase inr\nF✝ : Type ?u... | [
585,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | ofLex_div | [] | [
279,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Topology/SubsetProperties.lean | finite_of_compact_of_discrete | [] | [
791,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.mono | [] | [
78,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.algebraMap_apply' | [] | [
2693,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2692,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_apply | [] | [
180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.eq_rootMultiplicity_map | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝¹ : CommRing A\ninst✝ : CommRing B\np : A[X]\nf : A →+* B\nhf : Function.Injective ↑f\na : A\nhp0 : p = 0\n⊢ rootMultiplicity a p = rootMultiplicity (↑f a) (map f p)\n\ncase neg\nR : Type u\nS : Typ... | [
1157,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1151,
1
] |
Mathlib/Algebra/Homology/Homotopy.lean | homology_map_eq_of_homotopy | [
{
"state_after": "ι : Type u_1\nV : Type u\ninst✝⁵ : Category V\ninst✝⁴ : Preadditive V\nc : ComplexShape ι\nC D E : HomologicalComplex V c\nf g : C ⟶ D\nh✝ k : D ⟶ E\ni✝ : ι\ninst✝³ : HasEqualizers V\ninst✝² : HasCokernels V\ninst✝¹ : HasImages V\ninst✝ : HasImageMaps V\nh : Homotopy f g\ni : ι\n⊢ homology.map... | [
778,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.nat_rec | [
{
"state_after": "case some\nα : Type u_1\nβ : Type ?u.63305\nγ : Type ?u.63308\nσ : Type u_2\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → ℕ\ng : α →. σ\nh : α → ℕ × σ →. σ\nhf : Computable f\nhg : Partrec g\nhh : Partrec₂ h\nn : ℕ\na : α\ne : decode n ... | [
479,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coeff_X' | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m✝ : σ\ns : σ →₀ ℕ\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S₁\np q : MvPolynomial σ R\ninst✝ : DecidableEq σ\ni : σ\nm : σ →₀ ℕ\n⊢ coeff m (X i) = if Finsupp.single... | [
684,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.comp_sup'_eq_sup'_comp | [
{
"state_after": "F : Type ?u.259369\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Type ?u.259381\nκ : Type ?u.259384\ninst✝¹ : SemilatticeSup α\ns✝ : Finset β\nH✝ : Finset.Nonempty s✝\nf✝ : β → α\ninst✝ : SemilatticeSup γ\ns : Finset β\nH : Finset.Nonempty s\nf : β → α\ng : α → γ\ng_sup : ∀ (x y : α), g (x ⊔ ... | [
854,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
] |
Mathlib/Tactic/Positivity/Basic.lean | Mathlib.Meta.Positivity.int_natAbs_pos | [] | [
326,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
9
] |
Mathlib/Topology/MetricSpace/Basic.lean | edist_nndist | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.19532\nι : Type ?u.19535\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ edist x y = ↑(nndist x y)",
"tactic": "rw [edist_dist, dist_nndist, ENNReal.ofReal_coe_nnreal]"
}
] | [
318,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/Data/Finset/Slice.lean | Finset.biUnion_slice | [] | [
173,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Logic/Denumerable.lean | Nat.Subtype.exists_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.35974\nβ : Type ?u.35977\ns : Set ℕ\ninst✝ : Infinite ↑s\nx : ↑s\nh : ¬∃ n, ↑x + n + 1 ∈ s\na : ℕ\nha : a ∈ s\nhax : a ≥ succ ↑x\n⊢ ↑x + (a - (↑x + 1)) + 1 ∈ s",
"tactic": "rwa [add_right_comm, add_tsub_cancel_of_le hax]"
},
{
"state_afte... | [
232,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_cons_none | [
{
"state_after": "ι : Type ?u.341936\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nf : α → Option α\na : α\nl : List α\nh : f a = none\n⊢ (match f a with\n | some b => b :: l\n | none => lookmap.go f l (Array.push #[] a)) =\n a :: lookmap.go f l #[]",
"state_before": "ι : Type ?u... | [
3296,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3293,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.BinaryBiproduct.bicone_inl | [] | [
1316,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lsingle_range_le_ker_lapply | [
{
"state_after": "α : Type u_1\nM : Type u_2\nN : Type ?u.24141\nP : Type ?u.24144\nR : Type u_3\nS : Type ?u.24150\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\ns t : Set α\n... | [
143,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | posMulMonoRev_iff_posMulReflectLT | [] | [
1010,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
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