file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Fintype/Card.lean | Fintype.card_empty | [] | [
345,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_nonneg_of_nonpos | [
{
"state_after": "a : Int\nh : a ≤ 0\nthis : -0 ≤ -a\n⊢ 0 ≤ -a",
"state_before": "a : Int\nh : a ≤ 0\n⊢ 0 ≤ -a",
"tactic": "have : -0 ≤ -a := Int.neg_le_neg h"
},
{
"state_after": "no goals",
"state_before": "a : Int\nh : a ≤ 0\nthis : -0 ≤ -a\n⊢ 0 ≤ -a",
"tactic": "rwa [Int.neg_zero] at... | [
877,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
875,
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Mathlib/Analysis/Calculus/MeanValue.lean | Convex.norm_image_sub_le_of_norm_fderiv_le | [] | [
543,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
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Mathlib/ModelTheory/Ultraproducts.lean | FirstOrder.Language.Ultraproduct.term_realize_cast | [
{
"state_after": "case h.e'_3.h.e'_3\nα : Type u_2\nM : α → Type u_3\nu : Ultrafilter α\nL : Language\ninst✝ : (a : α) → Structure L (M a)\nβ : Type u_1\nx : β → (a : α) → M a\nt : Term L β\n⊢ (fun a => Term.realize (fun i => x i a) t) = Term.realize x t",
"state_before": "α : Type u_2\nM : α → Type u_3\nu ... | [
97,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Std/Data/List/Lemmas.lean | List.get_map | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\nn : Fin (length (map f l))\n⊢ Option.map f (some (get l { val := n.val, isLt := ?m.72539 })) =\n some (f (get l { val := n.val, isLt := (_ : n.val < length l) }))\n\nα : Type u_1\nβ : Type u_2\nf : α → β\nl : List α\nn : Fin (length (map f ... | [
574,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/Pi/Algebra.lean | Pi.one_apply | [] | [
51,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.812913\nδ : Type ?u.812916\ninst✝¹ : MeasurableSpace α\nK : Type ?u.812922\ninst✝ : Zero β\nf : α →ₛ β\ns : Set α\nhs : MeasurableSet s\nt : Set β\nht : ¬0 ∈ t\n⊢ ↑(restrict f s) ⁻¹' t = s ∩ ↑f ⁻¹' t",
"tactic": "simp ... | [
789,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_smul' | [
{
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54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
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Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.le_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : SemilatticeSup α\ninst✝ : SemilatticeSup β\nf : α → β\nhf : LeftOrdContinuous f\nh : Injective f\nx y : α\n⊢ f x ≤ f y ↔ x ≤ y",
"tactic": "simp only [← sup_eq_right, ← hf.map_sup, h.eq_iff]"
}
] | [
102,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Set/Basic.lean | Set.sep_setOf | [] | [
1484,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1483,
1
] |
Mathlib/GroupTheory/GroupAction/Basic.lean | MulAction.orbitRel.Quotient.orbit_mk | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.isEmpty_coe_sort | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.23485\nγ : Type ?u.23488\ns✝ s : Finset α\n⊢ IsEmpty { x // x ∈ s } ↔ s = ∅",
"tactic": "simpa using @Set.isEmpty_coe_sort α s"
}
] | [
631,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
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Mathlib/Data/Matrix/Kronecker.lean | Matrix.add_kroneckerTMul | [] | [
479,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Std/Data/Option/Lemmas.lean | Option.bind_id_eq_join | [] | [
119,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
119,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_smul | [
{
"state_after": "α : Type u_4\nE✝ : Type ?u.310418\nF : Type u_3\nF' : Type ?u.310424\nG : Type ?u.310427\n𝕜 : Type u_2\np : ℝ≥0∞\ninst✝¹¹ : NormedAddCommGroup E✝\ninst✝¹⁰ : NormedSpace ℝ E✝\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace ℝ F\ninst✝⁷ : NormedAddCommGroup F'\ninst✝⁶ : NormedSpace ℝ F'\nin... | [
510,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Data/Sym/Basic.lean | SymOptionSuccEquiv.encode_of_not_none_mem | [] | [
624,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_csInf_inter | [] | [
702,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Logic/Encodable/Basic.lean | Encodable.decode₂_inj | [] | [
226,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | comap_dist_left_atTop_le_cocompact | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.546511\nι : Type ?u.546514\ninst✝ : PseudoMetricSpace α\nx : α\n⊢ comap (dist x) atTop ≤ cocompact α",
"tactic": "simpa only [dist_comm _ x] using comap_dist_right_atTop_le_cocompact x"
}
] | [
2800,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2799,
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Mathlib/Data/Quot.lean | Trunc.nonempty | [] | [
584,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.sum_cramer_apply | [
{
"state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA : Matrix n n α\nb : n → α\nβ : Type u_1\ns : Finset β\nf : n → β → α\ni : n\n⊢ det (updateColumn A i (∑ x in s, fun j => f j x)) = det (updateColumn... | [
174,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Continuous.arsinh | [] | [
233,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_bot | [] | [
267,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Order/CompleteLattice.lean | sSup_apply | [] | [
1760,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1758,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotientInfEquivSupQuotient_apply_mk | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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] |
Mathlib/CategoryTheory/Preadditive/Injective.lean | CategoryTheory.Equivalence.enoughInjectives_iff | [
{
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"state_before": "C... | [
375,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
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Mathlib/Topology/Algebra/Order/ProjIcc.lean | Filter.Tendsto.IccExtend | [] | [
30,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
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] |
Mathlib/Combinatorics/SimpleGraph/Regularity/Uniform.lean | Finpartition.nonempty_of_not_uniform | [] | [
260,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_closedBall_one_iff | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.94910\n𝕜 : Type ?u.94913\nα : Type ?u.94916\nι : Type ?u.94919\nκ : Type ?u.94922\nE : Type u_1\nF : Type ?u.94928\nG : Type ?u.94931\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E... | [
640,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousCore'_mono | [] | [
123,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
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Mathlib/Analysis/InnerProductSpace/Symmetric.lean | LinearMap.IsSymmetric.continuous | [
{
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117,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.isLUB | [
{
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1082,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1075,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_isBot | [] | [
253,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.inclusion_injective | [] | [
554,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
552,
1
] |
src/lean/Init/Control/Lawful.lean | ReaderT.run_mapConst | [] | [
190,
77
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
189,
9
] |
Mathlib/Data/Set/Image.lean | Set.disjoint_image_iff | [] | [
1602,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1601,
1
] |
Mathlib/Topology/LocalAtTarget.lean | isClosedMap_iff_isClosedMap_of_iSup_eq_top | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set β\nι : Type ?u.21339\nU : ι → Opens β\nhU : iSup U = ⊤\n⊢ (∀ (i : ι), IsClosedMap (restrictPreimage (U i).carrier f)) → IsClosedMap f",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝... | [
118,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.relIso_enum' | [
{
"state_after": "α✝ : Type ?u.97545\nβ✝ : Type ?u.97548\nγ : Type ?u.97551\nr✝ : α✝ → α✝ → Prop\ns✝ : β✝ → β✝ → Prop\nt : γ → γ → Prop\nα β : Type u\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : IsWellOrder β s\nf : r ≃r s\no : Ordinal\n⊢ ∀ (α_1 : Type u) (r_1 : α_1 → α_1 → Prop) [inst... | [
546,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.limit.conePointUniqueUpToIso_hom_comp | [] | [
233,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Calculus/Deriv/Inv.lean | fderiv_inv | [
{
"state_after": "no goals",
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124,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_apply_of_aemeasurable | [
{
"state_after": "no goals",
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1225,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix'_toLinearMap₂' | [] | [
265,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleMap_mem_closedBall | [] | [
131,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.inr_desc | [] | [
1383,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1381,
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Mathlib/Data/Fin/Basic.lean | Fin.pos | [] | [
150,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
11
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.comap_map_eq | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.216907\n𝕜 : Type ?u.216910\nV : Type u\nW : Type v\nX : Type w\nG✝ : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\nf : V ↪ W\nG : SimpleGraph V\nx✝¹ x✝ : V\n⊢ Adj (SimpleGraph.comap (↑f) (SimpleGraph.map f G)) x✝¹ x✝ ↔ Adj G x✝¹ x✝",
"state_be... | [
1272,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1270,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.comp₂_mk_mk | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.SigmaFinite.out | [] | [
3446,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3445,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformGroup_inf | [
{
"state_after": "α : Type ?u.119171\nβ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : Group α\ninst✝¹ : UniformGroup α\ninst✝ : Group β\nu₁ u₂ : UniformSpace β\nh₁ : UniformGroup β\nh₂ : UniformGroup β\n⊢ UniformGroup β",
"state_before": "α : Type ?u.119171\nβ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : G... | [
242,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_bool | [
{
"state_after": "no goals",
"state_before": "α β : Type u\n⊢ (#Bool) = 2",
"tactic": "simp"
}
] | [
565,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/Data/Set/Prod.lean | Set.prod_univ | [
{
"state_after": "no goals",
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"tactic": "simp [prod_eq]"
}
] | [
131,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/MeasureTheory/Group/Arithmetic.lean | Multiset.measurable_prod | [
{
"state_after": "no goals",
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920,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_subtype | [
{
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295,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
9
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_right | [
{
"state_after": "no goals",
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}
] | [
151,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isPairSelfAdjoint_equiv | [
{
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1119,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1107,
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Mathlib/Computability/Reduce.lean | ManyOneReducible.mk | [] | [
52,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
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Mathlib/Order/Filter/Partial.lean | Filter.rmap_sets | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.adjoinIntegral_coe | [] | [
1625,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1622,
1
] |
Mathlib/Data/Pi/Lex.lean | Pi.lex_lt_of_lt | [
{
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76,
41
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73,
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Mathlib/Data/Nat/Bits.lean | Nat.bit_eq_zero_iff | [
{
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"state_before": "n✝ n : ℕ\nb : Bool\n⊢ bit b n = 0 ↔ n = 0 ∧ b = false",
"tactic": "constructor"
},
{
"state_after": "no goals",
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161,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
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Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.FiniteMeasure.limsup_measure_closed_le_of_tendsto | [
{
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373,
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340,
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Mathlib/Order/LocallyFinite.lean | Ico_ofDual | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.114883\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : LocallyFiniteOrder ... | [
866,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
1
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Mathlib/Algebra/Order/Rearrangement.lean | Monovary.sum_mul_comp_perm_eq_sum_mul_iff | [] | [
465,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.lsum_apply | [] | [
376,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_const | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.244483\nι : Sort x\nf f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm : α → β\nm' : β → γ\ns✝ : Set α\nt : Set β\ninst✝ : NeBot f\nc : β\ns : Set β\n⊢ s ∈ map (fun x => c) f ↔ s ∈ pure c",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\n... | [
2083,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2081,
1
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Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.cancel_left | [
{
"state_after": "no goals",
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202,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.prod_mul | [] | [
1795,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1792,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.disjoint_def' | [] | [
3645,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3643,
1
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Mathlib/Computability/TuringMachine.lean | Turing.Tape.move_right_n_head | [
{
"state_after": "case zero\nΓ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\n⊢ ((move Dir.right^[Nat.zero]) T).head = nth T ↑Nat.zero\n\ncase succ\nΓ : Type u_1\ninst✝ : Inhabited Γ\nn✝ : ℕ\nn_ih✝ : ∀ (T : Tape Γ), ((move Dir.right^[n✝]) T).head = nth T ↑n✝\nT : Tape Γ\n⊢ ((move Dir.right^[Nat.succ n✝]) T).head ... | [
656,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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Mathlib/Topology/Semicontinuous.lean | LowerSemicontinuous.add' | [] | [
476,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.liftAddHom_apply_single | [
{
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2036,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2035,
1
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Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.snd_pow | [] | [
634,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
632,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.bot_vsub | [] | [
1098,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
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Mathlib/Analysis/Calculus/ContDiffDef.lean | iteratedFDerivWithin_of_isOpen | [
{
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1596,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1583,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | iUnion_Ico_int_cast | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ (⋃ (n : ℤ), Ico (↑n) (↑n + 1)) = univ",
"tactic": "simpa only [zero_add] using iUnion_Ico_add_int_cast (0 : α)"
}
] | [
1114,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1113,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.tail_nil | [
{
"state_after": "no goals",
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"tactic": "simp [tail]"
}
] | [
706,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
706,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.sub | [
{
"state_after": "no goals",
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1322,
50
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1320,
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] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.coe_of_map_mul_inv | [] | [
1626,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1624,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_le_of_dvd | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ∀ {m : ℕ}, 2 ≤ m → m ∣ n → minFac n ≤ m",
"tactic": "by_cases n1 : n = 1 <;> [exact fun m2 _ => n1.symm ▸ le_trans (by decide) m2;\n apply (minFac_has_prop n1).2.2]"
},
{
"state_after": "no goals",
"state_before": "n m✝ : ℕ\nn1 : n = 1\... | [
340,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_add_le | [
{
"state_after": "𝕜 : Type ?u.211297\nE : Type u_1\nF : Type ?u.211303\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\nhs : Convex ℝ s\nabsorbs : Absorbent ℝ s\nx y : E\nε : ℝ\nhε : 0 < ε\n⊢ gauge s (x + y) < gauge s x + gauge s y + ε",
"state_before": "𝕜 : Type ?u.211297\nE : Type u_1\n... | [
389,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.liftAux_apply_I | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\ninst✝¹ : Ring A\ninst✝ : Algebra ℝ A\nI' : A\nhI' : I' * I' = -1\n⊢ ↑(liftAux I' hI') I = I'",
"tactic": "simp"
}
] | [
366,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | IsOpen.mul_right | [
{
"state_after": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : TopologicalSpace α\ninst✝¹ : Group α\ninst✝ : ContinuousConstSMul αᵐᵒᵖ α\ns t : Set α\nhs : IsOpen s\n⊢ IsOpen (⋃ (a : α) (_ : a ∈ t), MulOpposite.op a • s)",
"state_before": "α : Type u\nβ : Type v\nG : Type w\nH : Type x\ninst✝² : ... | [
1299,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.sum_inner_products_le | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_3\nF : Type ?u.3426813\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nι : Type u_1\nx : E\nv : ι → E\ns : Finset ι\nhv : Orthonormal 𝕜 v\nh₂ : ∑... | [
1897,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1880,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_of_subset_of_forall_diff_eq_zero | [] | [
389,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_zero | [] | [
518,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.frange_zero | [] | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diag_add | [] | [
632,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.core_eq | [] | [
293,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.inf_neBot_iff | [] | [
638,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.smul_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.156923\nβ : Type ?u.156926\nγ : Type ?u.156929\na b c✝ d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nι : Sort u_1\nR : Type u_2\ninst✝¹ : SMul R ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nf : ι → ℝ≥0∞\nc : R\n⊢ (c • ⨆ (i : ι), f i) = ⨆ (i ... | [
662,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
659,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.star_apply | [] | [
751,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
750,
11
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.map_bind₁ | [
{
"state_after": "σ : Type u_4\nτ : Type u_3\nR : Type u_1\nS : Type u_2\nT : Type ?u.836499\ninst✝² : CommSemiring R\ninst✝¹ : CommSemiring S\ninst✝ : CommSemiring T\nf✝ : σ → MvPolynomial τ R\nf : R →+* S\ng : σ → MvPolynomial τ R\nφ : MvPolynomial σ R\n⊢ ↑(eval₂Hom C fun i => ↑(map f) (g i)) (↑(map f) φ) = ↑... | [
296,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/Order/WellFounded.lean | WellFounded.isIrrefl | [] | [
40,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
11
] |
Mathlib/Order/Bounds/Basic.lean | bddBelow_iff_exists_le | [] | [
491,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Order/ModularLattice.lean | inf_lt_inf_of_lt_of_sup_le_sup | [] | [
255,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.cons_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.44964\nγ : Type ?u.44967\na : α\ns t : Multiset α\n⊢ a ::ₘ s + t = a ::ₘ (s + t)",
"tactic": "rw [← singleton_add, ← singleton_add, add_assoc]"
}
] | [
674,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
673,
1
] |
Mathlib/Analysis/Calculus/LagrangeMultipliers.lean | IsLocalExtrOn.linear_dependent_of_hasStrictFDerivAt | [
{
"state_after": "case intro\nE : Type u_2\nF : Type ?u.129783\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nf✝ : E → F\nφ : E → ℝ\nx₀ : E\nf'✝ : E →L[ℝ] F\nφ' : E →L[ℝ] ℝ\nι : Type u_1\ninst... | [
144,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.xgcdAux_rec | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\nr s t r' s' t' : R\nh : r ≠ 0\n⊢ (fun s t r' s' t' =>\n if _hr : r = 0 then (r', s', t')\n else\n let q := r' / r;\n xgcdAux (r' % r) (s' - q * s) (t' - q * t) r s t)\n s t r' s' t' =\n xgcdA... | [
247,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.homOfLe_apply | [] | [
591,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
590,
1
] |
Mathlib/Algebra/Lie/Basic.lean | lie_zero | [] | [
141,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
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