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/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.BinaryCofan.ι_app_left | [] | [
262,
46
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261,
1
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Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_zero_left | [
{
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251,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/List/Lemmas.lean | List.eq_of_mem_replicate | [] | [
282,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
282,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftAlgHom_apply | [] | [
1366,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1363,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.iSup_eapprox_apply | [
{
"state_after": "α : Type u_1\nβ : Type ?u.838044\nγ : Type ?u.838047\nδ : Type ?u.838050\ninst✝ : MeasurableSpace α\nK : Type ?u.838056\nf : α → ℝ≥0∞\nhf : Measurable f\na : α\n⊢ (⨆ (k : ℕ) (_ : ennrealRatEmbed k ≤ f a), ennrealRatEmbed k) = f a",
"state_before": "α : Type u_1\nβ : Type ?u.838044\nγ : Typ... | [
924,
47
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912,
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Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.ordConnected_range | [
{
"state_after": "α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns t : Set α\nE : Type u_1\ninst✝ : OrderIsoClass E α β\ne : E\n⊢ OrdConnected (↑e '' univ)",
"state_before": "α : Type u_2\nβ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ns t : Set α\nE : Type u_1\ninst✝ : Order... | [
214,
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Mathlib/Topology/Order.lean | setOf_isOpen_sSup | [] | [
965,
29
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Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_trivChange_source | [
{
"state_after": "ι : Type u_3\nB : Type u_1\nF : Type u_2\nX : Type ?u.29164\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nZ : FiberBundleCore ι B F\ni j : ι\np : B × F\n⊢ p.fst ∈ baseSet Z i ∩ baseSet Z j ∧ p.snd ∈ univ ↔ p.fst ∈ baseSet Z i ∩ baseSet Z j",
"state_... | [
499,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
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Mathlib/Data/Real/EReal.lean | EReal.abs_eq_zero_iff | [
{
"state_after": "case h_bot\n\n⊢ EReal.abs ⊥ = 0 ↔ ⊥ = 0\n\ncase h_real\na✝ : ℝ\n⊢ EReal.abs ↑a✝ = 0 ↔ ↑a✝ = 0\n\ncase h_top\n\n⊢ EReal.abs ⊤ = 0 ↔ ⊤ = 0",
"state_before": "x : EReal\n⊢ EReal.abs x = 0 ↔ x = 0",
"tactic": "induction x using EReal.rec"
},
{
"state_after": "no goals",
"state_... | [
1074,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1070,
1
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Mathlib/Algebra/GroupPower/Basic.lean | Commute.mul_pow | [
{
"state_after": "case zero\nα : Type ?u.18278\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na b : M\nh : Commute a b\n⊢ (a * b) ^ Nat.zero = a ^ Nat.zero * b ^ Nat.zero\n\ncase succ\nα : Type ?u.18278\nM : Type u\nN : ... | [
144,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleFactorsFinset_eq_list_toFinset | [
{
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1378,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
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Mathlib/Algebra/Quaternion.lean | Quaternion.coe_zero | [] | [
865,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
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Mathlib/Analysis/Convex/Gauge.lean | gauge_set_bddBelow | [] | [
79,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
9
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src/lean/Init/Data/String/Basic.lean | String.Iterator.sizeOf_eq | [] | [
308,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
307,
1
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_differentiableOn_iff | [
{
"state_after": "𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\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_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.72452\ninst✝¹... | [
115,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.inv | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ f : Perm α\nh : IsThreeCycle f\n⊢ IsThreeCycle f⁻¹",
"tactic": "rwa [IsThreeCycle, cycleType_inv]"
}
] | [
603,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
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Mathlib/Order/Filter/Prod.lean | Filter.Eventually.prod_mk | [] | [
169,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
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Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousLinearMap.compLeftContinuousCompact_apply | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
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Mathlib/MeasureTheory/Measure/Stieltjes.lean | StieltjesFunction.outer_le_length | [] | [
345,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
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Mathlib/Topology/Category/CompHaus/Basic.lean | topToCompHaus_obj | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Std/Logic.lean | exists_and_left | [] | [
463,
63
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
462,
9
] |
Std/Data/List/Lemmas.lean | List.sublist_append_right | [] | [
350,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
348,
9
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Mathlib/RingTheory/Ideal/QuotientOperations.lean | Ideal.quotientEquiv_mk | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.freeGroupCongr_trans | [] | [
885,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Topology/Instances/AddCircle.lean | AddCircle.equivIccQuot_comp_mk_eq_toIcoMod | [] | [
598,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
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Mathlib/Control/Traversable/Lemmas.lean | Traversable.comp_sequence | [
{
"state_after": "t : Type u → Type u\ninst✝⁵ : Traversable t\ninst✝⁴ : IsLawfulTraversable t\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : LawfulApplicative F\ninst✝¹ : Applicative G\ninst✝ : LawfulApplicative G\nα β γ : Type u\ng : α → F β\nh : β → G γ\nf : β → γ\nx✝ : t β\nx : t (F (G α))\n⊢ trave... | [
106,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Data/Set/Lattice.lean | Set.sInter_pair | [] | [
1163,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1162,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.divisorsAntidiagonal_one | [
{
"state_after": "case a\nn : ℕ\na✝ : ℕ × ℕ\n⊢ a✝ ∈ divisorsAntidiagonal 1 ↔ a✝ ∈ {(1, 1)}",
"state_before": "n : ℕ\n⊢ divisorsAntidiagonal 1 = {(1, 1)}",
"tactic": "ext"
},
{
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"state_before": "case a\nn : ℕ\na✝ : ℕ × ℕ\n⊢ a✝ ∈ divisorsAntidiagonal 1 ↔ a✝ ∈ {(1, 1)}... | [
210,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.closure_singleton_eq | [] | [
331,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/Data/List/Basic.lean | List.ilast'_mem | [
{
"state_after": "no goals",
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"tactic": "simp [ilast']"
},
{
"state_after": "ι : Type ?u.487859\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na b : ... | [
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4311,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.sqrt_normSq_eq_norm | [] | [
359,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
358,
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Mathlib/Topology/Separation.lean | exists_open_superset_and_isCompact_closure | [
{
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1417,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1413,
1
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Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.add_zero | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\na : X ⟶ Y\n⊢ a + 0 = a",
"tactic": "rw [add_def, neg_def, sub_self, sub_zero]"
}
] | [
428,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.empty_toList | [] | [
3365,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3364,
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Mathlib/Order/Filter/Basic.lean | Filter.frequently_top | [
{
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"tactic": "simp [Filter.Frequently]"
}
] | [
1390,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1390,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.transpose_row | [
{
"state_after": "case a.h\nl : Type ?u.1214001\nm : Type u_1\nn : Type ?u.1214007\no : Type ?u.1214010\nm' : o → Type ?u.1214015\nn' : o → Type ?u.1214020\nR : Type ?u.1214023\nS : Type ?u.1214026\nα : Type v\nβ : Type w\nγ : Type ?u.1214033\nv : m → α\ni✝ : m\nx✝ : Unit\n⊢ (row v)ᵀ i✝ x✝ = col v i✝ x✝",
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2687,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2685,
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Mathlib/Data/List/Basic.lean | List.zipWith_flip | [
{
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1904,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.isNormal_iff_lt_succ_and_bsup_eq | [
{
"state_after": "α : Type ?u.366416\nβ : Type ?u.366419\nγ : Type ?u.366422\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\nx✝ : (∀ (a : Ordinal), f a < f (succ a)) ∧ ∀ (o : Ordinal), IsLimit o → (bsup o fun x x_1 => f x) = f o\nh₁ : ∀ (a : Ordinal), f a < f (succ a)\nh₂ : ∀ (o : ... | [
1978,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1973,
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂'_apply | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumFinsuppEquivProdFinsupp_symm_inl | [] | [
1360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
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] |
Std/Data/List/Lemmas.lean | List.range'_1_concat | [
{
"state_after": "no goals",
"state_before": "s n : Nat\n⊢ range' s (n + 1) = range' s n ++ [s + n]",
"tactic": "simp [range'_concat]"
}
] | [
1884,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/Data/List/Chain.lean | List.Chain'.tail | [] | [
264,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/ContinuousLinearMap.lean | ContinuousLinearMap.measurable | [] | [
34,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
11
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_le_of_mem_edist | [
{
"state_after": "case refine_1\nι : Sort ?u.36912\nα : Type u\nβ : Type v\ninst✝¹ : PseudoEMetricSpace α\ninst✝ : PseudoEMetricSpace β\nx✝ y : α\ns t u : Set α\nΦ : α → β\nr : ℝ≥0∞\nH1 : ∀ (x : α), x ∈ s → ∃ y, y ∈ t ∧ edist x y ≤ r\nH2 : ∀ (x : α), x ∈ t → ∃ y, y ∈ s ∧ edist x y ≤ r\nx : α\nxs : x ∈ s\n⊢ infE... | [
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291,
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Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.pow_apply_mem_support | [
{
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"tactic": "simp only [mem_support, ne_eq, apply_pow_apply_eq_iff]"
}
] | [
371,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_iff_eventually | [
{
"state_after": "no goals",
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231,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.sInf_toSubmonoid | [] | [
682,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.ball_zero | [
{
"state_after": "no goals",
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"tactic": "rw [EMetric.ball_eq_empty_iff]"
}
] | [
628,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.abs_lt_real_iff_infinitesimal | [] | [
682,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Computability/RegularExpressions.lean | RegularExpression.add_rmatch_iff | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.41307\nγ : Type ?u.41310\ndec : DecidableEq α\na b : α\nP✝ Q✝ P Q : RegularExpression α\n⊢ rmatch (P + Q) [] = true ↔ rmatch P [] = true ∨ rmatch Q [] = true\n\ncase cons\nα : Type u_1\nβ : Type ?u.41307\nγ : Type ?u.41310\ndec : DecidableEq α\na b : α\nP✝ Q... | [
247,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.nnnorm_lt_iff | [] | [
239,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.toIdeal_homogeneousCore_eq_self | [
{
"state_after": "case h\nι : Type u_1\nσ : Type u_2\nR : Type ?u.107238\nA : Type u_3\ninst✝⁵ : Semiring A\ninst✝⁴ : SetLike σ A\ninst✝³ : AddSubmonoidClass σ A\n𝒜 : ι → σ\ninst✝² : DecidableEq ι\ninst✝¹ : AddMonoid ι\ninst✝ : GradedRing 𝒜\nI✝ : Ideal A\nI : HomogeneousIdeal 𝒜\n⊢ toIdeal (Ideal.homogeneousC... | [
219,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Set/Basic.lean | Set.setOf_mem_eq | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.homomorphism | [] | [
747,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.null_of_locally_null | [] | [
4015,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4013,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.injective | [
{
"state_after": "R : Type u\ninst✝⁷ : Ring R\nQ : TypeMax\ninst✝⁶ : AddCommGroup Q\ninst✝⁵ : Module R Q\nM N : Type (max u v)\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\ni✝ : M →ₗ[R] N\nf✝ : M →ₗ[R] Q\ninst✝ : Fact (Function.Injective ↑i✝)\nh : Baer R Q\nX Y : T... | [
467,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
11
] |
Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.edist_efixedPoint_le' | [
{
"state_after": "case h.e'_4.h.e'_5\nα : Type u_1\ninst✝ : EMetricSpace α\ncs : CompleteSpace α\nK : ℝ≥0\nf : α → α\ns : Set α\nhsc : IsComplete s\nhsf : MapsTo f s s\nhf : ContractingWith K (MapsTo.restrict f s s hsf)\nx : α\nhxs : x ∈ s\nhx : edist x (f x) ≠ ⊤\n⊢ edist x (f x) = edist x (f x) * ↑K ^ 0",
... | [
228,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingCoeff_eq_zero | [] | [
307,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atBot_iff_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.243936\nι' : Type ?u.243939\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.243948\ninst✝¹ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\ninst✝ : NeBot l\nh : Tendsto f l atBot\n⊢ Tendsto (fun x => f x * r) l atBot ↔ 0 < r",
"tactic": "simp onl... | [
1173,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1171,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_single | [] | [
485,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Data/Int/SuccPred.lean | Int.pred_iterate | [
{
"state_after": "a : ℤ\nn : ℕ\n⊢ (pred ∘ pred^[n]) a = a - ↑n - 1",
"state_before": "a : ℤ\nn : ℕ\n⊢ (pred^[n + 1]) a = a - ↑(n + 1)",
"tactic": "rw [Function.iterate_succ', Int.ofNat_succ, ← sub_sub]"
},
{
"state_after": "no goals",
"state_before": "a : ℤ\nn : ℕ\n⊢ (pred ∘ pred^[n]) a = a ... | [
64,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sum.mem_uniformity | [
{
"state_after": "case mp\nX : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\ns : Set ((X ⊕ Y) × (X ⊕ Y))\n⊢ s ∈ 𝓤 (X ⊕ Y) → ∃ ε, ε > 0 ∧ ∀ (a b : X ⊕ Y), Sum.dist a b < ε → (a, b) ∈ s\n\ncase mpr\nX : Type u\nY : Type v\nZ : Type w\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y... | [
244,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
9
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | List.formPerm_disjoint_iff | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl : Nodup l\nhl' : Nodup l'\nhn : 2 ≤ length l\nhn' : 2 ≤ length l'\n⊢ (∀ (x : α), ↑(formPerm l) x = x ∨ ↑(formPerm l') x = x) ↔ ∀ ⦃a : α⦄, a ∈ l → a ∈ l' → False",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nhl ... | [
73,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/RingTheory/Localization/FractionRing.lean | IsFractionRing.isUnit_map_of_injective | [] | [
177,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.reindex_trans | [] | [
885,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_le' | [] | [
1083,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1082,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.adjoin_eq_starClosure_adjoin | [] | [
435,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.trunc_toLaurent | [] | [
376,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
src/lean/Init/Core.lean | Thunk.sizeOf_eq | [
{
"state_after": "case mk\nα : Type u_1\ninst✝ : SizeOf α\nfn✝ : Unit → α\n⊢ sizeOf { fn := fn✝ } = 1 + sizeOf (Thunk.get { fn := fn✝ })",
"state_before": "α : Type u_1\ninst✝ : SizeOf α\na : Thunk α\n⊢ sizeOf a = 1 + sizeOf (Thunk.get a)",
"tactic": "cases a"
},
{
"state_after": "no goals",
... | [
71,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
70,
9
] |
Mathlib/Control/LawfulFix.lean | Part.Fix.approx_mem_approxChain | [] | [
130,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Std/Data/Array/Lemmas.lean | Array.foldr_induction | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nas : Array α\nmotive : Nat → β → Prop\ninit : β\nh0 : motive (size as) init\nf : α → β → β\nhf : ∀ (i : Fin (size as)) (b : β), motive (i.val + 1) b → motive i.val (f as[i] b)\nthis :\n (∀ (i : Fin (size as)) (b : β), motive (i.val + 1) b → SatisfiesM (motive i.val... | [
161,
16
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
155,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.Compacts.coe_equiv_apply_eq_preimage | [] | [
187,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_smul | [] | [
342,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
11
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.Nonempty.smul_finset | [] | [
1639,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1638,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.range_smul_range | [] | [
453,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.div_def | [] | [
304,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
304,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftOn_mk | [
{
"state_after": "case pos\nK : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\nP : Sort v\np q : K[X]\nf : K[X] → K[X] → P\nf0 : ∀ (p : K[X]), f p 0 = f 0 1\nH' : ∀ {p q p' q' : K[X]}, q ≠ 0 → q' ≠ 0 → q' * p = q * p' → f p q = f p' q'\nH :\n optParam (∀ {p q p' q' : K[X]}, q ∈ K[X]⁰ → q' ∈ K[X]⁰ → q' * p = ... | [
257,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/Data/Real/ConjugateExponents.lean | Real.IsConjugateExponent.one_div_nonneg | [] | [
68,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Order/Kleene.lean | kstar_one | [] | [
262,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filterMap_eq_map | [] | [
2132,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2130,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.eraseNone_none | [
{
"state_after": "case a\nα : Type u_1\nβ : Type ?u.13019\na✝ : α\n⊢ a✝ ∈ ↑eraseNone {none} ↔ a✝ ∈ ∅",
"state_before": "α : Type u_1\nβ : Type ?u.13019\n⊢ ↑eraseNone {none} = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nα : Type u_1\nβ : Type ?u.13019\na✝ : α\... | [
142,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_preimage | [] | [
302,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.cons_inj_left | [] | [
127,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Basic.lean | Set.MapsTo.closure_left | [] | [
1780,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1778,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_norm_le | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.561143\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\n⊢ 0 ≤ 1"... | [
569,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.mem_inv | [] | [
137,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Analysis/Convex/Strict.lean | strictConvex_singleton | [] | [
124,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasSum | [] | [
776,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
11
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_prod_left | [] | [
1022,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.weightedSumSquares_apply | [] | [
1172,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Uniform.lean | Pmf.mem_support_uniformOfFinset_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.8867\nγ : Type ?u.8870\ns : Finset α\nhs : Finset.Nonempty s\na✝ a : α\n⊢ a ∈ support (uniformOfFinset s hs) ↔ a ∈ s",
"tactic": "simp"
}
] | [
75,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Analysis/PSeries.lean | summable_condensed_iff_of_nonneg | [
{
"state_after": "case intro\nf : ℕ → ℝ≥0\nh_mono : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → (fun i => ↑(f i)) n ≤ (fun i => ↑(f i)) m\n⊢ (Summable fun k => 2 ^ ↑k * (fun i => ↑(f i)) (2 ^ k)) ↔ Summable fun i => ↑(f i)",
"state_before": "f : ℕ → ℝ\nh_nonneg : ∀ (n : ℕ), 0 ≤ f n\nh_mono : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f... | [
145,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.leftDual_v | [] | [
742,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.25922\nι : Type ?u.25925\ninst✝ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\n⊢ ball x ε = ∅ ↔ ε ≤ 0",
"tactic": "rw [← not_nonempty_iff_eq_empty, nonempty_ball, not_lt]"
}
] | [
439,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Algebra/Star/Basic.lean | Units.coe_star | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.wellFoundedOn_iff | [
{
"state_after": "ι : Type ?u.442\nα : Type u_1\nβ : Type ?u.448\nr r' : α → α → Prop\ns t : Set α\nx y : α\nf : (fun a b => r ↑a ↑b) ↪r fun a b => r a b ∧ a ∈ s ∧ b ∈ s\n⊢ WellFoundedOn s r ↔ WellFounded fun a b => r a b ∧ a ∈ s ∧ b ∈ s",
"state_before": "ι : Type ?u.442\nα : Type u_1\nβ : Type ?u.448\nr r... | [
88,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Equiv.embeddingCongr_refl | [] | [
430,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Std/Data/Int/Lemmas.lean | Int.ofNat_pos | [] | [
602,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
602,
20
] |
Mathlib/Analysis/Calculus/ParametricIntervalIntegral.lean | intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁶ : IsROrC 𝕜\nμ : MeasureTheory.Measure ℝ\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : CompleteSpace E\nH : Type u_2\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\na b ε : ℝ\nbound : ℝ → ℝ\nF : H → ℝ... | [
71,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
8
] |
Mathlib/Data/Nat/Basic.lean | Nat.div_mod_unique | [
{
"state_after": "m✝ n✝ k✝ n k m d : ℕ\nh : 0 < k\nx✝ : m + k * d = n ∧ m < k\nh₁ : m + k * d = n\nh₂ : m < k\n⊢ m / k + d = d ∧ m % k = m",
"state_before": "m✝ n✝ k✝ n k m d : ℕ\nh : 0 < k\nx✝ : m + k * d = n ∧ m < k\nh₁ : m + k * d = n\nh₂ : m < k\n⊢ (m + k * d) / k = d ∧ (m + k * d) % k = m",
"tactic... | [
722,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
11
] |
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