file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Nat/Prime.lean | Nat.not_prime_one | [] | [
62,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_lintegral | [] | [
784,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
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Mathlib/Order/LiminfLimsup.lean | Filter.exists_forall_mem_of_hasBasis_mem_blimsup | [
{
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1090,
39
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1082,
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Mathlib/Init/Data/Bool/Lemmas.lean | Bool.or_coe_iff | [
{
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}
] | [
162,
60
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162,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniform_extend_subtype | [
{
"state_after": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ne✝ : β → α\nh_e : UniformInducing e✝\nh_dense : DenseRange e✝\nf✝ : β → γ\nh_f : UniformContinuous f✝\ninst✝ : CompleteSpace γ\np : α → Prop\ne : α → β\nf : α → γ\nb : β\ns : Se... | [
458,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_sup | [] | [
204,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
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Mathlib/CategoryTheory/Limits/Preserves/Shapes/Biproducts.lean | CategoryTheory.Functor.inr_biprodComparison' | [] | [
352,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.algebraMap_apply | [] | [
1090,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1089,
1
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Mathlib/Data/Nat/Basic.lean | Nat.le_find_iff | [
{
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"tactic": "simp_rw [← not_lt, find_lt_iff, not_exists, not_and]"
}
] | [
840,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
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Mathlib/Algebra/Lie/Nilpotent.lean | LieIdeal.coe_lcs_eq | [
{
"state_after": "case zero\nR : Type u_2\nL : Type u_3\ninst✝⁶ : CommRing R\ninst✝⁵ : LieRing L\ninst✝⁴ : LieAlgebra R L\nI : LieIdeal R L\nM : Type u_1\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : LieRingModule L M\ninst✝ : LieModule R L M\nk : ℕ\n⊢ ↑(lcs I M Nat.zero) = ↑(lowerCentralSeries R { x ... | [
717,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
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Mathlib/Topology/Separation.lean | IsClosed.exists_closed_singleton | [
{
"state_after": "case intro.intro.intro.intro\nα✝ : Type u\nβ : Type v\ninst✝³ : TopologicalSpace α✝\nα : Type u_1\ninst✝² : TopologicalSpace α\ninst✝¹ : T0Space α\ninst✝ : CompactSpace α\nS : Set α\nhS : IsClosed S\nhne : Set.Nonempty S\nV : Set α\nVsub : V ⊆ S\nVne : Set.Nonempty V\nVcls : IsClosed V\nhV : ∀... | [
280,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
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Mathlib/Analysis/Complex/Basic.lean | IsROrC.summable_conj | [] | [
495,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
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Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.HasSeparableContraction.eq_degree | [
{
"state_after": "F : Type u_1\ninst✝ : CommSemiring F\nq : ℕ\nf✝ : F[X]\nhf✝ : HasSeparableContraction q f✝\nf : F[X]\nhf : HasSeparableContraction 1 f\na : ℕ\nha : degree hf * 1 ^ a = natDegree f\n⊢ degree hf = natDegree f",
"state_before": "F : Type u_1\ninst✝ : CommSemiring F\nq : ℕ\nf✝ : F[X]\nhf✝ : Ha... | [
97,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/RingTheory/DedekindDomain/Dvr.lean | Ring.DimensionLEOne.localization | [
{
"state_after": "R✝ : Type ?u.1246\nA : Type ?u.1249\nK : Type ?u.1252\ninst✝⁸ : CommRing R✝\ninst✝⁷ : CommRing A\ninst✝⁶ : IsDomain A\ninst✝⁵ : Field K\nR : Type u_1\nRₘ : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : IsDomain R\ninst✝² : CommRing Rₘ\ninst✝¹ : Algebra R Rₘ\nM : Submonoid R\ninst✝ : IsLocalization M... | [
87,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.trailingDegree_neg | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nn m : ℕ\ninst✝ : Ring R\np : R[X]\n⊢ Finset.min (support (-p)) = Finset.min (support p)",
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"tactic": "unfold trailingDegree"
... | [
463,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Nat/Order/Lemmas.lean | Nat.succ_div_of_dvd | [
{
"state_after": "no goals",
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"tactic": "rw [succ_div, if_pos hba]"
}
] | [
160,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_limit | [
{
"state_after": "a b : Ordinal\na0 : a ≠ 0\nh : IsLimit b\n⊢ (limitRecOn b 1 (fun x IH => IH * a) fun b x => bsup b) =\n bsup b fun c x => limitRecOn c 1 (fun x IH => IH * a) fun b x => bsup b",
"state_before": "a b : Ordinal\na0 : a ≠ 0\nh : IsLimit b\n⊢ a ^ b = bsup b fun c x => a ^ c",
"tactic": ... | [
67,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_le_succ | [
{
"state_after": "no goals",
"state_before": "a c : ℕ\n⊢ choose a c ≤ choose (succ a) c",
"tactic": "cases c <;> simp [Nat.choose_succ_succ]"
}
] | [
317,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableWithinAt_congr_set' | [] | [
797,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.le_prod_of_submultiplicative | [
{
"state_after": "ι : Type u_3\nα : Type ?u.11325\nβ : Type ?u.11328\nM : Type u_2\nN : Type u_1\nG : Type ?u.11337\nk : Type ?u.11340\nR : Type ?u.11343\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf : M → N\nh_one : f 1 = 1\nh_mul : ∀ (x y : M), f (x * y) ≤ f x * f y\ns : Finset ι\ng : ι → M\n⊢ Multis... | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | nndist_div_right | [
{
"state_after": "no goals",
"state_before": "M : Type u\nG : Type v\nX : Type w\ninst✝² : DivInvMonoid M\ninst✝¹ : PseudoMetricSpace M\ninst✝ : IsometricSMul Mᵐᵒᵖ M\na b c : M\n⊢ nndist (a / c) (b / c) = nndist a b",
"tactic": "simp only [div_eq_mul_inv, nndist_mul_right]"
}
] | [
394,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.iInf_finset_image | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.451621\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Type ?u.451633\nκ : Type ?u.451636\ninst✝¹ : CompleteLattice β\ninst✝ : DecidableEq α\nf : γ → α\ng : α → β\ns : Finset γ\n⊢ (⨅ (x : α) (_ : x ∈ image f s), g x) = ⨅ (y : γ) (_ : y ∈ s), g (f y)",... | [
1973,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1972,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.id_apply | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/List/Join.lean | List.join_drop_length_sub_one | [
{
"state_after": "case H0\nα : Type u_1\nβ : Type ?u.16380\nh : [] ≠ []\n⊢ join (drop (length [] - 1) []) = getLast [] h\n\ncase H1\nα : Type u_1\nβ : Type ?u.16380\nl✝ : List (List α)\na✝¹ : List α\na✝ : ∀ (h : l✝ ≠ []), join (drop (length l✝ - 1) l✝) = getLast l✝ h\nh : l✝ ++ [a✝¹] ≠ []\n⊢ join (drop (length ... | [
207,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_congr' | [] | [
482,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/Analysis/NormedSpace/Complemented.lean | Subspace.coe_prodEquivOfClosedCompl_symm | [] | [
113,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | Algebra.adjoin_range_eq_range_aeval | [] | [
1569,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1566,
1
] |
Mathlib/Data/Vector3.lean | exists_vector_succ | [
{
"state_after": "α : Type u_1\nm n : ℕ\nf : Vector3 α (succ n) → Prop\nx✝ : Exists f\nv : Vector3 α (succ n)\nfv : f v\n⊢ f v",
"state_before": "α : Type u_1\nm n : ℕ\nf : Vector3 α (succ n) → Prop\nx✝ : Exists f\nv : Vector3 α (succ n)\nfv : f v\n⊢ f (?m.40988 f x✝ v fv :: ?m.40989 f x✝ v fv)",
"tacti... | [
242,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
src/lean/Init/SimpLemmas.lean | eq_false | [] | [
18,
59
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
17,
1
] |
Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_fix | [] | [
1145,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Mathlib/GroupTheory/Solvable.lean | IsSimpleGroup.derivedSeries_succ | [
{
"state_after": "case zero\nG : Type u_1\nG' : Type ?u.73657\ninst✝² : Group G\ninst✝¹ : Group G'\nf : G →* G'\ninst✝ : IsSimpleGroup G\n⊢ derivedSeries G (Nat.succ Nat.zero) = _root_.commutator G\n\ncase succ\nG : Type u_1\nG' : Type ?u.73657\ninst✝² : Group G\ninst✝¹ : Group G'\nf : G →* G'\ninst✝ : IsSimple... | [
189,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Topology/Bornology/Constructions.lean | boundedSpace_val_set_iff | [] | [
171,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_comap | [] | [
1404,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.orderIsoMapComap_symm_apply' | [] | [
2536,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2534,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_nonpos_right' | [] | [
636,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Topology/MetricSpace/CantorScheme.lean | CantorScheme.ClosureAntitone.map_of_vanishingDiam | [
{
"state_after": "β : Type u_2\nα : Type u_1\nA : List β → Set α\ninst✝¹ : PseudoMetricSpace α\ninst✝ : CompleteSpace α\nhdiam : VanishingDiam A\nhanti : ClosureAntitone A\nhnonempty : ∀ (l : List β), Set.Nonempty (A l)\n⊢ ∀ (x : ℕ → β), x ∈ (inducedMap A).fst",
"state_before": "β : Type u_2\nα : Type u_1\n... | [
196,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.tendsto_approxOn_range_Lp_snorm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.635658\nβ : Type ?u.635661\nι : Type ?u.635664\nE : Type ?u.635667\nF : Type ?u.635670\n𝕜 : Type ?u.635673\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\nq : ℝ\np : ℝ≥0∞\ninst✝¹... | [
184,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Polynomial/Coeff.lean | Polynomial.coeff_bit0_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q r P Q : R[X]\nn : ℕ\n⊢ coeff (bit0 P * Q) n = 2 * coeff (P * Q) n",
"tactic": "simp [bit0, add_mul, two_mul]"
}
] | [
353,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.multiplicity_finite_of_degree_pos_of_monic | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommSemiring R\np q : R[X]\nhp : 0 < degree p\nhmp : Monic p\nhq : q ≠ 0\nzn0 : 0 ≠ 1\nx✝ : p ^ (natDegree q + 1) ∣ q\nr : R[X]\nhr : q = p ^ (natDegree q + 1) * r\nhp0 : p ≠ 0\n⊢ False",
"state_before": "R : Type u\nS... | [
90,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.sort_eq | [] | [
47,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
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Mathlib/Topology/Maps.lean | Inducing.continuous_iff | [
{
"state_after": "no goals",
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"tacti... | [
136,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_comm | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.74744\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\n⊢ hausdorffDist s t = hausdorffDist t s",
"tactic": "simp [hausdorffDist, hausdorffEdist_comm]"
}
] | [
725,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/NumberTheory/Padics/PadicNumbers.lean | PadicSeq.not_limZero_const_of_nonzero | [] | [
166,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Monad.lean | Pmf.bind_const | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.62680\np✝ : Pmf α\nf : α → Pmf β\ng : β → Pmf γ\np : Pmf α\nq : Pmf β\nx : β\n⊢ ↑(bind p fun x => q) x = ↑q x",
"tactic": "rw [bind_apply, ENNReal.tsum_mul_right, tsum_coe, one_mul]"
}
] | [
150,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_max | [] | [
314,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_empty | [] | [
152,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Data/Set/Basic.lean | Subsingleton.mem_iff_nonempty | [] | [
2837,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2836,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.FirstCountableTopology.tendsto_subseq | [] | [
568,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
566,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | Right.one_lt_mul' | [] | [
982,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_le_bound₂ | [] | [
606,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.FinMeasAdditive.map_iUnion_fin_meas_set_eq_sum | [
{
"state_after": "α : Type u_1\nE : Type ?u.37144\nF : Type ?u.37147\nF' : Type ?u.37150\nG : Type ?u.37153\n𝕜 : Type ?u.37156\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\ninst✝² : NormedSpace ℝ F'\n... | [
183,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_coe | [
{
"state_after": "F : Type ?u.65870\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.65879\nι : Type ?u.65882\nκ : Type ?u.65885\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns s₁ s₂ : Finset β\nf✝ g : β → α\na : α\nP : α → Prop\nPbot : P ⊥\nPsup : ∀ ⦃x y : α⦄, P x → P y → P (x ⊔ y)\nt : Finset β\nf : β → { x // P x ... | [
214,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.filter_nsmul | [
{
"state_after": "case refine'_1\nα : Type u_1\nβ : Type ?u.233049\nγ : Type ?u.233052\np : α → Prop\ninst✝ : DecidablePred p\ns : Multiset α\nn : ℕ\n⊢ filter p (n • 0) = n • filter p 0\n\ncase refine'_2\nα : Type u_1\nβ : Type ?u.233049\nγ : Type ?u.233052\np : α → Prop\ninst✝ : DecidablePred p\ns : Multiset α... | [
2033,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2024,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.prod_map_inv | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.93370\nγ : Type ?u.93373\ninst✝ : DivisionCommMonoid α\nm : Multiset ι\nf g : ι → α\n⊢ prod (map (fun i => (f i)⁻¹) m) = (prod (map f m))⁻¹",
"tactic": "simp_rw [←(m.map f).prod_map_inv', map_map, Function.comp_apply]"... | [
315,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_pos_of_pos_of_le_one | [
{
"state_after": "case h₁.h\nx : ℝ\nhx0 : 0 < x\nhx : x ≤ 1\n⊢ abs' x ^ 4 ≤ x\n\ncase h₂.h\nx : ℝ\nhx0 : 0 < x\nhx : x ≤ 1\n⊢ x ^ 3 ≤ x",
"state_before": "x : ℝ\nhx0 : 0 < x\nhx : x ≤ 1\n⊢ abs' x ^ 4 * (5 / 96) + x ^ 3 / 6 ≤ x * (5 / 96) + x / 6",
"tactic": "gcongr"
},
{
"state_after": "no goals... | [
1897,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1881,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_himp_right | [] | [
645,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.nsmul_toReal_eq_mul | [
{
"state_after": "n : ℕ\nh : n ≠ 0\nθ : Angle\n⊢ toReal (n • ↑(toReal θ)) = ↑n * toReal θ ↔ toReal θ ∈ Set.Ioc (-π / ↑n) (π / ↑n)",
"state_before": "n : ℕ\nh : n ≠ 0\nθ : Angle\n⊢ toReal (n • θ) = ↑n * toReal θ ↔ toReal θ ∈ Set.Ioc (-π / ↑n) (π / ↑n)",
"tactic": "nth_rw 1 [← coe_toReal θ]"
},
{
... | [
668,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Basis.lean | AffineBasis.coords_apply | [] | [
303,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.diff_ae_eq_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.106226\nγ : Type ?u.106229\nδ : Type ?u.106232\nι : Type ?u.106235\ninst✝ : MeasurableSpace α\nμ μ₁ μ₂ : Measure α\ns s₁ s₂ t : Set α\n⊢ s \\ t =ᵐ[μ] s ↔ ↑↑μ (s ∩ t) = 0",
"tactic": "simp [eventuallyLE_antisymm_iff, ae_le_set, diff_... | [
476,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.toMatrix'_mul | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.903066\nM✝ : Type ?u.903069\ninst✝¹⁸ : Semiring R\ninst✝¹⁷ : AddCommMonoid M✝\ninst✝¹⁶ : Module R M✝\nR₁ : Type ?u.903105\nM₁ : Type ?u.903108\ninst✝¹⁵ : Ring R₁\ninst✝¹⁴ : AddCommGroup M₁\ninst✝¹³ : Module R₁ M₁\nR₂ : Type u_1\nM₂ : Type ?u.903720\n... | [
270,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_hasDerivWithinAt_of_tendsto_ae_left | [
{
"state_after": "ι : Type ?u.1767200\n𝕜 : Type ?u.1767203\nE : Type u_1\nF : Type ?u.1767209\nA : Type ?u.1767212\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedSpace ℝ E\nf : ℝ → E\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ι\na b z : ℝ\nu v ua ub va vb : ι → ℝ\ninst✝²... | [
948,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.neg_le_of_neg_le | [] | [
808,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
11
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_def_nonempty | [] | [
2200,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2198,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.nonempty | [] | [
1134,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.eq_spanSingleton_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝⁶ : CommRing P\ninst✝⁵ : Algebra R P\nloc : IsLocalization S P\nR₁ : Type ?u.1739872\ninst✝⁴ : CommRing R₁\nK : Type ?u.1739878\ninst✝³ : Field K\ninst✝² : Algebra R₁ K\ninst✝¹ : IsFractionRi... | [
1543,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1541,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.ofAlgHom_coe_algHom | [] | [
506,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
504,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_zero | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\n⊢ num 0 = 0",
"tactic": "convert num_div' (0 : K[X]) one_ne_zero <;> simp"
}
] | [
1153,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1153,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_pos_lt_iff_one_lt_mul' | [
{
"state_after": "ι : Type ?u.41314\nα : Type u_1\nβ : Type ?u.41320\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\n⊢ 1 / a < b ↔ 1 < a * b",
"state_before": "ι : Type ?u.41314\nα : Type u_1\nβ : Type ?u.41320\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nha : 0 < a\n⊢ a... | [
227,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | Continuous.nnnorm' | [] | [
1212,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_lt_one_iff_real_of_norm_one | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.3244202\nE : Type ?u.3244205\nF : Type u_1\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\nx y : F\nhx : ‖x‖ = 1\nhy : ‖y‖ = 1\... | [
1729,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1728,
1
] |
Mathlib/Order/SemiconjSup.lean | IsOrderRightAdjoint.right_mono | [] | [
68,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_id | [] | [
1394,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/Order/Bounds/Basic.lean | MonotoneOn.mem_upperBounds_image_self | [] | [
1160,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
Mathlib/Combinatorics/Composition.lean | CompositionAsSet.blocks_sum | [
{
"state_after": "n : ℕ\nc : CompositionAsSet n\nthis : take (length c) (blocks c) = blocks c\n⊢ sum (blocks c) = n",
"state_before": "n : ℕ\nc : CompositionAsSet n\n⊢ sum (blocks c) = n",
"tactic": "have : c.blocks.take c.length = c.blocks := take_all_of_le (by simp [blocks])"
},
{
"state_after... | [
980,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.isRoot_of_aeval_algebraMap_eq_zero | [] | [
377,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Computability/Reduce.lean | ManyOneEquiv.le_congr_right | [] | [
250,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.11681\ninst✝ : MeasurableSpace α\nj : JordanDecomposition α\nr : ℝ\nhr : 0 ≤ r\n⊢ (r • j).posPart = Real.toNNReal r • j.posPart",
"tactic": "rw [real_smul_def, ← smul_posPart, if_pos hr]"
}
] | [
153,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_eq_pi_div_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arccos x = π / 2 ↔ x = 0",
"tactic": "simp [arccos]"
}
] | [
399,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_of_tendsto | [] | [
264,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.inner_products_summable | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.3502141\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_3\nx : E\nv : ι → E\nhv : Orthonormal 𝕜 v\n⊢ HasSum (fun i => ‖... | [
1918,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1909,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.lor'_to_nat | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.603128\n⊢ ∀ (m n : Num), ↑(lor m n) = Nat.lor' ↑m ↑n",
"tactic": "apply bitwise'_to_nat fun x y => pos (PosNum.lor x y) <;> intros <;> cases_type* Bool <;> rfl"
}
] | [
938,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_coe | [] | [
527,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_abs_abs | [] | [
830,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
829,
1
] |
Mathlib/Order/GameAdd.lean | Prod.GameAdd.fix_eq | [] | [
134,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/GDelta.lean | isGδ_iInter_of_open | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.1617\nγ : Type ?u.1620\nι : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : Encodable ι\nf : ι → Set α\nhf : ∀ (i : ι), IsOpen (f i)\n⊢ ∀ (t : Set α), t ∈ range f → IsOpen t",
"tactic": "rwa [forall_range_iff]"
},
{
"state_af... | [
79,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.coe_mk' | [
{
"state_after": "ι : Type u_1\nI J : Box ι\nx y l u : ι → ℝ\n⊢ ↑(if h : ∀ (i : ι), l i < u i then ↑{ lower := l, upper := u, lower_lt_upper := h } else ⊥) =\n Set.pi univ fun i => Ioc (l i) (u i)",
"state_before": "ι : Type u_1\nI J : Box ι\nx y l u : ι → ℝ\n⊢ ↑(mk' l u) = Set.pi univ fun i => Ioc (l i)... | [
339,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/List/Func.lean | List.Func.add_nil | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u\ninst✝ : AddMonoid α\nas : List α\n⊢ map (fun a => a + default) as = as",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type w\nα : Type u\ninst✝ : AddMonoid α\nas : List α\n⊢ add as [] = as",
"tactic": "rw [add, @pointwise_nil α α α ⟨0⟩ ... | [
351,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/Set/Basic.lean | Set.insert_nonempty | [] | [
1201,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1200,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.card_le_of_model_distinctConstantsTheory | [] | [
1093,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | InnerProductGeometry.sin_angle_mul_norm_mul_norm | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx✝ y✝ x y : V\n⊢ sin (arccos (inner x y / (‖x‖ * ‖y‖))) * (‖x‖ * ‖y‖) = sqrt (inner x x * inner y y - inner x y * inner x y)",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace... | [
206,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | LiouvilleWith.rat_mul_iff | [
{
"state_after": "no goals",
"state_before": "p q x y : ℝ\nr : ℚ\nm : ℤ\nn : ℕ\nhr : r ≠ 0\n⊢ LiouvilleWith p (↑r * x) ↔ LiouvilleWith p x",
"tactic": "rw [mul_comm, mul_rat_iff hr]"
}
] | [
145,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_const_mul_atBot_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.230840\nι' : Type ?u.230843\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.230852\ninst✝ : LinearOrderedField α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x => r * f x) l atBot ↔ Tendsto f l atTop",
"tactic": "simpa only [neg_mul, tend... | [
1107,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_bot | [] | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits_eq_nil_iff_eq_zero | [
{
"state_after": "case mp\nn✝ b n : ℕ\n⊢ digits b n = [] → n = 0\n\ncase mpr\nn✝ b n : ℕ\n⊢ n = 0 → digits b n = []",
"state_before": "n✝ b n : ℕ\n⊢ digits b n = [] ↔ n = 0",
"tactic": "constructor"
},
{
"state_after": "case mp\nn✝ b n : ℕ\nh : digits b n = []\n⊢ n = 0",
"state_before": "cas... | [
299,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.left_le_of_le_inf_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderTop α\na b c : α\nh : b ⊓ a ≤ c\nhd : Codisjoint b c\n⊢ a ⊓ b ≤ c",
"tactic": "rwa [inf_comm]"
}
] | [
395,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_smul_right | [] | [
125,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.sub_add_comm | [
{
"state_after": "n m k : Nat\nh : k ≤ n\n⊢ n + m = n - k + m + k",
"state_before": "n m k : Nat\nh : k ≤ n\n⊢ n + m - k = n - k + m",
"tactic": "rw [Nat.sub_eq_iff_eq_add (Nat.le_trans h (Nat.le_add_right ..))]"
},
{
"state_after": "no goals",
"state_before": "n m k : Nat\nh : k ≤ n\n⊢ n + ... | [
437,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
435,
11
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift_type_eq | [] | [
746,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Order/Lattice.lean | inf_inf_distrib_left | [] | [
536,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Integral.lean | MeasureTheory.StronglyMeasurable.integral_prod_left | [] | [
138,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
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