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/RingTheory/FiniteType.lean | AlgHom.FiniteType.of_comp_finiteType | [] | [
318,
42
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316,
1
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.biUnionIndex_le | [
{
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371,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/Analysis/SpecificLimits/Basic.lean | tsum_geometric_inv_two | [] | [
227,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Functor.asEquivalence_inverse | [] | [
544,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
1
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Mathlib/Data/Stream/Init.lean | Stream'.nth_unfolds_head_tail | [
{
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"tactic": "intro n"
},
{
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410,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.lintegral_nnnorm_zero | [
{
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"tactic": "simp"
}
] | [
87,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Set/NAry.lean | Set.image2_singleton_left | [
{
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192,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.lmul'_toLinearMap | [] | [
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6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.snormEssSup_indicator_const_eq | [
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579,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.prod_zero | [
{
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600,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Padics/Hensel.lean | deriv_norm_ne_zero | [
{
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118,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
9
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sup_succ_eq_lsub | [] | [
1636,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.nonarchimedean | [] | [
283,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.copy_eq | [] | [
261,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearIsometry.norm_toContinuousLinearMap_comp | [
{
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1791,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1788,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.smul_single_one | [
{
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1608,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Image.lean | Set.preimage_iterate_eq | [
{
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160,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
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Mathlib/Data/Finset/Basic.lean | Finset.union_val | [] | [
1336,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
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Std/Data/Array/Lemmas.lean | Array.get_set | [
{
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},
{
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54
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Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.sum | [
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301,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
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Mathlib/Data/Finset/Card.lean | Finset.card_erase_add_one | [] | [
142,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.max_power_factor | [
{
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1041,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mul | [] | [
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42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1896,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.snoc_comp_nat_add | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/Topology/Algebra/Group/Basic.lean | Subgroup.topologicalClosure_coe | [] | [
715,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.inter | [
{
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Mathlib/Data/Finset/Prod.lean | Finset.product_subset_product_left | [] | [
98,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Fin/Basic.lean | Fin.liftFun_iff_succ | [
{
"state_after": "case mp\nn m : ℕ\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsTrans α r\nf : Fin (n + 1) → α\n⊢ ((fun x x_1 => x < x_1) ⇒ r) f f → ∀ (i : Fin n), r (f (↑castSucc i)) (f (succ i))\n\ncase mpr\nn m : ℕ\nα : Type u_1\nr : α → α → Prop\ninst✝ : IsTrans α r\nf : Fin (n + 1) → α\n⊢ (∀ (i : Fin n), r (... | [
1878,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1868,
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Mathlib/Topology/Algebra/Order/MonotoneContinuity.lean | Monotone.continuous_of_denseRange | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ninst✝⁶ : LinearOrder α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : OrderTopology α\ninst✝³ : LinearOrder β\ninst✝² : TopologicalSpace β\ninst✝¹ : OrderTopology β\ninst✝ : DenselyOrdered β\nf : α → β\nh_mono : Monotone f\nh_dense : DenseRan... | [
284,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
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] |
Mathlib/Data/Set/Sups.lean | Set.Nonempty.of_sups_left | [] | [
124,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_add | [] | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
11
] |
src/lean/Init/SimpLemmas.lean | Bool.and_true | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ (b && true) = b",
"tactic": "cases b <;> rfl"
}
] | [
111,
87
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
111,
9
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.coe_toEmbedding | [] | [
667,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.dickson_zero | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.comap_exp_nhdsWithin_Ioi_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.151109\nx y z : ℝ\nl : Filter α\n⊢ comap exp (𝓝[Set.Ioi 0] 0) = atBot",
"tactic": "rw [← map_exp_atBot, comap_map exp_injective]"
}
] | [
328,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
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Mathlib/Algebra/Order/Floor.lean | Int.fract_add_fract_le | [
{
"state_after": "F : Type ?u.151819\nα : Type u_1\nβ : Type ?u.151825\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na✝ a b : α\n⊢ ↑⌊a + b⌋ - 1 ≤ ↑⌊a⌋ + ↑⌊b⌋",
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859,
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857,
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Mathlib/Data/Finset/Lattice.lean | Finset.min_eq_inf_withTop | [] | [
1243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
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Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.SplitMono.mono | [
{
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167,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableAt.differentiableWithinAt | [] | [
596,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.preimage_open_of_open | [] | [
440,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Data/List/Intervals.lean | List.Ico.append_consecutive | [
{
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"state_before": "n m l : ℕ\nhnm : n ≤ m\nhml : m ≤ l\n⊢ Ico n m ++ Ico m l = Ico n l",
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},
{
"state_after": "case h.e'_2.h.e'_6\nn m l : ℕ\nhnm : n ≤ m\n... | [
103,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_diff_add_ncard_eq_ncard | [
{
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"tactic": "classical\nrw [ncard_eq_toFinset_card _ ht, ncard_eq_toFinset_card _ (ht.subset h),\n n... | [
500,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.nfp_mul_opow_omega_add | [
{
"state_after": "case a\na c b : Ordinal\nha : 0 < a\nhc : 0 < c\nhca : c ≤ a ^ ω\n⊢ nfp (fun x => a * x) (a ^ ω * b + c) ≤ a ^ ω * succ b\n\ncase a\na c b : Ordinal\nha : 0 < a\nhc : 0 < c\nhca : c ≤ a ^ ω\n⊢ a ^ ω * succ b ≤ nfp (fun x => a * x) (a ^ ω * b + c)",
"state_before": "a c b : Ordinal\nha : 0 ... | [
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22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
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Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_sub_one | [
{
"state_after": "no goals",
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"tactic": "rw [← zpow_add_one, sub_add_cancel]"
}
] | [
211,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/GroupTheory/Commensurable.lean | Commensurable.commensurable_conj | [] | [
81,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_subtype_coe | [] | [
536,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_nat_cast | [
{
"state_after": "no goals",
"state_before": "x✝ y z x : ℝ\nn : ℕ\n⊢ x ^ ↑n = x ^ n",
"tactic": "simpa using rpow_int_cast x n"
}
] | [
361,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Group/Defs.lean | negSucc_zsmul | [
{
"state_after": "G✝ : Type ?u.52115\ninst✝¹ : DivInvMonoid G✝\na✝ b : G✝\nG : Type u_1\ninst✝ : SubNegMonoid G\na : G\nn : ℕ\n⊢ Int.negSucc n • a = -(↑(n + 1) • a)",
"state_before": "G✝ : Type ?u.52115\ninst✝¹ : DivInvMonoid G✝\na✝ b : G✝\nG : Type u_1\ninst✝ : SubNegMonoid G\na : G\nn : ℕ\n⊢ Int.negSucc n... | [
943,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
940,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | finprod_mem_biUnion | [
{
"state_after": "α : Type u_2\nβ : Type ?u.368420\nι : Type u_1\nG : Type ?u.368426\nM : Type u_3\nN : Type ?u.368432\ninst✝¹ : CommMonoid M\ninst✝ : CommMonoid N\nf g : α → M\na b : α\ns t✝ : Set α\nI : Set ι\nt : ι → Set α\nh : PairwiseDisjoint I t\nhI : Set.Finite I\nht : ∀ (i : ι), i ∈ I → Set.Finite (t i)... | [
1082,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1078,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | isPreconnected_iff_ordConnected | [] | [
434,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Splitting.ιSummand_epi_naturality | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX Y : SimplicialObject C\ns : Splitting X\nΔ₁ Δ₂ : SimplexCategoryᵒᵖ\nA : IndexSet Δ₁\np : Δ₁ ⟶ Δ₂\ninst✝ : Epi p.unop\n⊢ (ιCoprod s.N A ≫ map X s.ι Δ₁) ≫ X.map p = ιCoprod s.N (IndexSet.epiComp A p) ≫ map X s.ι Δ₂",
"state... | [
351,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.append_mk | [
{
"state_after": "no goals",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nl₁ l₂ : List Γ\n⊢ append l₁ (mk l₂) = mk (l₁ ++ l₂)",
"tactic": "induction l₁ <;>\n simp only [*, ListBlank.append, List.nil_append, List.cons_append, ListBlank.cons_mk]"
}
] | [
459,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.eq_trans₃ | [] | [
121,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.iSup_zero_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.869401\nβ : Type ?u.869404\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nι : Sort u_1\n⊢ (⨆ (x : ι), 0) = 0",
"tactic": "simp"
}
] | [
2484,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2484,
1
] |
Mathlib/Data/Rat/Floor.lean | Rat.fract_inv_num_lt_num_of_pos | [
{
"state_after": "q : ℚ\nq_pos : 0 < q\nq_num_pos : 0 < q.num\n⊢ (fract q⁻¹).num < q.num",
"state_before": "q : ℚ\nq_pos : 0 < q\n⊢ (fract q⁻¹).num < q.num",
"tactic": "have q_num_pos : 0 < q.num := Rat.num_pos_iff_pos.mpr q_pos"
},
{
"state_after": "q : ℚ\nq_pos : 0 < q\nq_num_pos : 0 < q.num\n... | [
169,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Algebra/Algebra/Tower.lean | Submodule.span_algebraMap_image | [] | [
333,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/Algebra/Order/Group/Bounds.lean | IsLUB.exists_between_sub_self' | [] | [
36,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
34,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurableSet_le' | [] | [
482,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Order/Lattice.lean | left_eq_sup | [] | [
190,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nh : sin x = 0\nh₃ : x - ↑⌊x / π⌋ * π > 0\n⊢ 0 = sin (x - ↑⌊x / π⌋ * π)",
"tactic": "simp [sub_eq_add_neg, sin_add, h, sin_int_mul_pi]"
}
] | [
517,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Set/Function.lean | Set.InjOn.rightInvOn_of_leftInvOn | [] | [
1148,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1146,
1
] |
Mathlib/Data/Set/Basic.lean | Set.powerset_empty | [] | [
2164,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2163,
1
] |
Mathlib/Analysis/InnerProductSpace/l2Space.lean | HilbertBasis.repr_self | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : IsROrC 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ncplt : CompleteSpace E\nG : ι → Type ?u.697102\ninst✝¹ : (i : ι) → NormedAddCommGroup (G i)\ninst✝ : (i : ι) → InnerProductSpace 𝕜 (G ... | [
438,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
11
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_ite_eq' | [] | [
1099,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1097,
1
] |
Mathlib/Data/Finsupp/Fin.lean | Finsupp.tail_cons | [
{
"state_after": "no goals",
"state_before": "n : ℕ\ni : Fin n\nM : Type u_1\ninst✝ : Zero M\ny : M\nt : Fin (n + 1) →₀ M\ns : Fin n →₀ M\nk : Fin n\n⊢ ↑(tail (cons y s)) k = ↑s k",
"tactic": "simp only [tail_apply, cons_succ]"
}
] | [
59,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Order/Ideal.lean | IsCoatom.isMaximal | [
{
"state_after": "no goals",
"state_before": "P : Type u_1\ninst✝² : LE P\ninst✝¹ : IsDirected P fun x x_1 => x ≤ x_1\ninst✝ : Nonempty P\nI : Ideal P\nhI : IsCoatom I\nsrc✝ : IsProper I := IsCoatom.isProper hI\nx✝ : Ideal P\nhJ : I < x✝\n⊢ ↑x✝ = univ",
"tactic": "simp [hI.2 _ hJ]"
}
] | [
245,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Topology/Semicontinuous.lean | upperSemicontinuousAt_sum | [
{
"state_after": "α : Type u_2\ninst✝⁵ : TopologicalSpace α\nβ : Type ?u.204861\ninst✝⁴ : Preorder β\nf✝ g : α → β\nx : α\ns t : Set α\ny z : β\nι : Type u_1\nγ : Type u_3\ninst✝³ : LinearOrderedAddCommMonoid γ\ninst✝² : TopologicalSpace γ\ninst✝¹ : OrderTopology γ\ninst✝ : ContinuousAdd γ\nf : ι → α → γ\na : F... | [
976,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
972,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\ninst✝ : NeZero n\na : Fin (n + 1)\nb : Fin n\nha : a ≠ 0\n⊢ ↑(succAbove a) b = 0 ↔ b = 0",
"tactic": "simp only [← succAbove_ne_zero_zero ha, OrderEmbedding.eq_iff_eq, iff_self]"
}
] | [
2044,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2042,
1
] |
Mathlib/Order/LocallyFinite.lean | WithTop.Ioo_coe_top | [] | [
1137,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1136,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.im | [
{
"state_after": "α : Type u_2\nE : Type ?u.6150522\nF : Type ?u.6150525\nG : Type ?u.6150528\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedAddCommGroup G\n𝕜 : Type u_1\ninst✝ : IsROrC 𝕜\nf : α → 𝕜\nhf : Memℒp f p\nth... | [
1615,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1609,
1
] |
Mathlib/CategoryTheory/NatIso.lean | CategoryTheory.NatIso.cancel_natIso_hom_left | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\nF G : C ⥤ D\nα : F ≅ G\nX : C\nZ : D\ng g' : G.obj X ⟶ Z\n⊢ α.hom.app X ≫ g = α.hom.app X ≫ g' ↔ g = g'",
"tactic": "simp only [cancel_epi, refl]"
}
] | [
132,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | compRel_assoc | [
{
"state_after": "case h.mk\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.12185\nr s t : Set (α × α)\na b : α\n⊢ (a, b) ∈ r ○ s ○ t ↔ (a, b) ∈ r ○ (s ○ t)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.12185\nr s t : Set (α × α)\n⊢ r ○ s ○ t = r ○ (s ○ ... | [
186,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Deprecated/Subgroup.lean | Additive.isNormalAddSubgroup_iff | [
{
"state_after": "case mk\nG : Type u_1\nH : Type ?u.20782\nA : Type ?u.20785\na a₁ a₂ b c : G\ninst✝ : Group G\ns : Set G\nh₁ : IsAddSubgroup s\nh₂ : ∀ (n : Additive G), n ∈ s → ∀ (g : Additive G), g + n + -g ∈ s\n⊢ IsNormalSubgroup s",
"state_before": "G : Type u_1\nH : Type ?u.20782\nA : Type ?u.20785\na... | [
197,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.equiv_apply | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_cubic | [] | [
1239,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1238,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.pellZd_sub | [
{
"state_after": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\nt : pellZd a1 (n + (m - n)) = pellZd a1 n * pellZd a1 (m - n) := pellZd_add a1 n (m - n)\n⊢ pellZd a1 (m - n) = pellZd a1 m * star (pellZd a1 n)",
"state_before": "a : ℕ\na1 : 1 < a\nm n : ℕ\nh : n ≤ m\n⊢ pellZd a1 (m - n) = pellZd a1 m * star (pellZd... | [
383,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/List/Basic.lean | List.set_eq_take_cons_drop | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.221077\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nn : ℕ\nl : List α\nh : n < length l\n⊢ set l n a = take n l ++ a :: drop (n + 1) l",
"tactic": "rw [set_eq_modifyNth, modifyNth_eq_take_cons_drop _ h]"
}
] | [
2293,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2291,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_add | [] | [
309,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Function/Egorov.lean | MeasureTheory.Egorov.notConvergentSeq_measurableSet | [] | [
81,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_comm | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\n⊢ n₁ /. ↑d₁ + n₂ /. ↑d₂ = n₂ /. ↑d₂ + n₁ /. ↑d₁",
"tactic": "simp [h₁, h₂, add_comm, mul_comm]"
}
] | [
213,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
11
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.equiv_of_mk_equiv | [
{
"state_after": "case left\nx y : PGame\nL : LeftMoves x ≃ LeftMoves y\nR : RightMoves x ≃ RightMoves y\nhl : ∀ (i : LeftMoves x), moveLeft x i ≈ moveLeft y (↑L i)\nhr : ∀ (j : RightMoves x), moveRight x j ≈ moveRight y (↑R j)\n⊢ (∀ (i : LeftMoves x), (∃ i', moveLeft x i ≤ moveLeft y i') ∨ ∃ j, moveRight (move... | [
891,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.emem_iff_mem_toList | [
{
"state_after": "α : Type u_1\nx : α\nt : Ordnode α\n⊢ Any (Eq x) t ↔ x ∈ toList t",
"state_before": "α : Type u_1\nx : α\nt : Ordnode α\n⊢ Emem x t ↔ x ∈ toList t",
"tactic": "unfold Emem"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx : α\nt : Ordnode α\n⊢ Any (Eq x) t ↔... | [
551,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | ContDiffAt.csinh | [] | [
560,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_mul_mul_cancel | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.73342\nβ : Type ?u.73345\nG : Type u_1\ninst✝ : CommGroup G\na✝ b✝ c✝ d a b c : G\n⊢ a / c * (b * c) = a * b",
"tactic": "rw [mul_left_comm, div_mul_cancel', mul_comm]"
}
] | [
995,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | AddMonoidHom.ext_nat | [] | [
213,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/RingTheory/Coprime/Basic.lean | IsCoprime.add_mul_left_left_iff | [] | [
324,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Data/Set/Function.lean | StrictMonoOn.injOn | [] | [
1545,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1543,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_finset_of_infinite | [] | [
1028,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.sInter | [] | [
183,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
11
] |
Mathlib/Data/Nat/Choose/Factorization.lean | Nat.factorization_centralBinom_eq_zero_of_two_mul_lt | [] | [
123,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_add_mul_I | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ x y : ℂ\n⊢ cos (x + y * I) = cos x * cosh y - sin x * sinh y * I",
"tactic": "rw [cos_add, cos_mul_I, sin_mul_I, mul_assoc]"
}
] | [
886,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.preimage_image_mk_closed | [
{
"state_after": "X : Type u_1\nY : Type ?u.49015\nZ : Type ?u.49018\nα : Type ?u.49021\nι : Type ?u.49024\nπ : ι → Type ?u.49029\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : (i : ι) → TopologicalSpace (π i)\nx y z : X\ns : Set X\nf : X → Y\nt : Set (Separation... | [
464,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/GroupTheory/Abelianization.lean | Abelianization.map_map_apply | [] | [
199,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.sameRay_vsub_left | [
{
"state_after": "case intro.intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.364088\nP : Type u_3\nP' : Type ?u.364094\ninst✝³ : StrictOrderedCommRing R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx z : P\nt : R\nht0 : 0 ≤ t\nright✝ : t ≤ 1\n⊢ SameRay R (↑(lineMap x z) t -ᵥ x) (z... | [
573,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/GroupTheory/Perm/ViaEmbedding.lean | Equiv.Perm.viaEmbedding_apply_of_not_mem | [] | [
39,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.eball_top_eq_univ | [] | [
1192,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | toLex_pow | [] | [
284,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.edist_of_im_eq | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.15266\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nz w : ℂ\nh : z.im = w.im\n⊢ edist z w = edist z.re w.re",
"tactic": "rw [edist_nndist, edist_nndist, nndist_of_im_eq h]"
}
] | [
127,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Constructions.lean | map_nhds_subtype_val | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.158814\nδ : Type ?u.158817\nε : Type ?u.158820\nζ : Type ?u.158823\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\np : α → Prop\ns : Set α\na : ↑s\n⊢ map Subtype.val (𝓝 a) = 𝓝[s] ↑a",
... | [
1068,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1067,
1
] |
Mathlib/Algebra/Homology/HomotopyCategory.lean | CategoryTheory.NatTrans.mapHomotopyCategory_id | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝⁴ : Category V\ninst✝³ : Preadditive V\nc✝ : ComplexShape ι\nW : Type u_3\ninst✝² : Category W\ninst✝¹ : Preadditive W\nc : ComplexShape ι\nF : V ⥤ W\ninst✝ : Functor.Additive F\n⊢ mapHomotopyCategory (𝟙 F) c = 𝟙 (Functor.mapHomo... | [
217,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
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