file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEmbedding.id | [
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Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.ext_iff | [] | [
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Mathlib/Topology/Separation.lean | specializes_iff_eq | [] | [
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_X' | [] | [
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_strictMono_of_injective | [] | [
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Mathlib/Data/Matrix/Basic.lean | LinearEquiv.mapMatrix_symm | [] | [
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Mathlib/Topology/Bases.lean | TopologicalSpace.countable_cover_nhdsWithin | [
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.cons_not_rev | [] | [
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31
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_eq_zero_of_dvd_of_eval_eq_zero | [] | [
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44
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Mathlib/RingTheory/Coprime/Lemmas.lean | IsCoprime.pow | [] | [
203,
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202,
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Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteCoproducts.leftUnitor_hom | [] | [
191,
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Mathlib/FieldTheory/Subfield.lean | Subfield.comap_iInf | [] | [
802,
26
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800,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioc_diff_Ioo_same | [
{
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"tactic": "rw [← Ioc_diff_right, diff_diff_cancel_left (singleton_subset_iff.2 <| right_mem_Ioc.2 h)]"
}
] | [
816,
93
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Mathlib/Data/Fintype/Card.lean | Function.LeftInverse.rightInverse_of_card_le | [] | [
684,
8
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678,
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.algHom_mk_adjoin_splits' | [
{
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasLimitsOfSizeShrink | [] | [
620,
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.zero_rpow_le_one | [
{
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137,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.apply_dualBasis_right | [
{
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Mathlib/Data/Finset/Pointwise.lean | Finset.smul_finset_sdiff₀ | [] | [
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45
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Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.coe_copy | [] | [
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Mathlib/Order/Filter/Lift.lean | Filter.lift_le | [] | [
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25
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Mathlib/Data/List/Forall2.lean | List.forall₂_drop_append | [
{
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236,
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Mathlib/Topology/MetricSpace/Holder.lean | holderOnWith_univ | [
{
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"tactic": "simp only [HolderOnWith, HolderWith, m... | [
81,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Basic.lean | Set.diff_subset_diff | [] | [
1881,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_ne_zero | [] | [
1273,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.map_val_Iic_atBot | [] | [
1586,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
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Mathlib/GroupTheory/Submonoid/Basic.lean | MonoidHom.eq_of_eqOn_topM | [] | [
609,
25
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Mathlib/Data/Multiset/Basic.lean | Multiset.filter_add_not | [
{
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Mathlib/LinearAlgebra/Determinant.lean | LinearMap.det_conj | [
{
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Mathlib/Data/Seq/Computation.lean | Computation.think_equiv | [] | [
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92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1021,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanExt_hom_app_right | [
{
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Mathlib/Algebra/Order/Floor.lean | Nat.preimage_Ioc | [
{
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"state_before": "F : Type ?u.65750\nα : Type u_1\nβ : Type ?u.65... | [
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Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.coe_prodMap | [] | [
278,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.ascFactorial_lt_pow_add | [
{
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},
{
"state_after": "n : ℕ\na✝ : 2 ≤ 1\n⊢ ascFactorial n 1 < (n + 1) ^ 1",
"state_before": "n : ℕ\n⊢ 2 ≤ 1 → ascFactorial n 1 < (n + 1) ^ 1",
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{
... | [
325,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_lcm | [] | [
740,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.mem_uniformity_dist | [] | [
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43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
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Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | HasSum.mul_right | [
{
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Icc' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.108702\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh₁ : c ≤ b\nx : α\n⊢ x ∈ Iic b ∪ Icc c d ↔ x ∈ Iic (max b d)",
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1460,
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Mathlib/Order/Closure.lean | LowerAdjoint.closure_sup_closure | [] | [
455,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
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Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.ι_retraction | [
{
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"tactic": "simp [retraction]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_triangle | [
{
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"state_before": "ι : S... | [
376,
95
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358,
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Mathlib/Data/List/Duplicate.lean | List.duplicate_cons_self_iff | [] | [
64,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.listTransvecCol_mul_last_col | [
{
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380,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_nonpos_of_nonnpos_of_neg_pi_le | [] | [
433,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
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Mathlib/Algebra/Category/GroupCat/Images.lean | AddCommGroupCat.image.lift_fac | [
{
"state_after": "case w\nG H : AddCommGroupCat\nf : G ⟶ H\nF' : MonoFactorisation f\nx : ↑(image f)\n⊢ ↑(lift F' ≫ F'.m) x = ↑(ι f) x",
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"tactic": "ext x"
},
{
"state_after": "case w\nG H : AddC... | [
94,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Heyting/Basic.lean | compl_sup_distrib | [
{
"state_after": "no goals",
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"tactic": "simp_rw [← himp_bot, sup_himp_distrib]"
}
] | [
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41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/Exponential.lean | exp_analytic | [] | [
456,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
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Mathlib/Algebra/Order/Sub/Defs.lean | tsub_le_iff_right | [] | [
69,
37
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Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pullbackObj_eq_pullbackObj | [] | [
470,
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468,
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.isStrictOrder | [] | [
379,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
11
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Mathlib/Data/Set/Finite.lean | Set.card_image_of_inj_on | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ns : Set α\ninst✝¹ : Fintype ↑s\nf : α → β\ninst✝ : Fintype ↑(f '' s)\nH : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → f x = f y → x = y\nthis : (a : Prop) → Decidable a\n⊢ ∀ (x : β), x ∈ Finset.image f (toFinset s) ↔ x ∈... | [
1221,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1213,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reverse_cons | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v w : V\nh : Adj G u v\np : Walk G v w\n⊢ reverse (cons h p) = append (reverse p) (cons (_ : Adj G v u) nil)",
"tactic": "simp [reverse]"
}
] | [
357,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_diff_image_subset | [] | [
1118,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/Data/Rat/Cast.lean | Rat.cast_inv_of_ne_zero | [
{
"state_after": "F : Type ?u.35260\nι : Type ?u.35263\nα : Type u_1\nβ : Type ?u.35269\ninst✝ : DivisionRing α\nn : ℤ\nd : ℕ\nh : d ≠ 0\nc : Nat.coprime (Int.natAbs n) d\nn0 : ↑n ≠ 0\nd0 : ↑d ≠ 0\nx✝ : n ≠ 0\n⊢ ↑(mk' n d)⁻¹ = (↑(mk' n d))⁻¹",
"state_before": "F : Type ?u.35260\nι : Type ?u.35263\nα : Type ... | [
178,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/Associated.lean | Associated.irreducible | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.218014\nγ : Type ?u.218017\nδ : Type ?u.218020\ninst✝ : Monoid α\np q : α\nh : p ~ᵤ q\nhp : Irreducible p\nu : αˣ\nhu : p * ↑u = q\na b : α\nhab : q = a * b\n⊢ p = p * ↑u * ↑u⁻¹",
"tactic": "simp"
},
{
"state_after": "α : Ty... | [
646,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
11
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_apply | [] | [
404,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Std/Data/List/Lemmas.lean | List.range_succ | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ range (succ n) = range n ++ [n]",
"tactic": "simp only [range_eq_range', range'_1_concat, Nat.zero_add]"
}
] | [
1924,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1923,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.singleton_vsub_singleton | [] | [
1514,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1513,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monic_of_natDegree_le_of_coeff_eq_one | [
{
"state_after": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.648061\nn : ℕ\npn : natDegree p ≤ n\np1 : coeff p n = 1\n⊢ leadingCoeff p = 1",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.648061\nn :... | [
861,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.IsPartition.infPrepartition | [] | [
218,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsSymm.smul | [] | [
929,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableWithinAt.cos | [] | [
940,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Algebra/Parity.lean | Even.pow_abs | [
{
"state_after": "F : Type ?u.112908\nα : Type ?u.112911\nβ : Type ?u.112914\nR : Type u_1\ninst✝ : LinearOrderedRing R\na✝ : R\nn p : ℕ\nhp : Even p\na : R\n⊢ 0 ≤ a ^ p",
"state_before": "F : Type ?u.112908\nα : Type ?u.112911\nβ : Type ?u.112914\nR : Type u_1\ninst✝ : LinearOrderedRing R\na✝ : R\nn p : ℕ\... | [
510,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.conj_mk | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\na✝ x✝ y a x : G\n⊢ a * x = a * x * a⁻¹ * a",
"state_before": "G : Type u_1\ninst✝ : Group G\na✝ x✝ y a x : G\n⊢ SemiconjBy a x (a * x * a⁻¹)",
"tactic": "unfold SemiconjBy"
},
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ :... | [
232,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Geometry/Manifold/Instances/UnitsOfNormedAlgebra.lean | Units.chartAt_source | [] | [
68,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Topology/Sheaves/Stalks.lean | TopCat.Presheaf.germ_exist | [
{
"state_after": "case intro.intro\nC : Type u\ninst✝³ : Category C\ninst✝² : HasColimits C\nX Y Z : TopCat\ninst✝¹ : ConcreteCategory C\ninst✝ : PreservesFilteredColimits (forget C)\nF : Presheaf C X\nx : ↑X\nt : (forget C).obj (stalk F x)\nU : (OpenNhds x)ᵒᵖ\ns : (((whiskeringLeft (OpenNhds x)ᵒᵖ (Opens ↑X)ᵒᵖ ... | [
422,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
414,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | pow_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11493\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 : M\n⊢ a ^ 1 = a",
"tactic": "rw [pow_succ, pow_zero, mul_one]"
}
] | [
100,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/GroupTheory/GroupAction/Sigma.lean | Sigma.smul_mk | [] | [
46,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Data/Set/Image.lean | Function.Surjective.image_surjective | [
{
"state_after": "ι : Sort ?u.104386\nα : Type u_1\nβ : Type u_2\nf : α → β\nhf : Surjective f\ns : Set β\n⊢ ∃ a, f '' a = s",
"state_before": "ι : Sort ?u.104386\nα : Type u_1\nβ : Type u_2\nf : α → β\nhf : Surjective f\n⊢ Surjective (image f)",
"tactic": "intro s"
},
{
"state_after": "ι : Sort... | [
1308,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1305,
1
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.unifIntegrable_finite | [
{
"state_after": "case intro\nα : Type u_3\nβ : Type u_2\nι : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\np : ℝ≥0∞\nf✝ : α → β\ninst✝ : Finite ι\nhp_one : 1 ≤ p\nhp_top : p ≠ ⊤\nf : ι → α → β\nhf : ∀ (i : ι), Memℒp (f i) p\nn : ℕ\nhn : Nonempty (ι ≃ Fin n)\n⊢ UnifIntegrable f ... | [
463,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/ModelTheory/Bundled.lean | FirstOrder.Language.Theory.coe_of | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.norm_lt_one_iff_dvd | [
{
"state_after": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nthis : ‖x‖ ≤ ↑p ^ (-↑1) ↔ x ∈ Ideal.span {↑p ^ 1}\n⊢ ‖x‖ < 1 ↔ ↑p ∣ x",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\n⊢ ‖x‖ < 1 ↔ ↑p ∣ x",
"tactic": "have := norm_le_pow_iff_mem_span_pow x 1"
},
{
"state_after": "p : ℕ\nh... | [
575,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.support_sup | [
{
"state_after": "case a\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → CanonicallyLinearOrderedAddMonoid (α i)\ninst✝ : DecidableEq ι\nf g : Π₀ (i : ι), α i\na✝ : ι\n⊢ a✝ ∈ support (f ⊔ g) ↔ a✝ ∈ support f ∪ support g",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → CanonicallyLin... | [
264,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_pos_of_neg | [
{
"state_after": "a : Int\nh : a < 0\nthis : -0 < -a\n⊢ 0 < -a",
"state_before": "a : Int\nh : a < 0\n⊢ 0 < -a",
"tactic": "have : -0 < -a := Int.neg_lt_neg h"
},
{
"state_after": "no goals",
"state_before": "a : Int\nh : a < 0\nthis : -0 < -a\n⊢ 0 < -a",
"tactic": "rwa [Int.neg_zero] at... | [
900,
29
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
898,
11
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieHom.range_coe | [] | [
313,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_nonneg | [] | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
11
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_prod_mk_right | [] | [
1643,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1642,
1
] |
Mathlib/Topology/Algebra/Equicontinuity.lean | uniformEquicontinuous_of_equicontinuousAt_one | [
{
"state_after": "ι : Type u_1\nG : Type u_2\nM : Type u_3\nhom : Type u_4\ninst✝⁶ : UniformSpace G\ninst✝⁵ : UniformSpace M\ninst✝⁴ : Group G\ninst✝³ : Group M\ninst✝² : UniformGroup G\ninst✝¹ : UniformGroup M\ninst✝ : MonoidHomClass hom G M\nF : ι → hom\nhf : EquicontinuousAt (FunLike.coe ∘ F) 1\n⊢ UniformCon... | [
49,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/CategoryTheory/Generator.lean | CategoryTheory.wellPowered_of_isDetector | [] | [
656,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.trans | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.31228\nα : Type u_1\nβ : Type ?u.31234\nf g : Perm α\np : α → Prop\nx y z : α\nx✝¹ : SameCycle f x y\nx✝ : SameCycle f y z\ni : ℤ\nhi : ↑(f ^ i) x = y\nj : ℤ\nhj : ↑(f ^ j) y = z\n⊢ ↑(f ^ (j + i)) x = z",
"tactic": "rw [zpow_add, mul_apply, hi, h... | [
103,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Topology/CompactOpen.lean | ContinuousMap.curry_apply | [] | [
378,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Std/Data/List/Init/Lemmas.lean | List.length_drop | [] | [
138,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
9
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.neg_fuzzy_iff | [
{
"state_after": "no goals",
"state_before": "x y : PGame\n⊢ -x ‖ y ↔ x ‖ -y",
"tactic": "rw [← neg_neg y, neg_fuzzy_neg_iff, neg_neg]"
}
] | [
1359,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1358,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_conj_eq | [] | [
761,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.isImage_preimage_prod | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.59757\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.59768\nZ : Type u_3\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nproj : Z → B\ninst✝² : TopologicalSpace Z\ninst✝¹ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx✝ : Z\... | [
729,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.div_I | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ -(z * I) * I = z",
"tactic": "simp [mul_assoc]"
}
] | [
806,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
805,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.ne_one | [
{
"state_after": "A : Type u_2\nB : Type u_1\nB' : Type ?u.21842\ninst✝⁵ : CommRing A\ninst✝⁴ : Ring B\ninst✝³ : Ring B'\ninst✝² : Algebra A B\ninst✝¹ : Algebra A B'\nx : B\ninst✝ : Nontrivial B\nh : minpoly A x = 1\n⊢ False",
"state_before": "A : Type u_2\nB : Type u_1\nB' : Type ?u.21842\ninst✝⁵ : CommRin... | [
98,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
] |
Mathlib/Algebra/Order/Module.lean | bddBelow_smul_iff_of_neg | [] | [
240,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.single_eq_monomial | [] | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Std/Data/List/Lemmas.lean | List.eq_replicate | [] | [
294,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
291,
1
] |
Mathlib/Data/Real/ENNReal.lean | Set.OrdConnected.preimage_ennreal_ofReal | [] | [
2519,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2518,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.isCompact_closure_image_coe_of_bounded | [] | [
1605,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1600,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.eq_iff_classes_eq | [] | [
101,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_union | [
{
"state_after": "α : Type u_1\nM : Type u_2\nN : Type ?u.110242\nP : Type ?u.110245\nR : Type u_3\nS : Type ?u.110251\ninst✝⁷ : Semiring R\ninst✝⁶ : Semiring S\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : AddCommMonoid P\ninst✝ : Module R P\ns t : Set ... | [
301,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Topology/ContinuousOn.lean | insert_mem_nhdsWithin_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.20353\nγ : Type ?u.20356\nδ : Type ?u.20359\ninst✝ : TopologicalSpace α\na : α\ns t : Set α\nh : t ∈ 𝓝[s] a\n⊢ insert a t ∈ 𝓝[insert a s] a",
"tactic": "simp [mem_of_superset h]"
}
] | [
295,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.val_mul | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.closure_singleton_one | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG' : Type ?u.220679\ninst✝² : Group G\ninst✝¹ : Group G'\nA : Type ?u.220688\ninst✝ : AddGroup A\nH K : Subgroup G\nk : Set G\n⊢ closure {1} = ⊥",
"tactic": "simp [eq_bot_iff_forall, mem_closure_singleton]"
}
] | [
1299,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.smul_mem | [] | [
149,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
11
] |
Mathlib/Topology/Basic.lean | closure_univ | [] | [
509,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.zero_ne_addChar | [] | [
134,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
133,
9
] |
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