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Mathlib/Data/Complex/Basic.lean | Complex.re_surjective | [] | [
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Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.star_val_eq | [] | [
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Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.comp_id | [
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.norm_integral_le_of_le_const | [
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Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.memℒp_finset_sum' | [
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Mathlib/Data/Real/Sqrt.lean | Filter.Tendsto.sqrt | [] | [
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Mathlib/Data/TypeVec.lean | TypeVec.diag_sub_val | [
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.equivTuple_apply | [] | [
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Mathlib/Order/LiminfLimsup.lean | Filter.IsCobounded.mono | [] | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_lt_coe | [] | [
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Mathlib/Algebra/Tropical/Basic.lean | Tropical.trop_monotone | [] | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.equiv_rfl | [] | [
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.toL1_zero | [] | [
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_mul | [] | [
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.add_smul_sub_mem | [
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Mathlib/Data/Pi/Algebra.lean | Pi.div_def | [] | [
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Mathlib/NumberTheory/Bernoulli.lean | bernoulli_spec' | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_affineCombinationLineMapWeights | [
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Std/Data/List/Lemmas.lean | List.dropLast_append_cons | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.inner_right_finsupp | [
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Mathlib/Topology/Order.lean | TopologicalSpace.nhds_mkOfNhds_single | [
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | Subsemigroup.mem_map_equiv | [] | [
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Mathlib/Data/PFun.lean | PFun.ext' | [] | [
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Mathlib/Topology/Basic.lean | isOpen_iff_forall_mem_open | [
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Mathlib/Order/Filter/Prod.lean | Filter.coprod_bot | [
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Mathlib/Data/Int/Order/Basic.lean | Int.ediv_le_of_le_mul | [] | [
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.isClosed | [
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Mathlib/Data/Finset/Pointwise.lean | Finset.subset_smul_finset_iff₀ | [] | [
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Mathlib/Data/List/Basic.lean | List.length_dropLast | [
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Std/Data/Int/DivMod.lean | Int.eq_mul_of_div_eq_right | [
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Mathlib/Logic/Relation.lean | Relation.ReflGen.to_reflTransGen | [
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Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.exists_finset_support | [
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isInt_neg | [] | [
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Mathlib/Order/CompleteLattice.lean | Monotone.le_map_iSup | [] | [
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Mathlib/Algebra/CharP/Basic.lean | CharP.false_of_nontrivial_of_char_one | [] | [
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Mathlib/Analysis/Normed/Group/AddTorsor.lean | Continuous.vsub | [] | [
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Mathlib/Data/Set/Image.lean | Function.Commute.set_image | [] | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_mul_left_self | [] | [
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Mathlib/Analysis/Calculus/Deriv/Basic.lean | hasDerivWithinAt_derivWithin_iff | [] | [
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Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_le_neg_one_of_neg | [
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Mathlib/Analysis/LocallyConvex/WeakDual.lean | LinearMap.weakBilin_withSeminorms | [] | [
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src/lean/Lean/Compiler/LCNF/PassManager.lean | Lean.Compiler.LCNF.Phase.le_refl | [
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Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_pow_sub | [
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_zero | [] | [
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.map_mk' | [] | [
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_inv | [] | [
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Mathlib/Analysis/Normed/Group/Basic.lean | Rat.norm_cast_real | [] | [
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Embedding.comp_codRestrict | [] | [
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.fst_linear | [] | [
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Mathlib/Algebra/Hom/GroupAction.lean | DistribMulActionHom.ext_iff | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_eq_zero_iff | [
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Mathlib/Algebra/Group/Semiconj.lean | SemiconjBy.inv_symm_left_iff | [] | [
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Mathlib/Data/Fin/Tuple/BubbleSortInduction.lean | Tuple.bubble_sort_induction' | [
{
"state_after": "n : ℕ\nα : Type u_1\ninst✝ : LinearOrder α\nf : Fin n → α\nP : (Fin n → α) → Prop\nhf : P f\nh :\n ∀ (σ : Equiv.Perm (Fin n)) (i j : Fin n),\n i < j → (f ∘ ↑σ) j < (f ∘ ↑σ) i → P (f ∘ ↑σ) → P (f ∘ ↑σ ∘ ↑(Equiv.swap i j))\nthis : Preorder (Equiv.Perm (Fin n)) := Preorder.lift fun σ => ↑toLe... | [
49,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
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Mathlib/Data/Seq/Computation.lean | Computation.Results.mem | [] | [
520,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | HasStrictFDerivAt.prod | [] | [
67,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
11
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_one | [] | [
97,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/FieldTheory/Laurent.lean | RatFunc.laurentAux_algebraMap | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : CommRing R\nhdomain : IsDomain R\nr s : R\np q : R[X]\nf : RatFunc R\n⊢ ↑(laurentAux r) (↑(algebraMap R[X] (RatFunc R)) p) = ↑(algebraMap ((fun x => R[X]) p) (RatFunc R)) (↑(taylor r) p)",
"tactic": "rw [← mk_one, ← mk_one, mk_eq_div, lau... | [
79,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.zero_ne_cons | [] | [
287,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Data/Sym/Sym2.lean | Sym2.map.injective | [
{
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"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.17037\nf : α → β\nhinj : Injective f\n⊢ Injective (map f)",
"tactic": "intro z z'"
},
{
"state_a... | [
275,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_apply | [] | [
1527,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMap₂'_apply' | [
{
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215,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/Finset/Option.lean | Finset.image_some_eraseNone | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.13337\ninst✝ : DecidableEq (Option α)\ns : Finset (Option α)\n⊢ image some (↑eraseNone s) = erase s none",
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}
] | [
147,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Data/Complex/Module.lean | imaginaryPart_I_smul | [
{
"state_after": "case a\nA : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : A\n⊢ ↑(↑ℑ (I • a)) = ↑(↑ℜ a)",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : A\n⊢ ↑... | [
492,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | uniformContinuous_of_continuousAt_one | [
{
"state_after": "no goals",
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404,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
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Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.id_comp | [] | [
209,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInv_leftInv_eq | [
{
"state_after": "M : Type u_1\ninst✝ : Monoid M\nS : Submonoid M\nhS : S ≤ IsUnit.submonoid M\n⊢ S ≤ leftInv (leftInv S)",
"state_before": "M : Type u_1\ninst✝ : Monoid M\nS : Submonoid M\nhS : S ≤ IsUnit.submonoid M\n⊢ leftInv (leftInv S) = S",
"tactic": "refine' le_antisymm S.leftInv_leftInv_le _"
... | [
93,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/PNat/Interval.lean | PNat.map_subtype_embedding_Ioo | [] | [
60,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.add_lt_add_left | [] | [
794,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
793,
11
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsPrenex.liftAt | [] | [
790,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Iic | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ Neg.neg '' Iic a = Ici (-a)",
"tactic": "simp"
}
] | [
294,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Commute.sum_right | [
{
"state_after": "case intro.intro\nι : Type ?u.819790\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝ : NonUnitalNonAssocSemiring β\ns : Finset α\nf : α → β\nb : β\nh : ∀ (i : α), i ∈ s → Commute b (f i)\ni : α\nhi : i ∈ s.val\nhb : f i ∈ Multiset.map (fun i => f i) s.val\n... | [
1774,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1770,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.sInter_empty | [
{
"state_after": "no goals",
"state_before": "⊢ ¬ZFSet.Nonempty ∅",
"tactic": "simp"
}
] | [
1074,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1074,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.dual | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx✝ : α\nr : Ordnode α\nsl : Sized l\nsr : Sized r\n⊢ size l + size r + 1 = size (Ordnode.dual r) + size (Ordnode.dual l) + 1",
"tactic": "simp [size_dual, add_comm]"
}
] | [
404,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
402,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isPrimitiveClassified_aux | [
{
"state_after": "case hz\nx y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhzpos : 0 < z\nm n : ℤ\nhm2n2 : 0 < m ^ 2 + n ^ 2\nhv2 : ↑x / ↑z = 2 * ↑m * ↑n / (↑m ^ 2 + ↑n ^ 2)\nhw2 : ↑y / ↑z = (↑m ^ 2 - ↑n ^ 2) / (↑m ^ 2 + ↑n ^ 2)\nH : Int.gcd (m ^ 2 - n ^ 2) (m ^ 2 + n ^ 2) = 1\nco : Int.gcd m n = ... | [
457,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Path.Ordered.ins | [
{
"state_after": "α : Type u_1\ncmp : α → α → Ordering\nparent : Path α\nx : α\nb a : RBNode α\nha : RBNode.Ordered cmp a\nhp : Ordered cmp parent\nxb : All (fun x_1 => cmpLT cmp x x_1) b\nxp : RootOrdered cmp parent x\nbp : All (RootOrdered cmp parent) b\nhb : RBNode.Ordered cmp b\nH : All (RootOrdered cmp (le... | [
306,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
294,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/SubboxInduction.lean | BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes | [] | [
240,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.support_smul_eq | [] | [
744,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.QuasiMeasurePreserving.liminf_preimage_iterate_ae_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.496746\nγ : Type ?u.496749\nδ : Type ?u.496752\nι : Type ?u.496755\nR : Type ?u.496758\nR' : Type ?u.496761\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set α\nμa μa' : Measure α\nμb μb' : ... | [
2567,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2560,
1
] |
Mathlib/NumberTheory/BernoulliPolynomials.lean | Polynomial.bernoulli_eval_zero | [
{
"state_after": "n : ℕ\n⊢ ∑ x in range n, eval 0 (↑(monomial (n - x)) (_root_.bernoulli x * ↑(Nat.choose n x))) +\n eval 0 (↑(monomial (n - n)) (_root_.bernoulli n * ↑(Nat.choose n n))) =\n _root_.bernoulli n",
"state_before": "n : ℕ\n⊢ eval 0 (bernoulli n) = _root_.bernoulli n",
"tactic": "rw ... | [
87,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_int_cast_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Ring R\nn : ℤ\nf : R[X]\n⊢ ↑derivative (↑n * f) = ↑n * ↑derivative f",
"tactic": "simp"
}
] | [
625,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mker_inl | [
{
"state_after": "case h\nM : Type u_1\nN : Type u_2\nP : Type ?u.143655\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.143676\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type ?u.143700\nmc : MonoidHomClass F M N\nx : M\n⊢ x ∈ mker (inl M N) ... | [
1235,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1233,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | le_csSup | [] | [
443,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Order/UpperLower/Basic.lean | isLowerSet_compl | [
{
"state_after": "case h.e'_3\nα : Type u_1\nβ : Type ?u.1894\nγ : Type ?u.1897\nι : Sort ?u.1900\nκ : ι → Sort ?u.1905\ninst✝¹ : LE α\ninst✝ : LE β\ns t : Set α\nh : IsLowerSet (sᶜ)\n⊢ s = sᶜᶜ",
"state_before": "α : Type u_1\nβ : Type ?u.1894\nγ : Type ?u.1897\nι : Sort ?u.1900\nκ : ι → Sort ?u.1905\ninst✝... | [
102,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.isClique_iff_induce_eq | [
{
"state_after": "α : Type u_1\nG H : SimpleGraph α\ns t : Set α\n⊢ Set.Pairwise s G.Adj ↔ induce s G = ⊤",
"state_before": "α : Type u_1\nG H : SimpleGraph α\ns t : Set α\n⊢ IsClique G s ↔ induce s G = ⊤",
"tactic": "rw [isClique_iff]"
},
{
"state_after": "case mp\nα : Type u_1\nG H : SimpleGra... | [
68,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Vector3.lean | Vector3.cons_fz | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Faithful.of_iso | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF F' : C ⥤ D\nG : D ⥤ E\ninst✝ : Faithful F\nα : F ≅ F'\nX✝ Y✝ : C\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : F'.map a₁✝ = F'.map a₂✝\n⊢ F.map a₁✝ = F.map a₂✝",
"tactic": "rw ... | [
304,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.sInf_N | [] | [
158,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Topology/Separation.lean | Continuous.isOpen_mulSupport | [] | [
390,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/LinearAlgebra/Matrix/Diagonal.lean | Matrix.proj_diagonal | [] | [
39,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | Filter.Tendsto.div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.23558\nG₀ : Type u_2\ninst✝³ : GroupWithZero G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : HasContinuousInv₀ G₀\ninst✝ : ContinuousMul G₀\nf g : α → G₀\nl : Filter α\na b : G₀\nhf : Tendsto f l (𝓝 a)\nhg : Tendsto g l (𝓝 b)\nhy : b ≠ 0\n... | [
166,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/MeasureTheory/Function/SpecialFunctions/Inner.lean | Measurable.inner | [] | [
29,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_cons | [] | [
237,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.fderivWithin_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜... | [
1037,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1032,
1
] |
Mathlib/FieldTheory/Separable.lean | Polynomial.rootMultiplicity_le_one_of_separable | [
{
"state_after": "case pos\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\np : R[X]\nhsep : Separable p\nx : R\nhp : p = 0\n⊢ rootMultiplicity x p ≤ 1\n\ncase neg\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\np : R[X]\nhsep : Separable p\nx : R\nhp : ¬p = 0\n⊢ rootMultiplicity x p ≤ 1",
"s... | [
253,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/RingTheory/Noetherian.lean | IsNoetherianRing.isNilpotent_nilradical | [
{
"state_after": "case intro\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsNoetherianRing R\nn : ℕ\nhn : Ideal.radical ⊥ ^ n ≤ ⊥\n⊢ IsNilpotent (nilradical R)",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsNoetherianRing R\n⊢ IsNilpotent (nilradical R)",
"tactic": "obtain ⟨n, hn⟩ := Ide... | [
603,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
600,
1
] |
Mathlib/RepresentationTheory/Action.lean | Action.smul_hom | [] | [
452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | finrank_eq_zero_of_basis_imp_not_finite | [
{
"state_after": "case intro.intro\nK : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : StrongRankCondition K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\ninst✝ : Free K V\nh : ∀ (s : Set V), Basis (↑s) K V → ¬Set.Finite s\nw✝ : Set V\nb : Basis (↑w✝) K V\n⊢ finrank K V = 0",
"state_before": "K : Type u\nV ... | [
185,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ioi_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.47227\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\ninst✝ : LocallyFiniteOrderTop α\n⊢ Ioc a b ⊆ Ioi a",
"tactic": "simpa [← coe_subset] using Set.Ioc_subset_Ioi_self"
}
] | [
405,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.toFun_eq_coe | [] | [
901,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Algebra/Homology/Augment.lean | ChainComplex.augmentTruncate_inv_f_succ | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
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