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Mathlib/Analysis/Seminorm.lean | Seminorm.smul_ball_preimage | [
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_le_bound | [] | [
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Mathlib/Data/MvPolynomial/Comap.lean | MvPolynomial.comap_id | [
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Mathlib/Algebra/Order/Interval.lean | Interval.length_add_le | [
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulEquiv.symm_comp_self | [] | [
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiagonal'_map | [
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.isRegular | [
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Mathlib/RingTheory/Subring/Basic.lean | SubringClass.coe_intCast | [] | [
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.setOf_wSameSide_eq_image2 | [
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Mathlib/Analysis/SpecificLimits/Basic.lean | geom_le | [
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.δ_comp_σ_succ | [
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Mathlib/RingTheory/Localization/Ideal.lean | IsLocalization.comap_map_of_isPrime_disjoint | [
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Mathlib/Analysis/InnerProductSpace/Basic.lean | Orthonormal.orthogonalFamily | [
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Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableAtFilter.inf_ae_iff | [
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_self_apply_pow | [] | [
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Mathlib/Algebra/Group/Units.lean | Units.eq_inv_of_mul_eq_one_right | [] | [
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Mathlib/Topology/MetricSpace/Contracting.lean | ContractingWith.efixedPoint_isFixedPt | [] | [
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Mathlib/Data/Set/Lattice.lean | Set.sInter_eq_compl_sUnion_compl | [
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Mathlib/RingTheory/Valuation/ValuationRing.lean | ValuationRing.iff_dvd_total | [
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Mathlib/Data/List/Basic.lean | List.nthLe_succ_scanl | [
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Mathlib/Topology/PathConnected.lean | Path.extend_range | [] | [
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Mathlib/Algebra/Order/CompleteField.lean | LinearOrderedField.inducedMap_inducedMap | [
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Mathlib/Order/Atoms.lean | GaloisInsertion.isAtom_of_u_bot | [] | [
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Mathlib/Algebra/Star/Basic.lean | star_inv | [] | [
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Mathlib/Algebra/Order/Hom/Basic.lean | map_ne_zero_iff_ne_one | [] | [
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Mathlib/Data/Set/Pointwise/Basic.lean | Set.singleton_mul_singleton | [] | [
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Mathlib/SetTheory/ZFC/Basic.lean | arity_zero | [] | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.mapTermRel_id_id_id | [
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Mathlib/Computability/Language.lean | Language.one_add_kstar_mul_self_eq_kstar | [
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Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.quasiMeasurePreserving | [] | [
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Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.srangeRestrict_surjective | [] | [
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegrable_zero_radius | [
{
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.lowerBound?_mem_lb | [] | [
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Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_inverse_atTop_nhds_0_nat | [] | [
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Mathlib/Algebra/Order/Ring/Lemmas.lean | pos_and_pos_or_neg_and_neg_of_mul_pos | [
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Mathlib/Order/Cover.lean | Wcovby.sup_eq | [] | [
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.map_add_left_Ioo | [
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Mathlib/Combinatorics/Composition.lean | CompositionAsSet.boundary_length | [
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.exists_measurable_superset_of_trim_eq_zero | [
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Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin.finiteDimensional | [] | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.le_of_mul_le_mul_left | [] | [
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Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.toList_prod | [
{
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Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_zmod_surjective | [] | [
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Mathlib/Order/WithBot.lean | WithTop.strictAnti_iff | [] | [
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Mathlib/Algebra/RingQuot.lean | RingCon.coe_algebraMap | [] | [
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Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.top_coe | [] | [
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Mathlib/Data/Fintype/Fin.lean | Fin.card_filter_univ_succ' | [
{
"state_after": "α : Type ?u.9629\nβ : Type ?u.9632\nn : ℕ\np : Fin (n + 1) → Prop\ninst✝ : DecidablePred p\n⊢ Finset.card (if p 0 then {0} else ∅) +\n Finset.card (filter (p ∘ ↑{ toFun := succ, inj' := (_ : Function.Injective succ) }) univ) =\n (if p 0 then 1 else 0) + Finset.card (filter (p ∘ succ) u... | [
78,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_insert_of_ne | [
{
"state_after": "α : Type u_1\nβ : Type ?u.210334\nγ : Type ?u.210337\ninst✝ : DecidableEq α\ns✝ t u v : Finset α\na✝ b✝ a b : α\ns : Finset α\nh : a ≠ b\nx : α\nthis : x ≠ b ∧ x = a ↔ x = a\n⊢ x ∈ erase (insert a s) b ↔ x ∈ insert a (erase s b)",
"state_before": "α : Type u_1\nβ : Type ?u.210334\nγ : Type... | [
1921,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1917,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.eqv_class_mem' | [
{
"state_after": "case h.e'_4.h.e'_2.h.a\nα : Type u_1\nc : Set (Set α)\nH : ∀ (a : α), ∃! b x, a ∈ b\nx x✝ : α\n⊢ Rel (mkClasses c H) x x✝ ↔ Rel (mkClasses c H) x✝ x",
"state_before": "α : Type u_1\nc : Set (Set α)\nH : ∀ (a : α), ∃! b x, a ∈ b\nx : α\n⊢ {y | Rel (mkClasses c H) x y} ∈ c",
"tactic": "c... | [
163,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.any_def | [] | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Std/Classes/LawfulMonad.lean | SatisfiesM.imp | [
{
"state_after": "m : Type u_1 → Type u_2\nα : Type u_1\np q : α → Prop\ninst✝¹ : Functor m\ninst✝ : LawfulFunctor m\nx✝ : m α\nh✝ : SatisfiesM p x✝\nH : ∀ {a : α}, p a → q a\nx : m { a // p a }\nh : Subtype.val <$> x = x✝\n⊢ (Subtype.val ∘ fun x =>\n match x with\n | { val := a, property := h } =... | [
89,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
87,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_mk | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Order/SymmDiff.lean | inf_sup_symmDiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.33973\nα : Type u_1\nβ : Type ?u.33979\nπ : ι → Type ?u.33984\ninst✝ : GeneralizedCoheytingAlgebra α\na b c d : α\n⊢ a ⊓ b ⊔ a ∆ b = a ⊔ b",
"tactic": "rw [sup_comm, symmDiff_sup_inf]"
}
] | [
204,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | AEMeasurable.real_toNNReal | [] | [
1759,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1757,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.NonemptyCompacts.coe_prod | [] | [
305,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.mul_comm | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1029930\n⊢ ∀ (a b : ZNum), a * b = b * a",
"tactic": "transfer"
}
] | [
1491,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1491,
9
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_congr_smul_measure | [
{
"state_after": "case pos\nα : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1677900\nG : Type ?u.1677903\n𝕜 : Type ?u.1677906\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 ... | [
1691,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1681,
1
] |
Mathlib/Data/Finset/Powerset.lean | Finset.mem_powerset | [
{
"state_after": "case mk\nα : Type u_1\ns t✝ t : Finset α\nval✝ : Multiset α\nnodup✝ : Nodup val✝\n⊢ { val := val✝, nodup := nodup✝ } ∈ powerset t ↔ { val := val✝, nodup := nodup✝ } ⊆ t",
"state_before": "α : Type u_1\ns✝ t✝ s t : Finset α\n⊢ s ∈ powerset t ↔ s ⊆ t",
"tactic": "cases s"
},
{
"s... | [
40,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Std/Data/Nat/Gcd.lean | Nat.gcd_rec | [
{
"state_after": "m n : Nat\nthis : n = n % 0\n⊢ gcd 0 n = gcd (n % 0) 0",
"state_before": "m n : Nat\n⊢ gcd 0 n = gcd (n % 0) 0",
"tactic": "have := (mod_zero n).symm"
},
{
"state_after": "no goals",
"state_before": "m n : Nat\nthis : n = n % 0\n⊢ gcd 0 n = gcd (n % 0) 0",
"tactic": "rw... | [
18,
32
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
15,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_incidenceFinset_eq_degree | [
{
"state_after": "ι : Sort ?u.275939\n𝕜 : Type ?u.275942\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\ninst✝¹ : Fintype ↑(neighborSet G v)\ninst✝ : DecidableEq V\n⊢ card (incidenceFinset G v) = Fintype.card ↑(incidenceSet G v)",
"state_before": "ι ... | [
1417,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | continuous_edist | [
{
"state_after": "α : Type u_1\nβ : Type ?u.422280\nγ : Type ?u.422283\ninst✝ : PseudoEMetricSpace α\n⊢ ∀ (x y : α × α), edist x.fst x.snd ≤ edist y.fst y.snd + 2 * edist x y",
"state_before": "α : Type u_1\nβ : Type ?u.422280\nγ : Type ?u.422283\ninst✝ : PseudoEMetricSpace α\n⊢ Continuous fun p => edist p.... | [
1453,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1445,
1
] |
Mathlib/Data/Part.lean | Part.get_eq_iff_mem | [] | [
240,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_image2_left | [
{
"state_after": "case h\nα : Type u_4\nα' : Type ?u.31876\nβ : Type u_5\nβ' : Type ?u.31882\nγ : Type u_3\nγ' : Type ?u.31888\nδ : Type u_2\nδ' : Type ?u.31894\nε : Type u_1\nε' : Type ?u.31900\nζ : Type ?u.31903\nζ' : Type ?u.31906\nν : Type ?u.31909\nf✝ f' : α → β → γ\ng✝ g' : α → β → γ → δ\ns s' : Set α\nt ... | [
261,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/Order/Minimal.lean | IsLeast.mem_minimals | [] | [
218,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropAt_congr_iff_of_eventuallyEq | [
{
"state_after": "no goals",
"state_before": "H : Type u_3\nM : Type u_1\nH' : Type u_4\nM' : Type u_2\nX : Type ?u.44946\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : Top... | [
431,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.homogeneousHull_eq_sInf | [] | [
629,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_assoc | [] | [
855,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
853,
1
] |
Mathlib/Topology/Spectral/Hom.lean | SpectralMap.comp_id | [] | [
208,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_eq_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.54851\nι : Sort ?u.54854\nι' : Sort ?u.54857\nf✝ : α → β\ns t : Set α\nf : α → β\nhf : Injective f\neq : f '' s = f '' t\n⊢ s = t",
"tactic": "rw [← preimage_image_eq s hf, ← preimage_image_eq t hf, eq]"
}
] | [
558,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Algebra/CharP/Basic.lean | add_pow_char_of_commute | [
{
"state_after": "R : Type u_1\ninst✝¹ : Semiring R\np : ℕ\nhp : Fact (Nat.Prime p)\ninst✝ : CharP R p\nx y : R\nh : Commute x y\nr : R\nhr : (x + y) ^ p = x ^ p + y ^ p + ↑p * r\n⊢ (x + y) ^ p = x ^ p + y ^ p",
"state_before": "R : Type u_1\ninst✝¹ : Semiring R\np : ℕ\nhp : Fact (Nat.Prime p)\ninst✝ : Char... | [
251,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Logic/Equiv/Fin.lean | finRotate_apply_zero | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ↑(finRotate (Nat.succ n)) 0 = 1",
"tactic": "rw [finRotate_succ_apply, zero_add]"
}
] | [
447,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/MeasureTheory/Function/AEEqFun.lean | MeasureTheory.AEEqFun.inf_le_right | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.465891\nδ : Type ?u.465894\ninst✝⁵ : MeasurableSpace α\nμ ν : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\ninst✝² : TopologicalSpace δ\ninst✝¹ : SemilatticeInf β\ninst✝ : ContinuousInf β\nf g : α →ₘ[μ] β\n⊢ ↑(f ⊓ g) ≤ᵐ[μ] ↑g",
... | [
515,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
11
] |
Mathlib/GroupTheory/Perm/Fin.lean | support_finRotate_of_le | [
{
"state_after": "case intro\nm : ℕ\nh : 2 ≤ 2 + m\n⊢ support (finRotate (2 + m)) = Finset.univ",
"state_before": "n : ℕ\nh : 2 ≤ n\n⊢ support (finRotate n) = Finset.univ",
"tactic": "obtain ⟨m, rfl⟩ := exists_add_of_le h"
},
{
"state_after": "no goals",
"state_before": "case intro\nm : ℕ\nh... | [
122,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Topology/Filter.lean | Continuous.nhds | [] | [
248,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
18
] |
Mathlib/Topology/Inseparable.lean | specializes_iff_mem_closure | [] | [
140,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_mul_natAbs_eq | [
{
"state_after": "no goals",
"state_before": "a b : Int\nc : Nat\nh : a * b = ↑c\n⊢ natAbs a * natAbs b = c",
"tactic": "rw [← natAbs_mul, h, natAbs]"
}
] | [
176,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
175,
1
] |
Mathlib/Logic/Equiv/List.lean | Denumerable.denumerable_list_aux | [
{
"state_after": "α : Type u_1\nβ : Type ?u.30505\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\n⊢ ∃ a, a ∈ some [] ∧ encodeList a = 0",
"state_before": "α : Type u_1\nβ : Type ?u.30505\ninst✝¹ : Denumerable α\ninst✝ : Denumerable β\n⊢ ∃ a, a ∈ decodeList 0 ∧ encodeList a = 0",
"tactic": "rw [decodeLis... | [
263,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.inl_snd' | [
{
"state_after": "case h\nC : Type u₁\ninst✝² : Category C\nZ X Y P : C\nf : Z ⟶ X\ng : Z ⟶ Y\ninl : X ⟶ P\ninr : Y ⟶ P\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nb : BinaryBicone X Y\nh : BinaryBicone.IsBilimit b\n⊢ IsPushout 0 b.inl 0 b.snd",
"state_before": "C : Type u₁\ninst✝² : Category C\n... | [
787,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr | [] | [
961,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | eq_zero_of_one_div_eq_zero | [] | [
421,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
420,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_ofDual | [] | [
2334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2333,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_X_pow_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b : R\nm n✝ : ℕ\nι : Type y\ninst✝ : Ring R\np : R[X]\nn : ℕ\nH : degree p ≤ ↑n\n⊢ Monic (X ^ (n + 1) - p)",
"tactic": "simpa [sub_eq_add_neg] using monic_X_pow_add (show degree (-p) ≤ n by rwa [← degree_neg p] at H)"
},
{
"... | [
380,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.zneg_toZNum | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.446504\nn : Num\n⊢ -toZNum n = toZNumNeg n",
"tactic": "cases n <;> rfl"
}
] | [
775,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
775,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.univ_not_mem_univ | [] | [
1564,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1563,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ico_toReal | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ ENNReal.toReal (↑↑volume (Set.pi univ fun i => Ico (a i) (b i))) = ∏ i : ι, (b i - a i)",
"tactic": "simp only [volume_pi_Ico, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))]"
}
] | [
256,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | IsCompact.nhdsSet_basis_uniformity | [
{
"state_after": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort u_1\ninst✝ : UniformSpace α\np : ι → Prop\ns : ι → Set (α × α)\nhU : HasBasis (𝓤 α) p s\nK : Set α\nhK : IsCompact K\nU : Set α\n⊢ U ∈ 𝓝ˢ K ↔ ∃ i, p i ∧ (⋃ (x : α) (_ : x ∈ K), ball x (s i)) ⊆ U",
"state_before": "α : Type ua\n... | [
834,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Analysis/Complex/Isometry.lean | LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_re | [
{
"state_after": "f : ℂ →ₗᵢ[ℝ] ℂ\nh₂ : ∀ (z : ℂ), (↑f z).re = z.re\nz : ℂ\nh₁ : ‖↑f z‖ = ‖z‖\n⊢ (↑f z).im = z.im ∨ (↑f z).im = -z.im",
"state_before": "f : ℂ →ₗᵢ[ℝ] ℂ\nh₂ : ∀ (z : ℂ), (↑f z).re = z.re\nz : ℂ\n⊢ (↑f z).im = z.im ∨ (↑f z).im = -z.im",
"tactic": "have h₁ := f.norm_map z"
},
{
"stat... | [
104,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.iterate_derivative_comp_one_sub_X | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : CommRing R\np✝ p : R[X]\n⊢ (↑derivative^[Nat.zero]) (comp p (1 - X)) = (-1) ^ Nat.zero * comp ((↑derivative^[Nat.zero]) p) (1 - X)\n\ncase succ\nR : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Ty... | [
650,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
646,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_coe_set | [] | [
994,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
992,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_integral_norm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12055077\n𝕜 : Type ?u.12055080\nE : Type u_1\nF : Type ?u.12055086\nA : Type ?u.12055089\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g : ℝ → E\nμ : MeasureTheory.Measure ℝ\nh : a ≤ b\n⊢ (∫ (x : ℝ) in... | [
556,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Analysis/Calculus/LocalExtr.lean | Polynomial.card_roots_toFinset_le_derivative | [] | [
375,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.sum_right | [] | [
100,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Algebra/Order/Monoid/Units.lean | Units.val_lt_val | [] | [
34,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_def | [] | [
2829,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2827,
1
] |
Mathlib/Data/List/Duplicate.lean | List.not_duplicate_nil | [] | [
71,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/Complex/LocallyUniformLimit.lean | Complex.exists_cthickening_tendstoUniformlyOn | [
{
"state_after": "case intro.intro\nE : Type u_1\nι : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nU K : Set ℂ\nz : ℂ\nM r δ✝ : ℝ\nφ : Filter ι\nF : ι → ℂ → E\nf g : ℂ → E\nhf : TendstoLocallyUniformlyOn F f φ U\nhF : ∀ᶠ (n : ι) in φ, DifferentiableOn ℂ (F n) U\nhK... | [
141,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.coe_apply | [] | [
1794,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1793,
1
] |
Mathlib/Data/Real/Irrational.lean | irrational_nrt_of_n_not_dvd_multiplicity | [
{
"state_after": "case inl\nx : ℝ\nm : ℤ\nhm : m ≠ 0\np : ℕ\nhp : Fact (Nat.Prime p)\nhxr : x ^ 0 = ↑m\nhv : Part.get (multiplicity (↑p) m) (_ : multiplicity.Finite (↑p) m) % 0 ≠ 0\n⊢ Irrational x\n\ncase inr\nx : ℝ\nn : ℕ\nm : ℤ\nhm : m ≠ 0\np : ℕ\nhp : Fact (Nat.Prime p)\nhxr : x ^ n = ↑m\nhv : Part.get (mult... | [
92,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.image_eq_preimage | [] | [
349,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_succ' | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\ni : Fin (n + 1)\n⊢ σ X i ≫ δ X (Fin.succ i) = 𝟙 (X.obj [n].op)",
"state_before": "C : Type u\ninst✝ : Category C\nX : SimplicialObject C\nn : ℕ\nj : Fin (n + 2)\ni : Fin (n + 1)\nH : j = Fin.succ i\n⊢ σ X i ≫ δ X j = 𝟙 (X.obj... | [
180,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
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