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Mathlib/Topology/Constructions.lean
nhds_inl
[]
[ 952, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 951, 1 ]
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
ProjectiveSpectrum.zeroLocus_anti_mono_homogeneousIdeal
[]
[ 191, 39 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 189, 1 ]
Mathlib/Algebra/RingQuot.lean
RingQuot.liftAlgHom_mkAlgHom_apply
[ { "state_after": "R : Type u₁\ninst✝⁢ : Semiring R\nS : Type uβ‚‚\ninst✝⁡ : CommSemiring S\nA : Type u₃\ninst✝⁴ : Semiring A\ninst✝³ : Algebra S A\nr : R β†’ R β†’ Prop\nT : Type uβ‚„\ninst✝² : Semiring T\nB : Type uβ‚„\ninst✝¹ : Semiring B\ninst✝ : Algebra S B\nf : A →ₐ[S] B\ns : A β†’ A β†’ Prop\nw : βˆ€ ⦃x y : A⦄, s x y β†’ ↑...
[ 670, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 667, 1 ]
Mathlib/LinearAlgebra/Matrix/Adjugate.lean
Matrix.cramer_row_self
[ { "state_after": "m : Type u\nn : Type v\nΞ± : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing Ξ±\nA : Matrix n n Ξ±\nb : n β†’ Ξ±\ni : n\nh : βˆ€ (j : n), b j = A j i\n⊒ ↑(cramer Aα΅€α΅€) b = Pi.single i (det Aα΅€)", "state_before": "m : Type u\nn : Type v...
[ 126, 17 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 123, 1 ]
Mathlib/Topology/Instances/ENNReal.lean
NNReal.tsum_eq_toNNReal_tsum
[ { "state_after": "case pos\nΞ± : Type ?u.309286\nΞ² : Type u_1\nΞ³ : Type ?u.309292\nf : Ξ² β†’ ℝβ‰₯0\nh : Summable f\n⊒ (βˆ‘' (b : Ξ²), f b) = ENNReal.toNNReal (βˆ‘' (b : Ξ²), ↑(f b))\n\ncase neg\nΞ± : Type ?u.309286\nΞ² : Type u_1\nΞ³ : Type ?u.309292\nf : Ξ² β†’ ℝβ‰₯0\nh : Β¬Summable f\n⊒ (βˆ‘' (b : Ξ²), f b) = ENNReal.toNNReal (βˆ‘' (...
[ 1103, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1098, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.inv_lt_inv
[]
[ 1479, 27 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1478, 11 ]
Mathlib/LinearAlgebra/Projection.lean
Submodule.existsUnique_add_of_isCompl
[]
[ 211, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 208, 1 ]
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean
TopCat.Sheaf.existsUnique_gluing
[]
[ 250, 57 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 248, 1 ]
Mathlib/MeasureTheory/Measure/AEMeasurable.lean
MeasurableEmbedding.aemeasurable_map_iff
[ { "state_after": "ΞΉ : Type ?u.3357463\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type u_3\nΞ΄ : Type ?u.3357475\nR : Type ?u.3357478\nm0 : MeasurableSpace Ξ±\ninst✝² : MeasurableSpace Ξ²\ninst✝¹ : MeasurableSpace Ξ³\ninst✝ : MeasurableSpace Ξ΄\nf g✝ : Ξ± β†’ Ξ²\nΞΌ Ξ½ : MeasureTheory.Measure Ξ±\ng : Ξ² β†’ Ξ³\nhf : MeasurableEmbedding f...
[ 267, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 262, 1 ]
Mathlib/Order/Lattice.lean
Monotone.le_map_sup
[]
[ 1099, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1097, 1 ]
Mathlib/Data/Fin/VecNotation.lean
Matrix.vecAlt1_vecAppend
[ { "state_after": "case h\nΞ± : Type u\nm n o : β„•\nm' : Type ?u.42128\nn' : Type ?u.42131\no' : Type ?u.42134\nv : Fin (n + 1) β†’ Ξ±\ni : Fin (n + 1)\n⊒ vecAlt1 (_ : n + 1 + (n + 1) = n + 1 + (n + 1)) (vecAppend (_ : n + 1 + (n + 1) = n + 1 + (n + 1)) v v) i =\n (v ∘ bit1) i", "state_before": "Ξ± : Type u\nm ...
[ 356, 40 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 338, 1 ]
Mathlib/Topology/Algebra/Monoid.lean
continuous_pow
[ { "state_after": "no goals", "state_before": "ι : Type ?u.177283\nα : Type ?u.177286\nX : Type ?u.177289\nM : Type u_1\nN : Type ?u.177295\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\n⊒ Continuous fun a => a ^ 0", "tactic": "simpa using continuou...
[ 564, 47 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 560, 1 ]
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean
intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right
[ { "state_after": "no goals", "state_before": "ΞΉ : Type u_2\nπ•œ : Type ?u.1353399\nE : Type u_1\nF : Type ?u.1353405\nA : Type ?u.1353408\ninst✝⁡ : NormedAddCommGroup E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedSpace ℝ E\nf : ℝ β†’ E\na b : ℝ\nc ca cb : E\nl l' la la' lb lb' : Filter ℝ\nlt : Filter ΞΉ\nΞΌ : Meas...
[ 456, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 448, 1 ]
Mathlib/Analysis/SpecialFunctions/Sqrt.lean
DifferentiableAt.sqrt
[]
[ 140, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 138, 1 ]
Mathlib/Computability/Reduce.lean
OneOneEquiv.trans
[]
[ 197, 53 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 195, 1 ]
Mathlib/Topology/Algebra/Order/Floor.lean
tendsto_floor_right_pure_floor
[]
[ 73, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 71, 1 ]
Mathlib/Topology/Inseparable.lean
SeparationQuotient.inducing_mk
[]
[ 469, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 467, 1 ]
Mathlib/NumberTheory/ArithmeticFunction.lean
Nat.ArithmeticFunction.toFun_eq
[]
[ 89, 65 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 89, 1 ]
Mathlib/Data/Multiset/Basic.lean
Multiset.sub_cons
[]
[ 1650, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1649, 1 ]
Mathlib/Algebra/DirectLimit.lean
Module.DirectLimit.lift_unique
[ { "state_after": "R : Type u\ninst✝⁷ : Ring R\nΞΉ : Type v\ndec_ΞΉ : DecidableEq ΞΉ\ninst✝⁢ : Preorder ΞΉ\nG : ΞΉ β†’ Type w\ninst✝⁡ : (i : ΞΉ) β†’ AddCommGroup (G i)\ninst✝⁴ : (i : ΞΉ) β†’ Module R (G i)\nf : (i j : ΞΉ) β†’ i ≀ j β†’ G i β†’β‚—[R] G j\nP : Type u₁\ninst✝³ : AddCommGroup P\ninst✝² : Module R P\ng : (i : ΞΉ) β†’ G i β†’β‚—[...
[ 171, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 167, 1 ]
Mathlib/LinearAlgebra/Eigenspace/Basic.lean
Module.End.hasEigenvalue_of_hasGeneralizedEigenvalue
[ { "state_after": "K R : Type v\nV M : Type w\ninst✝⁡ : CommRing R\ninst✝⁴ : AddCommGroup M\ninst✝³ : Module R M\ninst✝² : Field K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nf : End R M\nΞΌ : R\nk : β„•\nhΞΌ : HasGeneralizedEigenvalue f ΞΌ k\ncontra : eigenspace f ΞΌ = βŠ₯\n⊒ False", "state_before": "K R : Type v...
[ 361, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 357, 1 ]
Mathlib/LinearAlgebra/Prod.lean
LinearMap.coprod_comp_prod
[]
[ 259, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 257, 1 ]
Mathlib/Topology/Separation.lean
Continuous.ext_on
[]
[ 1197, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1195, 1 ]
Mathlib/AlgebraicTopology/TopologicalSimplex.lean
SimplexCategory.toTopObj.ext
[]
[ 50, 14 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 49, 1 ]
Mathlib/Data/Sign.lean
SignType.neg_one_le
[]
[ 206, 9 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 205, 1 ]
Mathlib/Order/Heyting/Boundary.lean
Coheyting.boundary_sup_sup_boundary_inf
[]
[ 131, 54 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 128, 1 ]
Mathlib/GroupTheory/MonoidLocalization.lean
Submonoid.LocalizationMap.ofMulEquivOfDom_id
[ { "state_after": "case h\nM : Type u_1\ninst✝³ : CommMonoid M\nS : Submonoid M\nN : Type u_2\ninst✝² : CommMonoid N\nP : Type ?u.3102959\ninst✝¹ : CommMonoid P\nf : LocalizationMap S N\ng : M β†’* P\nhg : βˆ€ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nT : Submonoid P\nQ : Type ?u.3111444\ninst✝ : CommMonoid Q\nx✝ : M\n⊒...
[ 1544, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1540, 1 ]
Mathlib/SetTheory/Ordinal/FixedPoint.lean
Ordinal.deriv_mul_eq_opow_omega_mul
[ { "state_after": "a : Ordinal\nha : 0 < a\n⊒ βˆ€ (b : Ordinal), deriv (fun x => a * x) b = a ^ Ο‰ * b", "state_before": "a : Ordinal\nha : 0 < a\nb : Ordinal\n⊒ deriv (fun x => a * x) b = a ^ Ο‰ * b", "tactic": "revert b" }, { "state_after": "a : Ordinal\nha : 0 < a\n⊒ deriv (fun x => a * x) 0 = (fu...
[ 726, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 718, 1 ]
Mathlib/Topology/MetricSpace/EMetricSpace.lean
EMetric.tendstoLocallyUniformlyOn_iff
[ { "state_after": "Ξ± : Type u\nΞ² : Type v\nX : Type ?u.29841\ninst✝¹ : PseudoEMetricSpace Ξ±\nΞΉ : Type u_1\ninst✝ : TopologicalSpace Ξ²\nF : ΞΉ β†’ Ξ² β†’ Ξ±\nf : Ξ² β†’ Ξ±\np : Filter ΞΉ\ns : Set Ξ²\nH :\n βˆ€ (Ξ΅ : ℝβ‰₯0∞), Ξ΅ > 0 β†’ βˆ€ (x : Ξ²), x ∈ s β†’ βˆƒ t, t ∈ 𝓝[s] x ∧ βˆ€αΆ  (n : ΞΉ) in p, βˆ€ (y : Ξ²), y ∈ t β†’ edist (f y) (F n y) < Ξ΅\...
[ 349, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 342, 1 ]
Mathlib/GroupTheory/Subgroup/Basic.lean
Subgroup.le_centralizer_iff
[]
[ 2300, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2299, 1 ]
Mathlib/RingTheory/Int/Basic.lean
Int.normalize_coe_nat
[]
[ 116, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 115, 1 ]
Mathlib/Algebra/Algebra/Spectrum.lean
spectrum.mem_resolventSet_iff
[]
[ 135, 10 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 134, 1 ]
Mathlib/Data/Real/ENNReal.lean
ENNReal.coe_mono
[]
[ 336, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 336, 1 ]
Mathlib/GroupTheory/Submonoid/Basic.lean
Submonoid.mem_sInf
[]
[ 324, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 323, 1 ]
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean
SimpleGraph.Walk.copy_copy
[ { "state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu'' v'' : V\np : Walk G u'' v''\n⊒ Walk.copy (Walk.copy p (_ : u'' = u'') (_ : v'' = v'')) (_ : u'' = u'') (_ : v'' = v'') =\n Walk.copy p (_ : u'' = u'') (_ : v'' = v'')", "state_befor...
[ 146, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 142, 1 ]
Mathlib/Algebra/Module/Submodule/Pointwise.lean
Submodule.zero_eq_bot
[]
[ 176, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 175, 1 ]
Mathlib/Topology/SubsetProperties.lean
IsCompact.elim_finite_subcover
[]
[ 197, 99 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 194, 1 ]
Mathlib/GroupTheory/FreeAbelianGroup.lean
FreeAbelianGroup.liftMonoid_symm_coe
[]
[ 548, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 546, 1 ]
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean
CategoryTheory.Limits.coprodZeroIso_inv
[]
[ 156, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 155, 1 ]
Mathlib/Analysis/SpecialFunctions/Exp.lean
Real.isBoundedUnder_le_exp_comp
[]
[ 213, 56 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 211, 1 ]
Mathlib/Algebra/Associated.lean
dvdNotUnit_of_dvdNotUnit_associated
[ { "state_after": "case intro\nΞ± : Type u_1\nΞ² : Type ?u.348972\nΞ³ : Type ?u.348975\nΞ΄ : Type ?u.348978\ninst✝¹ : CommMonoidWithZero Ξ±\ninst✝ : Nontrivial Ξ±\np r : Ξ±\nu : Ξ±Λ£\nh : DvdNotUnit p (r * ↑u)\nh' : r * ↑u ~α΅€ r\n⊒ DvdNotUnit p r", "state_before": "Ξ± : Type u_1\nΞ² : Type ?u.348972\nΞ³ : Type ?u.348975\...
[ 1178, 66 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1173, 1 ]
Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean
AlgebraicTopology.DoldKan.Ξ“β‚€_obj_termwise_mapMono_comp_PInfty
[ { "state_after": "case h\nC : Type u_2\ninst✝³ : Category C\ninst✝² : Preadditive C\nX : SimplicialObject C\nΞ” Ξ”' : SimplexCategory\ni✝ : Ξ” ⟢ Ξ”'\ninst✝¹ : Mono i✝\nn : β„•\ni : [n] ⟢ Ξ”'\ninst✝ : Mono i\n⊒ Ξ“β‚€.Obj.Termwise.mapMono K[X] i ≫ HomologicalComplex.Hom.f PInfty (len [n]) =\n HomologicalComplex.Hom.f PI...
[ 125, 18 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 84, 1 ]
Mathlib/Order/Bounds/Basic.lean
AntitoneOn.map_bddBelow
[]
[ 1245, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1244, 1 ]
Mathlib/Topology/MetricSpace/Gluing.lean
Metric.Sigma.isometry_mk
[ { "state_after": "no goals", "state_before": "ΞΉ : Type u_2\nE : ΞΉ β†’ Type u_1\ninst✝ : (i : ΞΉ) β†’ MetricSpace (E i)\ni : ΞΉ\nx y : E i\n⊒ dist { fst := i, snd := x } { fst := i, snd := y } = dist x y", "tactic": "simp" } ]
[ 439, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 438, 1 ]
Mathlib/Data/List/MinMax.lean
List.argmin_cons
[]
[ 202, 29 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 199, 1 ]
Mathlib/RingTheory/HahnSeries.lean
HahnSeries.addVal_le_of_coeff_ne_zero
[ { "state_after": "Ξ“ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedCancelAddCommMonoid Ξ“\ninst✝¹ : Ring R\ninst✝ : IsDomain R\nx : HahnSeries Ξ“ R\ng : Ξ“\nh : coeff x g β‰  0\n⊒ order x ≀ g", "state_before": "Ξ“ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedCancelAddCommMonoid Ξ“\ninst✝¹ : Ring R\ninst✝ : IsD...
[ 1379, 36 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1376, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.bind_def
[]
[ 2045, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2044, 1 ]
Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean
MeasureTheory.tendstoInMeasure_of_tendsto_snorm
[ { "state_after": "case pos\nΞ± : Type u_2\nΞΉ : Type u_1\nE : Type u_3\nm : MeasurableSpace Ξ±\nΞΌ : Measure Ξ±\ninst✝ : NormedAddCommGroup E\np : ℝβ‰₯0∞\nf : ΞΉ β†’ Ξ± β†’ E\ng : Ξ± β†’ E\nl : Filter ΞΉ\nhp_ne_zero : p β‰  0\nhf : βˆ€ (n : ΞΉ), AEStronglyMeasurable (f n) ΞΌ\nhg : AEStronglyMeasurable g ΞΌ\nhfg : Tendsto (fun n => sno...
[ 355, 85 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 349, 1 ]
Mathlib/Algebra/Homology/HomologicalComplex.lean
HomologicalComplex.hom_f_injective
[ { "state_after": "no goals", "state_before": "ΞΉ : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ΞΉ\nC C₁ Cβ‚‚ : HomologicalComplex V c\n⊒ Function.Injective fun f => f.f", "tactic": "aesop_cat" } ]
[ 246, 64 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 245, 1 ]
Mathlib/Topology/UniformSpace/Basic.lean
closure_eq_inter_uniformity
[ { "state_after": "no goals", "state_before": "Ξ± : Type ua\nΞ² : Type ub\nΞ³ : Type uc\nΞ΄ : Type ud\nΞΉ : Sort ?u.88389\ninst✝ : UniformSpace Ξ±\nt : Set (Ξ± Γ— Ξ±)\n⊒ (β‹‚ (V : Set (Ξ± Γ— Ξ±)) (_ : V ∈ 𝓀 Ξ±), V β—‹ t β—‹ V) = β‹‚ (V : Set (Ξ± Γ— Ξ±)) (_ : V ∈ 𝓀 Ξ±), V β—‹ (t β—‹ V)", "tactic": "simp only [compRel_assoc]" } ]
[ 979, 63 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 972, 1 ]
Mathlib/Data/Int/Parity.lean
Int.even_iff
[ { "state_after": "no goals", "state_before": "m✝ n : β„€\nx✝ : Even n\nm : β„€\nhm : n = m + m\n⊒ n % 2 = 0", "tactic": "simp [← two_mul, hm]" }, { "state_after": "no goals", "state_before": "m n : β„€\nh : n % 2 = 0\n⊒ n % 2 + 2 * (n / 2) = n / 2 + n / 2", "tactic": "simp [← two_mul, h]" } ...
[ 42, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 40, 1 ]
Mathlib/LinearAlgebra/Dfinsupp.lean
Dfinsupp.coprodMap_apply_single
[ { "state_after": "no goals", "state_before": "ΞΉ : Type u_4\nR : Type u_1\nS : Type ?u.308054\nM : ΞΉ β†’ Type u_2\nN : Type u_3\ndec_ΞΉ : DecidableEq ΞΉ\ninst✝⁢ : Semiring R\ninst✝⁡ : (i : ΞΉ) β†’ AddCommMonoid (M i)\ninst✝⁴ : (i : ΞΉ) β†’ Module R (M i)\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\ninst✝¹ : Decidab...
[ 282, 25 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 280, 1 ]
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean
DifferentiableOn.arctan
[]
[ 205, 79 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 204, 1 ]
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean
IsBoundedBilinearMap.map_sub_right
[]
[ 396, 42 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 394, 1 ]
Mathlib/RingTheory/Valuation/Basic.lean
Valuation.ne_zero_iff
[]
[ 238, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 237, 1 ]
Mathlib/GroupTheory/Perm/Option.lean
Equiv.optionCongr_sign
[ { "state_after": "case refine_1\nΞ± : Type u_1\ninst✝¹ : DecidableEq Ξ±\ninst✝ : Fintype Ξ±\ne : Perm Ξ±\n⊒ ↑Perm.sign (optionCongr 1) = ↑Perm.sign 1\n\ncase refine_2\nΞ± : Type u_1\ninst✝¹ : DecidableEq Ξ±\ninst✝ : Fintype Ξ±\ne : Perm Ξ±\n⊒ βˆ€ (f : Perm Ξ±) (x y : Ξ±),\n x β‰  y β†’\n ↑Perm.sign (optionCongr f) = ↑P...
[ 43, 59 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 38, 1 ]
Mathlib/Algebra/BigOperators/Multiset/Basic.lean
Multiset.prod_eq_zero
[ { "state_after": "case intro\nΞΉ : Type ?u.89646\nΞ± : Type u_1\nΞ² : Type ?u.89652\nΞ³ : Type ?u.89655\ninst✝ : CommMonoidWithZero Ξ±\ns : Multiset Ξ±\nh : 0 ∈ s\ns' : Multiset Ξ±\nhs' : s = 0 ::β‚˜ s'\n⊒ prod s = 0", "state_before": "ΞΉ : Type ?u.89646\nΞ± : Type u_1\nΞ² : Type ?u.89652\nΞ³ : Type ?u.89655\ninst✝ : Co...
[ 285, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 283, 1 ]
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.measure_ne_top
[]
[ 3060, 32 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 3059, 1 ]
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean
Pmf.mem_support_filter_iff
[]
[ 284, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 283, 1 ]
Mathlib/Topology/Constructions.lean
interior_pi_set
[ { "state_after": "case h\nΞ± : Type u\nΞ² : Type v\nΞ³ : Type ?u.313054\nΞ΄ : Type ?u.313057\nΞ΅ : Type ?u.313060\nΞΆ : Type ?u.313063\nΞΉ : Type u_1\nΟ€ : ΞΉ β†’ Type u_2\nΞΊ : Type ?u.313074\ninst✝¹ : TopologicalSpace Ξ±\ninst✝ : (i : ΞΉ) β†’ TopologicalSpace (Ο€ i)\nf : Ξ± β†’ (i : ΞΉ) β†’ Ο€ i\nI : Set ΞΉ\nhI : Set.Finite I\ns : (i...
[ 1357, 76 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1354, 1 ]
Mathlib/Order/Filter/Basic.lean
Filter.comap_mono
[]
[ 2162, 30 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 2161, 1 ]
Mathlib/Data/Complex/Exponential.lean
Complex.isCauSeq_exp
[]
[ 369, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 368, 1 ]
Mathlib/AlgebraicGeometry/PrimeSpectrum/IsOpenComapC.lean
AlgebraicGeometry.Polynomial.isOpenMap_comap_C
[ { "state_after": "case intro\nR : Type u_1\ninst✝ : CommRing R\nf : R[X]\nU : Set (PrimeSpectrum R[X])\ns : Set R[X]\nz : zeroLocus s = Uᢜ\n⊒ IsOpen (↑(PrimeSpectrum.comap C) '' U)", "state_before": "R : Type u_1\ninst✝ : CommRing R\nf : R[X]\n⊒ IsOpenMap ↑(PrimeSpectrum.comap C)", "tactic": "rintro U ⟨...
[ 82, 48 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 77, 1 ]
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean
EMetric.exists_forall_closedBall_subset_aux₁
[ { "state_after": "ΞΉ : Type u_2\nX : Type u_1\ninst✝ : EMetricSpace X\nK U : ΞΉ β†’ Set X\nhK : βˆ€ (i : ΞΉ), IsClosed (K i)\nhU : βˆ€ (i : ΞΉ), IsOpen (U i)\nhKU : βˆ€ (i : ΞΉ), K i βŠ† U i\nhfin : LocallyFinite K\nx : X\nthis :\n βˆ€αΆ  (x_1 : ℝ) in 𝓝 0,\n βˆ€αΆ  (y : X) in 𝓝 x,\n βˆ€ (i : ΞΉ),\n (ENNReal.ofReal x_1,...
[ 74, 34 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 66, 1 ]
Mathlib/GroupTheory/OrderOfElement.lean
LinearOrderedRing.orderOf_le_two
[ { "state_after": "case inl\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : β„•\ninst✝ : LinearOrderedRing G\nh : abs x β‰  1\n⊒ orderOf x ≀ 2\n\ncase inr\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : β„•\ninst✝ : LinearOrderedRing G\nh : abs x = 1\n⊒ orderOf x ≀ 2", "state_before": "G : Type u\nA : Type v\nx ...
[ 1096, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1091, 1 ]
Mathlib/GroupTheory/DoubleCoset.lean
Doset.right_bot_eq_right_quot
[ { "state_after": "G : Type u_1\ninst✝¹ : Group G\nΞ± : Type ?u.70749\ninst✝ : Mul Ξ±\nJ : Subgroup G\ng : G\nH : Subgroup G\n⊒ _root_.Quotient (setoid ↑H.toSubmonoid ↑βŠ₯) = _root_.Quotient (QuotientGroup.rightRel H)", "state_before": "G : Type u_1\ninst✝¹ : Group G\nΞ± : Type ?u.70749\ninst✝ : Mul Ξ±\nJ : Subgro...
[ 215, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 209, 1 ]
Mathlib/Analysis/Calculus/FDeriv/Linear.lean
ContinuousLinearMap.differentiableAt
[]
[ 83, 33 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 82, 11 ]
Mathlib/Data/Multiset/FinsetOps.lean
Multiset.length_ndinsert_of_not_mem
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\ninst✝ : DecidableEq Ξ±\ns✝ : Multiset Ξ±\na : Ξ±\ns : Multiset Ξ±\nh : Β¬a ∈ s\n⊒ ↑card (ndinsert a s) = ↑card s + 1", "tactic": "simp [h]" } ]
[ 83, 52 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 82, 1 ]
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean
HasDerivAt.cexp
[]
[ 97, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 95, 1 ]
Mathlib/Algebra/Algebra/Equiv.lean
AlgEquiv.toRingEquiv_symm
[]
[ 379, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 378, 1 ]
Mathlib/SetTheory/Cardinal/Basic.lean
Cardinal.power_lt_aleph0
[ { "state_after": "Ξ± Ξ² : Type u\na b : Cardinal\nm n : β„•\nha : ↑m < β„΅β‚€\nhb : ↑n < β„΅β‚€\n⊒ ↑(m ^ n) < β„΅β‚€", "state_before": "Ξ± Ξ² : Type u\na b : Cardinal\nm n : β„•\nha : ↑m < β„΅β‚€\nhb : ↑n < β„΅β‚€\n⊒ ↑m ^ ↑n < β„΅β‚€", "tactic": "rw [← natCast_pow]" }, { "state_after": "no goals", "state_before": "Ξ± Ξ² : Ty...
[ 1595, 75 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1593, 1 ]
Mathlib/Order/Filter/Bases.lean
Filter.asBasis_filter
[]
[ 411, 44 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 410, 1 ]
Mathlib/Analysis/Calculus/FDerivMeasurable.lean
RightDerivMeasurableAux.measurableSet_b
[]
[ 510, 74 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 509, 1 ]
Mathlib/Algebra/Order/Ring/Lemmas.lean
MulPosReflectLT.toMulPosMonoRev
[]
[ 1015, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1013, 1 ]
Mathlib/Data/Set/Image.lean
Set.subset_preimage_univ
[]
[ 85, 16 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 84, 1 ]
Mathlib/FieldTheory/Subfield.lean
Subfield.sum_mem
[]
[ 317, 12 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 315, 11 ]
Mathlib/Algebra/Order/Ring/Defs.lean
lt_mul_right
[ { "state_after": "case h.e'_3\nα : Type u\nβ : Type ?u.63411\ninst✝ : StrictOrderedSemiring α\na b c d : α\nhn : 0 < a\nhm : 1 < b\n⊒ a = a * 1", "state_before": "α : Type u\nβ : Type ?u.63411\ninst✝ : StrictOrderedSemiring α\na b c d : α\nhn : 0 < a\nhm : 1 < b\n⊒ a < a * b", "tactic": "convert mul_lt_...
[ 570, 15 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 568, 1 ]
Mathlib/Order/SymmDiff.lean
bihimp_left_comm
[ { "state_after": "no goals", "state_before": "ΞΉ : Type ?u.80811\nΞ± : Type u_1\nΞ² : Type ?u.80817\nΟ€ : ΞΉ β†’ Type ?u.80822\ninst✝ : BooleanAlgebra Ξ±\na b c d : Ξ±\n⊒ a ⇔ (b ⇔ c) = b ⇔ (a ⇔ c)", "tactic": "simp_rw [← bihimp_assoc, bihimp_comm]" } ]
[ 634, 97 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 634, 1 ]
Mathlib/Order/Filter/AtTopBot.lean
Filter.Tendsto.atBot_div_const
[ { "state_after": "no goals", "state_before": "ΞΉ : Type ?u.249256\nΞΉ' : Type ?u.249259\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.249268\ninst✝ : LinearOrderedField Ξ±\nl : Filter Ξ²\nf : Ξ² β†’ Ξ±\nr : Ξ±\nhr : 0 < r\nhf : Tendsto f l atBot\n⊒ Tendsto (fun x => f x / r) l atBot", "tactic": "simpa only [div_eq_mu...
[ 1222, 70 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1220, 1 ]
Mathlib/Topology/MetricSpace/Basic.lean
Continuous.dist
[]
[ 1809, 43 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1807, 11 ]
Mathlib/Data/Nat/Digits.lean
Nat.digits_one_succ
[]
[ 115, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 114, 1 ]
Mathlib/Analysis/Calculus/ContDiff.lean
contDiff_smul
[]
[ 1493, 37 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1492, 1 ]
Mathlib/Analysis/InnerProductSpace/Adjoint.lean
ContinuousLinearMap.adjoint_adjoint
[]
[ 136, 26 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 135, 1 ]
Mathlib/Algebra/Quaternion.lean
QuaternionAlgebra.star_mk
[]
[ 641, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 640, 1 ]
Mathlib/MeasureTheory/Integral/SetToL1.lean
MeasureTheory.SimpleFunc.setToSimpleFunc_congr_left
[ { "state_after": "Ξ± : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.205114\nG : Type ?u.205117\nπ•œ : Type ?u.205120\np : ℝβ‰₯0∞\ninst✝⁢ : NormedAddCommGroup E\ninst✝⁡ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :...
[ 403, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 395, 1 ]
Mathlib/Data/Finset/Card.lean
Finset.card_union_add_card_inter
[ { "state_after": "no goals", "state_before": "Ξ± : Type u_1\nΞ² : Type ?u.31550\ns✝ t✝ : Finset Ξ±\nf : Ξ± β†’ Ξ²\nn : β„•\ninst✝ : DecidableEq Ξ±\ns t : Finset Ξ±\n⊒ card (s βˆͺ βˆ…) + card (s ∩ βˆ…) = card s + card βˆ…", "tactic": "simp" }, { "state_after": "no goals", "state_before": "Ξ± : Type u_1\nΞ² : Type...
[ 411, 46 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 408, 1 ]
Mathlib/Data/List/Sigma.lean
List.dlookup_kunion_right
[ { "state_after": "case nil\nΞ± : Type u\nΞ² : Ξ± β†’ Type v\nl l₁ lβ‚‚βœ : List (Sigma Ξ²)\ninst✝ : DecidableEq Ξ±\na : Ξ±\nlβ‚‚ : List (Sigma Ξ²)\nh : Β¬a ∈ keys []\n⊒ dlookup a (kunion [] lβ‚‚) = dlookup a lβ‚‚\n\ncase cons\nΞ± : Type u\nΞ² : Ξ± β†’ Type v\nl l₁ lβ‚‚βœ : List (Sigma Ξ²)\ninst✝ : DecidableEq Ξ±\na : Ξ±\nhead✝ : Sigma Ξ²\nta...
[ 763, 61 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 759, 1 ]
Mathlib/LinearAlgebra/LinearIndependent.lean
linearIndependent_inl_union_inr'
[ { "state_after": "no goals", "state_before": "ΞΉ : Type u'\nΞΉ' : Type u_3\nR : Type u_1\nK : Type ?u.650261\nM : Type u_2\nM' : Type u_4\nM'' : Type ?u.650270\nV : Type u\nV' : Type ?u.650275\nv✝ : ΞΉ β†’ M\ninst✝⁢ : Ring R\ninst✝⁡ : AddCommGroup M\ninst✝⁴ : AddCommGroup M'\ninst✝³ : AddCommGroup M''\ninst✝² : ...
[ 995, 62 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 990, 1 ]
Mathlib/LinearAlgebra/AffineSpace/Independent.lean
Affine.Simplex.reindex_symm_reindex
[ { "state_after": "no goals", "state_before": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nm n : β„•\ns : Simplex k P m\ne : Fin (n + 1) ≃ Fin (m + 1)\n⊒ reindex (reindex s e.symm) e = s", "tactic": "rw [← reindex_trans, ...
[ 897, 101 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 896, 1 ]
Mathlib/MeasureTheory/Integral/Lebesgue.lean
MeasureTheory.SimpleFunc.lintegral_eq_lintegral
[ { "state_after": "Ξ± : Type u_1\nΞ² : Type ?u.69212\nΞ³ : Type ?u.69215\nΞ΄ : Type ?u.69218\nm✝ : MeasurableSpace Ξ±\nμ✝ Ξ½ : Measure Ξ±\nm : MeasurableSpace Ξ±\nf : Ξ± β†’β‚› ℝβ‰₯0∞\nΞΌ : Measure Ξ±\n⊒ (⨆ (g : Ξ± β†’β‚› ℝβ‰₯0∞) (_ : ↑g ≀ fun a => ↑f a), lintegral g ΞΌ) = lintegral f ΞΌ", "state_before": "Ξ± : Type u_1\nΞ² : Type ?u.6...
[ 124, 100 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 120, 1 ]
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean
StructureGroupoid.LocalInvariantProp.liftPropOn_congr_iff
[]
[ 444, 94 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 443, 1 ]
Mathlib/CategoryTheory/Extensive.lean
CategoryTheory.finitaryExtensive_iff_of_isTerminal
[ { "state_after": "J : Type v'\ninst✝³ : Category J\nC✝ : Type u\ninst✝² : Category C✝\nX Y : C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : HasFiniteCoproducts C\nT : C\nHT : IsTerminal T\ncβ‚€ : BinaryCofan T T\nhcβ‚€ : IsColimit cβ‚€\nH : IsVanKampenColimit cβ‚€\n⊒ FinitaryExtensive C", "state_before": "J : Type v'...
[ 311, 60 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 299, 1 ]
Mathlib/Data/Set/Lattice.lean
Set.inter_biInter
[ { "state_after": "α✝ : Type ?u.105347\nΞ² : Type ?u.105350\nΞ³ : Type ?u.105353\nι✝ : Sort ?u.105356\nΞΉ' : Sort ?u.105359\nΞΉβ‚‚ : Sort ?u.105362\nΞΊ : ι✝ β†’ Sort ?u.105367\nκ₁ : ι✝ β†’ Sort ?u.105372\nΞΊβ‚‚ : ι✝ β†’ Sort ?u.105377\nΞΊ' : ΞΉ' β†’ Sort ?u.105382\nΞΉ : Type u_1\nΞ± : Type u_2\ns : Set ΞΉ\nhs : Set.Nonempty s\nf : ΞΉ β†’...
[ 960, 20 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 957, 1 ]
Mathlib/Probability/Independence/Basic.lean
ProbabilityTheory.IndepSets.symm
[ { "state_after": "Ξ© : Type u_1\nΞΉ : Type ?u.432097\ns₁ sβ‚‚ : Set (Set Ξ©)\ninst✝ : MeasurableSpace Ξ©\nΞΌ : MeasureTheory.Measure Ξ©\nh : IndepSets s₁ sβ‚‚\nt1 t2 : Set Ξ©\nht1 : t1 ∈ sβ‚‚\nht2 : t2 ∈ s₁\n⊒ ↑↑μ (t1 ∩ t2) = ↑↑μ t1 * ↑↑μ t2", "state_before": "Ξ© : Type u_1\nΞΉ : Type ?u.432097\ns₁ sβ‚‚ : Set (Set Ξ©)\ninst✝...
[ 151, 55 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 148, 1 ]
Mathlib/Data/Polynomial/Expand.lean
Polynomial.isLocalRingHom_expand
[ { "state_after": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : β„•\nhp : 0 < p\nf : R[X]\nhf1 : IsUnit (↑↑(expand R p) f)\n⊒ IsUnit f", "state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : β„•\nhp : 0 < p\n⊒ IsLocalRingHom ↑(expand R p)", "tactic": "refine' ⟨fun f hf1 => _⟩"...
[ 278, 77 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 273, 1 ]
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean
AffineSubspace.subtype_apply
[]
[ 431, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 430, 1 ]
Mathlib/Algebra/CubicDiscriminant.lean
Cubic.disc_ne_zero_iff_roots_nodup
[ { "state_after": "R : Type ?u.1296918\nS : Type ?u.1296921\nF : Type u_1\nK : Type u_2\nP : Cubic F\ninst✝¹ : Field F\ninst✝ : Field K\nΟ† : F β†’+* K\nx y z : K\nha : P.a β‰  0\nh3 : roots (map Ο† P) = {x, y, z}\n⊒ x β‰  y ∧ x β‰  z ∧ y β‰  z ↔ Nodup {x, y, z}", "state_before": "R : Type ?u.1296918\nS : Type ?u.129692...
[ 594, 8 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 588, 1 ]
Mathlib/LinearAlgebra/Multilinear/Basic.lean
MultilinearMap.mkPiRing_apply_one_eq_self
[ { "state_after": "case H\nR : Type u\nΞΉ : Type u'\nn : β„•\nM : Fin (Nat.succ n) β†’ Type v\nM₁ : ΞΉ β†’ Type v₁\nMβ‚‚ : Type vβ‚‚\nM₃ : Type v₃\nM' : Type v'\ninst✝⁷ : CommSemiring R\ninst✝⁢ : (i : ΞΉ) β†’ AddCommMonoid (M₁ i)\ninst✝⁡ : (i : Fin (Nat.succ n)) β†’ AddCommMonoid (M i)\ninst✝⁴ : AddCommMonoid Mβ‚‚\ninst✝³ : (i : F...
[ 1072, 41 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 1066, 1 ]
Mathlib/Topology/MetricSpace/Isometry.lean
IsometryEquiv.preimage_sphere
[ { "state_after": "no goals", "state_before": "ΞΉ : Type ?u.1073874\nΞ± : Type u\nΞ² : Type v\nΞ³ : Type w\ninst✝¹ : PseudoMetricSpace Ξ±\ninst✝ : PseudoMetricSpace Ξ²\nh✝ h : Ξ± ≃ᡒ Ξ²\nx : Ξ²\nr : ℝ\n⊒ ↑h ⁻¹' Metric.sphere x r = Metric.sphere (↑(IsometryEquiv.symm h) x) r", "tactic": "rw [← h.isometry.preimage_s...
[ 618, 69 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 616, 1 ]
Mathlib/GroupTheory/Coset.lean
Subgroup.quotientEquivOfEq_mk
[]
[ 632, 6 ]
5a919533f110b7d76410134a237ee374f24eaaad
https://github.com/leanprover-community/mathlib4
[ 630, 1 ]