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https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Set/Pointwise/BigOperators.lean
Set.list_prod_subset_list_prod
[ 108, 1 ]
[ 114, 56 ]
[{"tactic": "induction' t with h tl ih", "annotated_tactic": ["induction' t with h tl ih", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u_2\n\u03b2 : Type u_3\nF : Type u_4\ninst\u271d\u00b2 : CommMonoid \u03b1\ninst\u271d\u00b9 : CommMonoid \u03b2\ninst\u271d : MonoidHomClass F \u03b1 \u03b2\nt : List \u03b9...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
HasDerivWithinAt.ccos
[ 185, 1 ]
[ 187, 60 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Algebra/Basic.lean
algebraMap.coe_pow
[ 165, 1 ]
[ 166, 31 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Opposites.lean
MulOpposite.unop_smul
[ 323, 1 ]
[ 324, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Logic/Embedding/Basic.lean
subtypeOrLeftEmbedding_apply_left
[ 481, 1 ]
[ 484, 13 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/LinearAlgebra/AffineSpace/Combination.lean
Finset.sum_centroidWeightsIndicator_eq_one_of_nonempty
[ 920, 1 ]
[ 923, 53 ]
[{"tactic": "rw [sum_centroidWeightsIndicator]", "annotated_tactic": ["rw [<a>sum_centroidWeightsIndicator</a>]", [{"full_name": "Finset.sum_centroidWeightsIndicator", "def_path": "Mathlib/LinearAlgebra/AffineSpace/Combination.lean", "def_pos": [904, 9], "def_end_pos": [904, 37]}]], "state_before": "k : Type u_1\nV : T...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Set/Prod.lean
Set.offDiag_eq_sep_prod
[ 596, 1 ]
[ 597, 30 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Real/ENNReal.lean
ENNReal.range_coe'
[ 160, 1 ]
[ 160, 61 ]
[]
https://github.com/leanprover/std4
869c615eb10130c0637a7bc038e2b80253559913
lake-packages/std/Std/Data/Sum/Lemmas.lean
Sum.liftRel_subrelation_lex
[ 200, 1 ]
[ 200, 85 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Heyting/Basic.lean
PUnit.sup_eq
[ 1356, 1 ]
[ 1357, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/MeasureTheory/Function/Jacobian.lean
exists_partition_approximatesLinearOn_of_hasFDerivWithinAt
[ 254, 1 ]
[ 269, 94 ]
[{"tactic": "rcases exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAt f s f' hf' r rpos with\n \u27e8t, A, t_closed, st, t_approx, ht\u27e9", "annotated_tactic": ["rcases <a>exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAt</a> f s f' hf' r rpos with\n \u27e8t, A, t_closed, st, t_approx, ht\...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/ModelTheory/Encoding.lean
FirstOrder.Language.BoundedFormula.listEncode_sigma_injective
[ 306, 1 ]
[ 308, 43 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/GroupPower/Order.lean
Left.one_le_pow_of_le
[ 113, 1 ]
[ 117, 57 ]
[{"tactic": "rw [pow_succ]", "annotated_tactic": ["rw [<a>pow_succ</a>]", [{"full_name": "pow_succ", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [645, 9], "def_end_pos": [645, 17]}]], "state_before": "\u03b2 : Type u_1\nA : Type u_2\nG : Type u_3\nM : Type u_4\nR : Type u_5\ninst\u271d\u00b2 : Monoid M\ni...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Sequences.lean
SeqCompact.lebesgue_number_lemma_of_metric
[ 407, 8 ]
[ 410, 55 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Fin/Basic.lean
Fin.succAbove_pred
[ 1424, 1 ]
[ 1427, 54 ]
[{"tactic": "rw [succAbove_above, succ_pred]", "annotated_tactic": ["rw [<a>succAbove_above</a>, <a>succ_pred</a>]", [{"full_name": "Fin.succAbove_above", "def_path": "Mathlib/Data/Fin/Basic.lean", "def_pos": [1356, 9], "def_end_pos": [1356, 24]}, {"full_name": "Fin.succ_pred", "def_path": "lake-packages/std/Std/Data/F...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/DFinsupp/Order.lean
DFinsupp.bot_eq_zero
[ 155, 11 ]
[ 156, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/Convex/Between.lean
Wbtw.right_mem_affineSpan_of_left_ne
[ 696, 1 ]
[ 699, 42 ]
[{"tactic": "rcases h.right_mem_image_Ici_of_left_ne hne with \u27e8r, \u27e8-, rfl\u27e9\u27e9", "annotated_tactic": ["rcases h.right_mem_image_Ici_of_left_ne hne with \u27e8r, \u27e8-, rfl\u27e9\u27e9", []], "state_before": "R : Type u_1\nV : Type u_2\nV' : Type u_3\nP : Type u_4\nP' : Type u_5\ninst\u271d\u00b3 : Li...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean
Matrix.nondegenerate_of_det_ne_zero
[ 50, 1 ]
[ 63, 18 ]
[{"tactic": "intro v hv", "annotated_tactic": ["intro v hv", []], "state_before": "m : Type u_1\nR : Type u_2\nA : Type u_3\ninst\u271d\u2074 : Fintype m\ninst\u271d\u00b3 : CommRing R\ninst\u271d\u00b2 : CommRing A\ninst\u271d\u00b9 : IsDomain A\ninst\u271d : DecidableEq m\nM : Matrix m m A\nhM : det M \u2260 0\n\u22a...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/LinearAlgebra/Multilinear/Basic.lean
MultilinearMap.map_neg
[ 1132, 1 ]
[ 1135, 88 ]
[{"tactic": "rw [\u2190 MultilinearMap.map_add, add_left_neg, f.map_coord_zero i (update_same i 0 m)]", "annotated_tactic": ["rw [\u2190 <a>MultilinearMap.map_add</a>, <a>add_left_neg</a>, f.map_coord_zero i (<a>update_same</a> i 0 m)]", [{"full_name": "MultilinearMap.map_add", "def_path": "Mathlib/LinearAlgebra/Multil...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/Ideal/Quotient.lean
Ideal.Quotient.maximal_of_isField
[ 234, 1 ]
[ 243, 77 ]
[{"tactic": "apply Ideal.isMaximal_iff.2", "annotated_tactic": ["apply <a>Ideal.isMaximal_iff</a>.2", [{"full_name": "Ideal.isMaximal_iff", "def_path": "Mathlib/RingTheory/Ideal/Basic.lean", "def_pos": [302, 9], "def_end_pos": [302, 22]}]], "state_before": "R : Type u\ninst\u271d : CommRing R\nI\u271d : Ideal R\na b : ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/FreeAlgebra.lean
FreeAlgebra.algebraMap_eq_zero_iff
[ 498, 1 ]
[ 499, 68 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Multiset/Basic.lean
Multiset.count_cons_of_ne
[ 2364, 1 ]
[ 2365, 27 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Probability/Process/Stopping.lean
MeasureTheory.IsStoppingTime.measurable
[ 579, 11 ]
[ 582, 90 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Ideal.lean
IsCoatom.isMaximal
[ 241, 1 ]
[ 242, 81 ]
[{"tactic": "simp [hI.2 _ hJ]", "annotated_tactic": ["simp [hI.2 _ hJ]", []], "state_before": "P : Type u_1\ninst\u271d\u00b2 : LE P\ninst\u271d\u00b9 : IsDirected P fun x x_1 => x \u2264 x_1\ninst\u271d : Nonempty P\nI : Ideal P\nhI : IsCoatom I\nsrc\u271d : IsProper I := IsCoatom.isProper hI\nx\u271d : Ideal P\nhJ : ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/DenseEmbedding.lean
DenseInducing.continuous
[ 54, 11 ]
[ 55, 27 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Filter/Bases.lean
Filter.hasBasis_generate
[ 241, 1 ]
[ 243, 84 ]
[{"tactic": "simp only [mem_generate_iff, exists_prop, and_assoc, and_left_comm]", "annotated_tactic": ["simp only [<a>mem_generate_iff</a>, <a>exists_prop</a>, <a>and_assoc</a>, <a>and_left_comm</a>]", [{"full_name": "Filter.mem_generate_iff", "def_path": "Mathlib/Order/Filter/Basic.lean", "def_pos": [363, 9], "def_en...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/CategoryTheory/Monoidal/Center.lean
CategoryTheory.Center.rightUnitor_hom_f
[ 284, 1 ]
[ 285, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Squarefree.lean
squarefree_one
[ 46, 1 ]
[ 47, 24 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/List/Basic.lean
List.map_injective_iff
[ 1774, 1 ]
[ 1784, 33 ]
[{"tactic": "constructor <;> intro h x y hxy", "annotated_tactic": ["constructor <;> intro h x y hxy", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : Type u\n\u03b2 : Type v\n\u03b3 : Type w\nl\u2081 l\u2082 : List \u03b1\nf : \u03b1 \u2192 \u03b2\n\u22a2 Injective (map f) \u2194 Injective f", "state_after": "case m...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/NormedSpace/Star/Spectrum.lean
unitary.spectrum_subset_circle
[ 31, 1 ]
[ 41, 61 ]
[{"tactic": "nontriviality E", "annotated_tactic": ["nontriviality E", []], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\u2075 : NormedField \ud835\udd5c\nE : Type u_2\ninst\u271d\u2074 : NormedRing E\ninst\u271d\u00b3 : StarRing E\ninst\u271d\u00b2 : CstarRing E\ninst\u271d\u00b9 : NormedAlgebra \ud835\udd5c E...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Maps.lean
quotientMap_iff_closed
[ 282, 1 ]
[ 285, 49 ]
[{"tactic": "simp only [isOpen_compl_iff, preimage_compl]", "annotated_tactic": ["simp only [<a>isOpen_compl_iff</a>, <a>preimage_compl</a>]", [{"full_name": "isOpen_compl_iff", "def_path": "Mathlib/Topology/Basic.lean", "def_pos": [205, 17], "def_end_pos": [205, 33]}, {"full_name": "Set.preimage_compl", "def_path": "M...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean
BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition
[ 268, 1 ]
[ 270, 26 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/GroupPower/Lemmas.lean
SemiconjBy.cast_int_mul_right
[ 1038, 1 ]
[ 1039, 48 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Sigma/Basic.lean
Function.Injective.of_sigma_map
[ 134, 1 ]
[ 137, 73 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/UniformSpace/UniformConvergence.lean
tendstoUniformlyOn_iff_tendstoUniformlyOnFilter
[ 107, 1 ]
[ 112, 7 ]
[{"tactic": "simp only [TendstoUniformlyOn, TendstoUniformlyOnFilter]", "annotated_tactic": ["simp only [<a>TendstoUniformlyOn</a>, <a>TendstoUniformlyOnFilter</a>]", [{"full_name": "TendstoUniformlyOn", "def_path": "Mathlib/Topology/UniformSpace/UniformConvergence.lean", "def_pos": [103, 5], "def_end_pos": [103, 23]},...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/List/Perm.lean
List.singleton_perm
[ 211, 1 ]
[ 212, 26 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean
ProjectiveSpectrum.zeroLocus_vanishingIdeal_eq_closure
[ 360, 1 ]
[ 368, 46 ]
[{"tactic": "apply Set.Subset.antisymm", "annotated_tactic": ["apply <a>Set.Subset.antisymm</a>", [{"full_name": "Set.Subset.antisymm", "def_path": "Mathlib/Data/Set/Basic.lean", "def_pos": [370, 9], "def_end_pos": [370, 24]}]], "state_before": "R : Type u_1\nA : Type u_2\ninst\u271d\u00b3 : CommSemiring R\ninst\u271d\...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/Ideal/Norm.lean
Ideal.irreducible_of_irreducible_absNorm
[ 408, 1 ]
[ 416, 58 ]
[{"tactic": "simpa only [Ideal.isUnit_iff, Nat.isUnit_iff, absNorm_eq_one_iff] using h", "annotated_tactic": ["simpa only [<a>Ideal.isUnit_iff</a>, <a>Nat.isUnit_iff</a>, <a>absNorm_eq_one_iff</a>] using h", [{"full_name": "Ideal.isUnit_iff", "def_path": "Mathlib/RingTheory/Ideal/Operations.lean", "def_pos": [1336, 9],...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean
Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegree
[ 382, 1 ]
[ 396, 52 ]
[{"tactic": "rw [coeff_mul]", "annotated_tactic": ["rw [<a>coeff_mul</a>]", [{"full_name": "Polynomial.coeff_mul", "def_path": "Mathlib/Data/Polynomial/Coeff.lean", "def_pos": [116, 9], "def_end_pos": [116, 18]}]], "state_before": "R : Type u\nS : Type v\na b : R\nn m : \u2115\ninst\u271d : Semiring R\np q r : R[X]\n\u...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/Calculus/FDeriv/Measurable.lean
RightDerivMeasurableAux.le_of_mem_A
[ 522, 1 ]
[ 527, 78 ]
[{"tactic": "rcases hx with \u27e8r', r'mem, hr'\u27e9", "annotated_tactic": ["rcases hx with \u27e8r', r'mem, hr'\u27e9", []], "state_before": "F : Type u_1\ninst\u271d\u00b9 : NormedAddCommGroup F\ninst\u271d : NormedSpace \u211d F\nf : \u211d \u2192 F\nK : Set F\nr \u03b5 : \u211d\nL : F\nx : \u211d\nhx : x \u2208 A...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/AlgebraicGeometry/StructureSheaf.lean
AlgebraicGeometry.StructureSheaf.stalkAlgebra_map
[ 938, 1 ]
[ 940, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/Valuation/ValuationSubring.lean
Valuation.mem_valuationSubring_iff
[ 437, 1 ]
[ 437, 90 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Geometry/Manifold/MFDeriv.lean
tangentMapWithin_comp_at
[ 1028, 1 ]
[ 1035, 6 ]
[{"tactic": "simp only [tangentMapWithin, mfld_simps]", "annotated_tactic": ["simp only [<a>tangentMapWithin</a>, mfld_simps]", [{"full_name": "tangentMapWithin", "def_path": "Mathlib/Geometry/Manifold/MFDeriv.lean", "def_pos": [304, 5], "def_end_pos": [304, 21]}]], "state_before": "\ud835\udd5c : Type u_1\ninst\u271d\...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Set/Prod.lean
Set.mem_pi
[ 670, 1 ]
[ 671, 10 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Set/Sigma.lean
Set.sigma_univ_range_eq
[ 197, 1 ]
[ 199, 25 ]
[{"tactic": "simp [range]", "annotated_tactic": ["simp [<a>range</a>]", [{"full_name": "Set.range", "def_path": "Mathlib/Data/Set/Image.lean", "def_pos": [668, 5], "def_end_pos": [668, 10]}]], "state_before": "\u03b9 : Type u_1\n\u03b9' : Type u_2\n\u03b1 : \u03b9 \u2192 Type u_3\n\u03b2 : \u03b9 \u2192 Type u_4\ns s\u...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean
span_gramSchmidtNormed_range
[ 329, 1 ]
[ 331, 67 ]
[{"tactic": "simpa only [image_univ.symm] using span_gramSchmidtNormed f univ", "annotated_tactic": ["simpa only [image_univ.symm] using <a>span_gramSchmidtNormed</a> f <a>univ</a>", [{"full_name": "span_gramSchmidtNormed", "def_path": "Mathlib/Analysis/InnerProductSpace/GramSchmidtOrtho.lean", "def_pos": [316, 9], "de...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Int/ModEq.lean
Dvd.dvd.zero_modEq_int
[ 90, 1 ]
[ 91, 24 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/GroupTheory/Subgroup/Finite.lean
Subgroup.eq_bot_of_card_eq
[ 162, 1 ]
[ 163, 35 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Group/WithOne/Defs.lean
WithOne.one_ne_coe
[ 151, 1 ]
[ 152, 18 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/CategoryTheory/Iso.lean
CategoryTheory.Iso.trans_assoc
[ 181, 1 ]
[ 183, 45 ]
[{"tactic": "ext", "annotated_tactic": ["ext", []], "state_before": "C : Type u\ninst\u271d : Category.{v, u} C\nX Y Z Z' : C\n\u03b1 : X \u2245 Y\n\u03b2 : Y \u2245 Z\n\u03b3 : Z \u2245 Z'\n\u22a2 (\u03b1 \u226a\u226b \u03b2) \u226a\u226b \u03b3 = \u03b1 \u226a\u226b \u03b2 \u226a\u226b \u03b3", "state_after": "case w...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Matrix/Kronecker.lean
Matrix.det_kroneckerTMul
[ 562, 1 ]
[ 570, 36 ]
[{"tactic": "refine' (det_kroneckerMapBilinear (TensorProduct.mk R \u03b1 \u03b2) tmul_mul_tmul _ _).trans _", "annotated_tactic": ["refine' (<a>det_kroneckerMapBilinear</a> (<a>TensorProduct.mk</a> R \u03b1 \u03b2) <a>tmul_mul_tmul</a> _ _).<a>trans</a> _", [{"full_name": "Matrix.det_kroneckerMapBilinear", "def_path":...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/Normed/Group/SemiNormedGroupCat/Kernels.lean
SemiNormedGroupCat.explicitCokernelIso_hom_desc
[ 394, 1 ]
[ 399, 40 ]
[{"tactic": "ext1", "annotated_tactic": ["ext1", []], "state_before": "X Y Z : SemiNormedGroupCat\nf : X \u27f6 Y\ng : Y \u27f6 Z\nw : f \u226b g = 0\n\u22a2 (explicitCokernelIso f).hom \u226b cokernel.desc f g w = explicitCokernelDesc w", "state_after": "case h\nX Y Z : SemiNormedGroupCat\nf : X \u27f6 Y\ng : Y \u27f6...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Polynomial/EraseLead.lean
Polynomial.eraseLead_add_of_natDegree_lt_right
[ 170, 1 ]
[ 178, 57 ]
[{"tactic": "ext n", "annotated_tactic": ["ext n", []], "state_before": "R : Type u_1\ninst\u271d : Semiring R\nf p q : R[X]\npq : natDegree p < natDegree q\n\u22a2 eraseLead (p + q) = p + eraseLead q", "state_after": "case a\nR : Type u_1\ninst\u271d : Semiring R\nf p q : R[X]\npq : natDegree p < natDegree q\nn : \u21...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/UniformSpace/Completion.lean
CauchyFilter.uniformEmbedding_pureCauchy
[ 170, 1 ]
[ 172, 72 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/UniqueFactorizationDomain.lean
irreducible_iff_prime_of_exists_unique_irreducible_factors
[ 375, 1 ]
[ 412, 23 ]
[{"tactic": "simp [ha0]", "annotated_tactic": ["simp [ha0]", []], "state_before": "\u03b1 : Type u_1\ninst\u271d : CancelCommMonoidWithZero \u03b1\neif : \u2200 (a : \u03b1), a \u2260 0 \u2192 \u2203 f, (\u2200 (b : \u03b1), b \u2208 f \u2192 Irreducible b) \u2227 Multiset.prod f ~\u1d64 a\nuif :\n \u2200 (f g : Multi...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Finset/LocallyFinite.lean
Finset.Ico_inter_Ico_consecutive
[ 620, 1 ]
[ 621, 46 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Order/NhdsSet.lean
Iio_mem_nhdsSet_Ico
[ 115, 1 ]
[ 116, 47 ]
[{"tactic": "simpa", "annotated_tactic": ["simpa", []], "state_before": "\u03b1 : Type u_1\ninst\u271d\u00b2 : LinearOrder \u03b1\ninst\u271d\u00b9 : TopologicalSpace \u03b1\ninst\u271d : OrderClosedTopology \u03b1\na b c d : \u03b1\nh : b \u2264 c\n\u22a2 Iio c \u2208 \ud835\udcdd\u02e2 (Iio b)", "state_after": "no go...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/MeasureTheory/Measure/MeasureSpace.lean
MeasureTheory.mem_ae_map_iff
[ 2460, 1 ]
[ 2462, 80 ]
[{"tactic": "simp only [mem_ae_iff, map_apply_of_aemeasurable hf hs.compl, preimage_compl]", "annotated_tactic": ["simp only [<a>mem_ae_iff</a>, <a>map_apply_of_aemeasurable</a> hf hs.compl, <a>preimage_compl</a>]", [{"full_name": "MeasureTheory.mem_ae_iff", "def_path": "Mathlib/MeasureTheory/Measure/MeasureSpaceDef.le...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/Convex/StrictConvexBetween.lean
Wbtw.dist_le_max_dist
[ 41, 1 ]
[ 46, 35 ]
[{"tactic": "by_cases hp\u2081 : p\u2082 = p\u2081", "annotated_tactic": ["by_cases hp\u2081 : p\u2082 = p\u2081", []], "state_before": "V : Type u_1\nP : Type u_2\ninst\u271d\u2074 : NormedAddCommGroup V\ninst\u271d\u00b3 : NormedSpace \u211d V\ninst\u271d\u00b2 : PseudoMetricSpace P\ninst\u271d\u00b9 : NormedAddTorso...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/NormedSpace/OperatorNorm.lean
ContinuousLinearMap.op_nnnorm_prod
[ 630, 1 ]
[ 631, 34 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/LinearAlgebra/LinearIndependent.lean
eq_of_linearIndependent_of_span_subtype
[ 1013, 1 ]
[ 1025, 29 ]
[{"tactic": "let f : t \u21aa s :=\n \u27e8fun x => \u27e8x.1, h x.2\u27e9, fun a b hab => Subtype.coe_injective (Subtype.mk.inj hab)\u27e9", "annotated_tactic": ["let f : t \u21aa s :=\n \u27e8fun x => \u27e8x.1, h x.2\u27e9, fun a b hab => <a>Subtype.coe_injective</a> (Subtype.mk.inj hab)\u27e9", [{"full_name": "...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Algebra/GroupWithZero.lean
ContinuousWithinAt.inv₀
[ 121, 8 ]
[ 123, 13 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Finset/Sigma.lean
Finset.pairwiseDisjoint_map_sigmaMk
[ 75, 1 ]
[ 81, 43 ]
[{"tactic": "intro i _ j _ hij", "annotated_tactic": ["intro i _ j _ hij", []], "state_before": "\u03b9 : Type u_1\n\u03b1 : \u03b9 \u2192 Type u_2\n\u03b2 : Type u_3\ns s\u2081 s\u2082 : Finset \u03b9\nt t\u2081 t\u2082 : (i : \u03b9) \u2192 Finset (\u03b1 i)\n\u22a2 Set.PairwiseDisjoint \u2191s fun i => map (Embeddin...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Invertible/Basic.lean
Ring.inverse_invertible
[ 170, 1 ]
[ 171, 41 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean
Complex.hasDerivAt_sinh
[ 112, 1 ]
[ 113, 39 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/Ideal/Basic.lean
Ring.isField_iff_isSimpleOrder_ideal
[ 782, 1 ]
[ 790, 37 ]
[{"tactic": "cases subsingleton_or_nontrivial R", "annotated_tactic": ["cases <a>subsingleton_or_nontrivial</a> R", [{"full_name": "subsingleton_or_nontrivial", "def_path": "Mathlib/Logic/Nontrivial/Defs.lean", "def_pos": [94, 9], "def_end_pos": [94, 35]}]], "state_before": "\u03b1 : Type u\n\u03b2 : Type v\nR : Type u...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Algebra/Module/Basic.lean
ContinuousLinearEquiv.coe_funUnique
[ 2525, 1 ]
[ 2526, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Polynomial/Reverse.lean
Polynomial.reflect_monomial
[ 167, 1 ]
[ 168, 80 ]
[{"tactic": "rw [\u2190 one_mul (X ^ n), \u2190 one_mul (X ^ revAt N n), \u2190 C_1, reflect_C_mul_X_pow]", "annotated_tactic": ["rw [\u2190 <a>one_mul</a> (<a>X</a> ^ n), \u2190 <a>one_mul</a> (<a>X</a> ^ <a>revAt</a> N n), \u2190 <a>C_1</a>, <a>reflect_C_mul_X_pow</a>]", [{"full_name": "one_mul", "def_path": "Mathlib...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Group/Basic.lean
mul_div_cancel''
[ 740, 1 ]
[ 741, 51 ]
[{"tactic": "rw [div_eq_mul_inv, mul_inv_cancel_right a b]", "annotated_tactic": ["rw [<a>div_eq_mul_inv</a>, <a>mul_inv_cancel_right</a> a b]", [{"full_name": "div_eq_mul_inv", "def_path": "Mathlib/Algebra/Group/Defs.lean", "def_pos": [977, 9], "def_end_pos": [977, 23]}, {"full_name": "mul_inv_cancel_right", "def_path...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Compare.lean
Ordering.Compares.eq_lt
[ 82, 1 ]
[ 85, 77 ]
[{"tactic": "injection h", "annotated_tactic": ["injection h", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\ninst\u271d : Preorder \u03b1\na b : \u03b1\nh\u271d : Compares eq a b\nh : eq = lt\n\u22a2 a < b", "state_after": "no goals"}, {"tactic": "injection h", "annotated_tactic": ["injection h", []], "st...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Finset/Basic.lean
Finset.singleton_inter_of_mem
[ 1706, 1 ]
[ 1707, 78 ]
[{"tactic": "rw [insert_inter_of_mem H, empty_inter]", "annotated_tactic": ["rw [<a>insert_inter_of_mem</a> H, <a>empty_inter</a>]", [{"full_name": "Finset.insert_inter_of_mem", "def_path": "Mathlib/Data/Finset/Basic.lean", "def_pos": [1680, 9], "def_end_pos": [1680, 28]}, {"full_name": "Finset.empty_inter", "def_path"...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Computability/Partrec.lean
Computable.of_eq
[ 280, 1 ]
[ 281, 26 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Logic/Function/Basic.lean
Function.partialInv_left
[ 419, 1 ]
[ 420, 48 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean
exists_stronglyMeasurable_limit_of_tendsto_ae
[ 1685, 1 ]
[ 1697, 18 ]
[{"tactic": "borelize \u03b2", "annotated_tactic": ["borelize \u03b2", []], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b9 : Type u_4\ninst\u271d\u00b3 : Countable \u03b9\nm : MeasurableSpace \u03b1\n\u03bc : Measure \u03b1\ninst\u271d\u00b2 : TopologicalSpace \u03b2\ninst\u271d\u00b9 ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Order/Ring/Lemmas.lean
mul_le_mul_right
[ 214, 1 ]
[ 215, 64 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/JordanHolder.lean
CompositionSeries.append_succ_natAdd
[ 535, 1 ]
[ 537, 48 ]
[{"tactic": "rw [coe_append, append_succ_natAdd_aux _ _ i]", "annotated_tactic": ["rw [<a>coe_append</a>, <a>append_succ_natAdd_aux</a> _ _ i]", [{"full_name": "CompositionSeries.coe_append", "def_path": "Mathlib/Order/JordanHolder.lean", "def_pos": [511, 9], "def_end_pos": [511, 19]}, {"full_name": "CompositionSeries....
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Bounds/Basic.lean
IsGreatest.dual
[ 157, 1 ]
[ 158, 4 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/AdjoinRoot.lean
AdjoinRoot.coe_injective'
[ 417, 1 ]
[ 418, 19 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Filter/Pointwise.lean
Filter.mul_eq_bot_iff
[ 320, 1 ]
[ 321, 18 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/InnerProductSpace/Adjoint.lean
IsSelfAdjoint.conj_adjoint
[ 290, 1 ]
[ 294, 45 ]
[{"tactic": "rw [isSelfAdjoint_iff'] at hT \u22a2", "annotated_tactic": ["rw [<a>isSelfAdjoint_iff'</a>] at hT \u22a2", [{"full_name": "ContinuousLinearMap.isSelfAdjoint_iff'", "def_path": "Mathlib/Analysis/InnerProductSpace/Adjoint.lean", "def_pos": [223, 9], "def_end_pos": [223, 27]}]], "state_before": "\ud835\udd5c ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Sum/Order.lean
Sum.not_inl_le_inr
[ 149, 1 ]
[ 150, 22 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Finset/Basic.lean
Finset.union_sdiff_distrib
[ 2244, 1 ]
[ 2245, 12 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/GroupTheory/Nilpotent.lean
nilpotencyClass_quotient_center
[ 619, 1 ]
[ 636, 73 ]
[{"tactic": "generalize hn : Group.nilpotencyClass G = n", "annotated_tactic": ["generalize hn : <a>Group.nilpotencyClass</a> G = n", [{"full_name": "Group.nilpotencyClass", "def_path": "Mathlib/GroupTheory/Nilpotent.lean", "def_pos": [362, 19], "def_end_pos": [362, 40]}]], "state_before": "G : Type u_1\ninst\u271d\u00...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean
CategoryTheory.Limits.MultispanIndex.multispan_obj_left
[ 266, 1 ]
[ 267, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Geometry/Manifold/ContMDiff.lean
SmoothOn.comp'
[ 985, 8 ]
[ 987, 14 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/IndicatorFunction.lean
Set.mulIndicator_le'
[ 795, 1 ]
[ 796, 75 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/RingTheory/Ideal/Operations.lean
Ideal.mem_colon_singleton
[ 399, 1 ]
[ 401, 84 ]
[{"tactic": "simp only [\u2190 Ideal.submodule_span_eq, Submodule.mem_colon_singleton, smul_eq_mul]", "annotated_tactic": ["simp only [\u2190 <a>Ideal.submodule_span_eq</a>, <a>Submodule.mem_colon_singleton</a>, <a>smul_eq_mul</a>]", [{"full_name": "Ideal.submodule_span_eq", "def_path": "Mathlib/RingTheory/Ideal/Basic....
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/LinearAlgebra/BilinearForm/TensorProduct.lean
BilinForm.tensorDistribEquiv_tmul
[ 128, 1 ]
[ 132, 6 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Real/ENNReal.lean
ENNReal.toReal_sSup
[ 2452, 1 ]
[ 2454, 83 ]
[{"tactic": "simp only [ENNReal.toReal, toNNReal_sSup s hf, NNReal.coe_sSup, Set.image_image]", "annotated_tactic": ["simp only [<a>ENNReal.toReal</a>, <a>toNNReal_sSup</a> s hf, <a>NNReal.coe_sSup</a>, <a>Set.image_image</a>]", [{"full_name": "ENNReal.toReal", "def_path": "Mathlib/Data/Real/ENNReal.lean", "def_pos": [...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Int/Basic.lean
Int.neg_nat_succ
[ 183, 1 ]
[ 183, 75 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/Monotone/Basic.lean
monotone_fst
[ 1185, 1 ]
[ 1185, 70 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Algebra/Symmetrized.lean
SymAlg.sym_injective
[ 99, 1 ]
[ 100, 16 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Multiset/LocallyFinite.lean
Multiset.Ioo_self
[ 109, 1 ]
[ 109, 81 ]
[{"tactic": "rw [Ioo, Finset.Ioo_self, Finset.empty_val]", "annotated_tactic": ["rw [<a>Ioo</a>, <a>Finset.Ioo_self</a>, <a>Finset.empty_val</a>]", [{"full_name": "Multiset.Ioo", "def_path": "Mathlib/Order/LocallyFinite.lean", "def_pos": [546, 5], "def_end_pos": [546, 8]}, {"full_name": "Finset.Ioo_self", "def_path": "...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/Vector/Basic.lean
Vector.get_set_of_ne
[ 628, 1 ]
[ 633, 18 ]
[{"tactic": "cases v", "annotated_tactic": ["cases v", []], "state_before": "n : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\nv : Vector \u03b1 n\ni j : Fin n\nh : i \u2260 j\na : \u03b1\n\u22a2 get (set v i a) j = get v j", "state_after": "case mk\nn : \u2115\n\u03b1 : Type u_1\n\u03b2 : Type u_2\n...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/Algebra/Module/Alternating.lean
ContinuousAlternatingMap.toAlternatingMap_injective
[ 98, 1 ]
[ 100, 50 ]
[{"tactic": "convert FunLike.ext'_iff.1 h", "annotated_tactic": ["convert <a>FunLike.ext'_iff</a>.1 h", [{"full_name": "FunLike.ext'_iff", "def_path": "Mathlib/Data/FunLike/Basic.lean", "def_pos": [173, 9], "def_end_pos": [173, 17]}]], "state_before": "R : Type u_1\nM : Type u_2\nM' : Type u_3\nN : Type u_4\nN' : Type ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/MeasureTheory/Integral/Lebesgue.lean
MeasureTheory.lintegral_sub_le'
[ 938, 1 ]
[ 945, 46 ]
[{"tactic": "rw [tsub_le_iff_right]", "annotated_tactic": ["rw [<a>tsub_le_iff_right</a>]", [{"full_name": "tsub_le_iff_right", "def_path": "Mathlib/Algebra/Order/Sub/Defs.lean", "def_pos": [65, 9], "def_end_pos": [65, 26]}]], "state_before": "\u03b1 : Type u_1\n\u03b2 : Type u_2\n\u03b3 : Type u_3\n\u03b4 : Type u_4\n...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Order/BooleanAlgebra.lean
inf_sdiff_inf
[ 111, 1 ]
[ 111, 89 ]
[{"tactic": "rw [inf_comm, inf_inf_sdiff]", "annotated_tactic": ["rw [<a>inf_comm</a>, <a>inf_inf_sdiff</a>]", [{"full_name": "inf_comm", "def_path": "Mathlib/Order/Lattice.lean", "def_pos": [500, 9], "def_end_pos": [500, 17]}, {"full_name": "inf_inf_sdiff", "def_path": "Mathlib/Order/BooleanAlgebra.lean", "def_pos": [...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Topology/LocalHomeomorph.lean
LocalHomeomorph.ext
[ 328, 11 ]
[ 330, 52 ]
[]
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Data/List/Lemmas.lean
List.mapAccumr_eq_foldr
[ 93, 1 ]
[ 100, 58 ]
[{"tactic": "simp only [mapAccumr, foldr, mapAccumr_eq_foldr f as]", "annotated_tactic": ["simp only [<a>mapAccumr</a>, <a>foldr</a>, mapAccumr_eq_foldr f as]", [{"full_name": "List.mapAccumr", "def_path": "Mathlib/Init/Data/List/Lemmas.lean", "def_pos": [139, 5], "def_end_pos": [139, 14]}, {"full_name": "List.foldr", ...
https://github.com/leanprover-community/mathlib4
3ce43c18f614b76e161f911b75a3e1ef641620ff
Mathlib/Analysis/Convex/Basic.lean
Convex.smul_mem_of_zero_mem
[ 505, 1 ]
[ 507, 62 ]
[{"tactic": "simpa using hs.add_smul_mem zero_mem (by simpa using hx) ht", "annotated_tactic": ["simpa using hs.add_smul_mem zero_mem (by simpa using hx) ht", []], "state_before": "\ud835\udd5c : Type u_1\nE : Type u_2\nF : Type u_3\n\u03b2 : Type u_4\ninst\u271d\u2074 : OrderedRing \ud835\udd5c\ninst\u271d\u00b3 : Add...