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Mathlib/Data/Matrix/Basic.lean | Matrix.bit1_apply_eq | [
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.mem_bot | [] | [
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.eq_of_xn_modEq_lem3 | [
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.coe_sub | [] | [
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.isPrime_radical | [
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Mathlib/Topology/LocallyFinite.lean | LocallyFinite.exists_forall_eventually_eq_prod | [
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Mathlib/Data/Fintype/Card.lean | Infinite.exists_superset_card_eq | [
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Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | le_mul_self | [
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{
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Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsEisensteinAt.irreducible | [] | [
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Mathlib/Algebra/Quaternion.lean | Quaternion.sub_im | [] | [
939,
71
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_zero | [] | [
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Mathlib/GroupTheory/GroupAction/FixingSubgroup.lean | fixedPoints_subgroup_sup | [] | [
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44
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Mathlib/Order/Cover.lean | Covby.Ioo_eq | [] | [
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.continuousOn_iff_continuousOn_comp_left | [] | [
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.isSeparator_iff_faithful_coyoneda_obj | [] | [
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95
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Mathlib/Order/SupIndep.lean | CompleteLattice.independent_def | [] | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_sum | [
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Mathlib/Data/Multiset/Nodup.lean | Multiset.count_eq_one_of_mem | [] | [
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_prod | [] | [
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55
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_ite_eq | [
{
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Mathlib/GroupTheory/Sylow.lean | card_sylow_dvd_index | [] | [
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.coe_zero | [] | [
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Mathlib/LinearAlgebra/Span.lean | LinearEquiv.coord_apply_smul | [] | [
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce_toWord | [
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Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.prime | [
{
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Mathlib/LinearAlgebra/FiniteDimensional.lean | bot_eq_top_of_rank_eq_zero | [
{
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Mathlib/Data/List/Basic.lean | List.find?_nil | [] | [
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Mathlib/Algebra/Lie/Submodule.lean | LieHom.isIdealMorphism_def | [] | [
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Mathlib/Algebra/Tropical/BigOperators.lean | Finset.trop_inf | [
{
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"state_before": "R : Type u_1\nS : Type u_2\ninstβΒΉ : LinearOrder R\ninstβ : OrderTop R\ns : Fins... | [
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.monic_mul_leadingCoeff_inv | [
{
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"tactic": "rw [Monic, leadingCoeff_mul, leadingCoeff_C,\n mul_inv_cancel (show leadingCoeff p β 0 from mt le... | [
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Std/Logic.lean | and_congr | [] | [
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Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.range_eval | [] | [
254,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
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Std/Data/List/Init/Lemmas.lean | List.take_length_le | [
{
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"tactic": "have := take_append_drop i l"
},
{
"state_after": "Ξ± : Type u_1\ni : Nat\nl :... | [
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Mathlib/Analysis/Normed/Group/Quotient.lean | quotient_norm_mk_le' | [] | [
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26
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Mathlib/Data/Complex/Exponential.lean | Real.expNear_sub | [
{
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Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.nsmul_comp | [] | [
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32
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Mathlib/Order/CompleteLattice.lean | IsGLB.sInf_eq | [] | [
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_elem | [] | [
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Mathlib/RingTheory/WittVector/WittPolynomial.lean | xInTermsOfW_vars_aux | [
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_one_mul_apply | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | LinearMap.antilipschitz_of_comap_nhds_le | [
{
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.coe_evalβHom | [] | [
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.bounds_nonempty | [] | [
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25
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_int_eq | [
{
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Mathlib/Computability/Primrec.lean | Primrecβ.compβ | [] | [
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Mathlib/Data/List/ProdSigma.lean | List.length_product | [
{
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16
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.degree_eq_bot_iff | [
{
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{
"state_after": "R : Type u_1\ninstβ : Sem... | [
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15
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489,
1
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.le_biUnion_iff | [
{
"state_after": "case refine'_1\nΞΉ : Type u_1\nI Jβ Jβ Jβ : Box ΞΉ\nΟ Οβ Οβ : Prepartition I\nx : ΞΉ β β\nΟiβ Οiβ Οiβ Οi : (J : Box ΞΉ) β Prepartition J\nΟ' : Prepartition I\nH : Ο' β€ biUnion Ο Οi\nJ : Box ΞΉ\nhJ : J β Ο\nβ’ restrict Ο' J β€ Οi J\n\ncase refine'_2\nΞΉ : Type u_1\nI J Jβ Jβ : Box ΞΉ\nΟ Οβ Οβ : Preparti... | [
565,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
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Mathlib/Order/Filter/Basic.lean | Filter.sup_bind | [] | [
2766,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2766,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Chebyshev.lean | Polynomial.Chebyshev.T_real_cos | [
{
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}
] | [
119,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
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Mathlib/Geometry/Euclidean/Angle/Unoriented/Basic.lean | Submodule.angle_coe | [] | [
75,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.rotateL_lemmaβ | [
{
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Mathlib/Data/List/Basic.lean | List.zipLeft'_cons_nil | [] | [
4052,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.evalβ_pow | [
{
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1015,
78
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Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean | CategoryTheory.Limits.hasColimit_of_coequalizer_and_coproduct | [] | [
350,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
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Mathlib/MeasureTheory/Measure/AEDisjoint.lean | MeasureTheory.AEDisjoint.union_left_iff | [
{
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] | [
109,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
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Mathlib/Data/List/Basic.lean | List.getI_append_right | [] | [
4495,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4493,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_one | [] | [
215,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
20
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Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.algebraMap_apply_eq_map_map_submonoid | [] | [
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79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/FieldTheory/Fixed.lean | FixedPoints.coe_algebraMap | [] | [
127,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Data/Finset/Lattice.lean | Finset.sup'_induction | [
{
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37
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857,
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Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mem_top | [] | [
199,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
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Mathlib/Data/Set/Intervals/Monotone.lean | AntitoneOn.Iic | [] | [
69,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Extreme.lean | inter_extremePoints_subset_extremePoints_of_subset | [] | [
168,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
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Mathlib/Algebra/ContinuedFractions/ConvergentsEquiv.lean | GeneralizedContinuedFraction.succ_nth_convergent_eq_squashGCF_nth_convergent | [
{
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332,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
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Mathlib/Data/Set/Finite.lean | Set.Finite.of_subsingleton | [] | [
708,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pushoutCoconeOfRightIso_ΞΉ_app_right | [] | [
1880,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1879,
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Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.distortion_eq_of_sub_eq_div | [
{
"state_after": "ΞΉ : Type u_1\nIβ Jβ : Box ΞΉ\nx y : ΞΉ β β\ninstβ : Fintype ΞΉ\nI J : Box ΞΉ\nr : β\nh : β (i : ΞΉ), upper I i - lower I i = (upper J i - lower J i) / r\nβ’ (Finset.sup Finset.univ fun i =>\n (Finset.sup Finset.univ fun b => βReal.nnabs (upper J b - lower J b) / βReal.nnabs r) /\n (βReal... | [
510,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
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src/lean/Init/Data/AC.lean | Lean.Data.AC.Context.eq_of_norm | [
{
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320,
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] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
317,
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Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffOn_univ | [] | [
274,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.norm_sq_re_conj_add | [
{
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] | [
770,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
769,
1
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Mathlib/Data/List/Perm.lean | List.Perm.inter_left | [
{
"state_after": "no goals",
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] | [
1013,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1012,
1
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.abs_isBoundedUnder_iff | [
{
"state_after": "π : Type u_1\ninstβΒΉ : NormedLinearOrderedField π\nP Q : π[X]\ninstβ : OrderTopology π\nh : IsBoundedUnder (fun x x_1 => x β€ x_1) atTop fun x => abs (eval x P)\nβ’ degree P β€ 0",
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100,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.not_succ_of_isLimit | [] | [
257,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/Order/CompleteLattice.lean | sSup_le_sSup_of_forall_exists_le | [] | [
180,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Set/Basic.lean | Set.mem_union_left | [] | [
738,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.sqLe_add_mixed | [
{
"state_after": "no goals",
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}
] | [
440,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
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Mathlib/Data/Fin/Basic.lean | Fin.succ_le_succ_iff | [] | [
889,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_add_right' | [
{
"state_after": "no goals",
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}
] | [
305,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_omega | [] | [
811,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
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Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean | TopCat.snd_openEmbedding_of_left_openEmbedding | [
{
"state_after": "case h.e'_5.h\nJ : Type v\ninstβ : SmallCategory J\nXβ Yβ Z : TopCat\nX Y S : TopCat\nf : X βΆ S\nH : OpenEmbedding ((forget TopCat).map f)\ng : Y βΆ S\ne_2β : (forget TopCat).obj Y = βY\nβ’ (forget TopCat).map pullback.snd =\n β(homeoOfIso (asIso pullback.snd)) β\n (forget TopCat).map (p... | [
322,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
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Mathlib/Data/List/Sigma.lean | List.mem_ext | [] | [
161,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.map_subset_map | [] | [
1328,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_bot | [] | [
118,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.symm_symm | [
{
"state_after": "case mk\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.24956\nΞ΄ : Type ?u.24959\ne' : LocalEquiv Ξ² Ξ³\ntoFunβ : Ξ± β Ξ²\ninvFunβ : Ξ² β Ξ±\nsourceβ : Set Ξ±\ntargetβ : Set Ξ²\nmap_source'β : β β¦x : Ξ±β¦, x β sourceβ β toFunβ x β targetβ\nmap_target'β : β β¦x : Ξ²β¦, x β targetβ β invFunβ x β sourceβ\nleft_inv'β... | [
332,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
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Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.mem_degreeLE | [
{
"state_after": "R : Type u\nS : Type ?u.4503\ninstβ : Semiring R\nn : WithBot β\nf : R[X]\nβ’ (β (i : β), βi > n β β(lcoeff R i) f = 0) β β (m : β), n < βm β coeff f m = 0",
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"... | [
68,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm'_zero | [
{
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187,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Fin/Interval.lean | Fin.card_Ioo | [
{
"state_after": "no goals",
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"tactic": "rw [β Nat.card_Ioo, β map_valEmbedding_Ioo, card_map]"
}
] | [
95,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Order/RelClasses.lean | IsTrichotomous.swap | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u\nΞ² : Type v\nrβ : Ξ± β Ξ± β Prop\ns : Ξ² β Ξ² β Prop\nr : Ξ± β Ξ± β Prop\ninstβ : IsTrichotomous Ξ± r\na b : Ξ±\nβ’ Function.swap r a b β¨ a = b β¨ Function.swap r b a",
"tactic": "simpa [Function.swap, or_comm, or_left_comm] using trichotomous_of r a b"
}... | [
96,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
95,
1
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Mathlib/Logic/Function/Conjugate.lean | Function.Semiconjβ.isIdempotent_right | [
{
"state_after": "no goals",
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... | [
176,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_atBot_isLUB | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_2\nΞ² : Type ?u.6300\nΞΉ : Type u_1\ninstβΒ³ : Preorder ΞΉ\ninstβΒ² : TopologicalSpace Ξ±\ninstβΒΉ : Preorder Ξ±\ninstβ : SupConvergenceClass Ξ±\nf : ΞΉ β Ξ±\na : Ξ±\nh_anti : Antitone f\nha : IsLUB (range f) a\nβ’ Tendsto f atBot (π a)",
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106,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.extraction_forall_of_eventually | [] | [
493,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.coeff_eq_zero_of_lt_natTrailingDegree | [
{
"state_after": "case h\nR : Type u\nS : Type v\na b : R\nnβ m : β\ninstβ : Semiring R\npβ q r p : R[X]\nn : β\nh : n < natTrailingDegree p\nβ’ βn < trailingDegree p",
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276,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
269,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.rangeS_algebraMap | [
{
"state_after": "no goals",
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1316,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1313,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.mul_eq_sum_sum | [
{
"state_after": "case a\nR : Type u\na b : R\nm n : β\ninstβ : Semiring R\np q : R[X]\nβ’ (p * q).toFinsupp = (β i in support p, sum q fun j a => β(monomial (i + j)) (coeff p i * a)).toFinsupp",
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956,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_pair | [
{
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Mathlib/Topology/MetricSpace/Holder.lean | holderWith_one | [] | [
95,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_nnnorm_le_bound' | [
{
"state_after": "no goals",
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/Countable.lean | Set.Countable.prod | [
{
"state_after": "Ξ± : Type u\nΞ² : Type v\nΞ³ : Type w\nΞΉ : Sort x\ns : Set Ξ±\nt : Set Ξ²\nhs : Set.Countable s\nht : Set.Countable t\nthis : Countable βs\nβ’ Set.Countable (s ΓΛ’ t)",
"state_before": "Ξ± : Type u\nΞ² : Type v\nΞ³ : Type w\nΞΉ : Sort x\ns : Set Ξ±\nt : Set Ξ²\nhs : Set.Countable s\nht : Set.Countable ... | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_bUnion | [
{
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"state_before": "R : Type u_2\nA : Type u_1\ninstβΒ³ : CommSemiring R\ninstβΒ² : CommRing A\ninstβΒΉ : Algebra R A\nπ : β β Submodule R A\ninstβ : GradedAlgebra π\ns : Set (Set A)\nβ’ zeroLocus π (β (s' : Set A) (_ : s' β s), s') = β (s' : Set A) (_ : s' β s), zeroLocus π s'",
... | [
270,
34
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268,
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