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Mathlib/Topology/Constructions.lean | nhds_inl | [] | [
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Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_anti_mono_homogeneousIdeal | [] | [
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Mathlib/Algebra/RingQuot.lean | RingQuot.liftAlgHom_mkAlgHom_apply | [
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_row_self | [
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Mathlib/Topology/Instances/ENNReal.lean | NNReal.tsum_eq_toNNReal_tsum | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_lt_inv | [] | [
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Mathlib/LinearAlgebra/Projection.lean | Submodule.existsUnique_add_of_isCompl | [] | [
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Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Sheaf.existsUnique_gluing | [] | [
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Mathlib/MeasureTheory/Measure/AEMeasurable.lean | MeasurableEmbedding.aemeasurable_map_iff | [
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Mathlib/Order/Lattice.lean | Monotone.le_map_sup | [] | [
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Mathlib/Data/Fin/VecNotation.lean | Matrix.vecAlt1_vecAppend | [
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Mathlib/Topology/Algebra/Monoid.lean | continuous_pow | [
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Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right | [
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Mathlib/Analysis/SpecialFunctions/Sqrt.lean | DifferentiableAt.sqrt | [] | [
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Mathlib/Computability/Reduce.lean | OneOneEquiv.trans | [] | [
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_floor_right_pure_floor | [] | [
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Mathlib/Topology/Inseparable.lean | SeparationQuotient.inducing_mk | [] | [
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Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.toFun_eq | [] | [
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Mathlib/Data/Multiset/Basic.lean | Multiset.sub_cons | [] | [
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Mathlib/Algebra/DirectLimit.lean | Module.DirectLimit.lift_unique | [
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Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.hasEigenvalue_of_hasGeneralizedEigenvalue | [
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.coprod_comp_prod | [] | [
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Mathlib/Topology/Separation.lean | Continuous.ext_on | [] | [
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Mathlib/AlgebraicTopology/TopologicalSimplex.lean | SimplexCategory.toTopObj.ext | [] | [
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Mathlib/Data/Sign.lean | SignType.neg_one_le | [] | [
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Mathlib/Order/Heyting/Boundary.lean | Coheyting.boundary_sup_sup_boundary_inf | [] | [
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.ofMulEquivOfDom_id | [
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_mul_eq_opow_omega_mul | [
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.tendstoLocallyUniformlyOn_iff | [
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_centralizer_iff | [] | [
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Mathlib/RingTheory/Int/Basic.lean | Int.normalize_coe_nat | [] | [
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Mathlib/Algebra/Algebra/Spectrum.lean | spectrum.mem_resolventSet_iff | [] | [
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_mono | [] | [
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_sInf | [] | [
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.copy_copy | [
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Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.zero_eq_bot | [] | [
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Mathlib/Topology/SubsetProperties.lean | IsCompact.elim_finite_subcover | [] | [
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Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.liftMonoid_symm_coe | [] | [
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Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.coprodZeroIso_inv | [] | [
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Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isBoundedUnder_le_exp_comp | [] | [
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Mathlib/Algebra/Associated.lean | dvdNotUnit_of_dvdNotUnit_associated | [
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Mathlib/AlgebraicTopology/DoldKan/NCompGamma.lean | AlgebraicTopology.DoldKan.Ξβ_obj_termwise_mapMono_comp_PInfty | [
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Mathlib/Order/Bounds/Basic.lean | AntitoneOn.map_bddBelow | [] | [
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Mathlib/Topology/MetricSpace/Gluing.lean | Metric.Sigma.isometry_mk | [
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Mathlib/Data/List/MinMax.lean | List.argmin_cons | [] | [
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.addVal_le_of_coeff_ne_zero | [
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Mathlib/Order/Filter/Basic.lean | Filter.bind_def | [] | [
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Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean | MeasureTheory.tendstoInMeasure_of_tendsto_snorm | [
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Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.hom_f_injective | [
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Mathlib/Topology/UniformSpace/Basic.lean | closure_eq_inter_uniformity | [
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Mathlib/Data/Int/Parity.lean | Int.even_iff | [
{
"state_after": "no goals",
"state_before": "mβ n : β€\nxβ : Even n\nm : β€\nhm : n = m + m\nβ’ n % 2 = 0",
"tactic": "simp [β two_mul, hm]"
},
{
"state_after": "no goals",
"state_before": "m n : β€\nh : n % 2 = 0\nβ’ n % 2 + 2 * (n / 2) = n / 2 + n / 2",
"tactic": "simp [β two_mul, h]"
}
... | [
42,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
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Mathlib/LinearAlgebra/Dfinsupp.lean | Dfinsupp.coprodMap_apply_single | [
{
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282,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | DifferentiableOn.arctan | [] | [
205,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsBoundedBilinearMap.map_sub_right | [] | [
396,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.ne_zero_iff | [] | [
238,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
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Mathlib/GroupTheory/Perm/Option.lean | Equiv.optionCongr_sign | [
{
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43,
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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\ninstβ : CommMonoidWithZero Ξ±\ns : Multiset Ξ±\nh : 0 β s\ns' : Multiset Ξ±\nhs' : s = 0 ::β s'\nβ’ prod s = 0",
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285,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measure_ne_top | [] | [
3060,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3059,
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_filter_iff | [] | [
284,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/Topology/Constructions.lean | interior_pi_set | [
{
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1357,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
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Mathlib/Order/Filter/Basic.lean | Filter.comap_mono | [] | [
2162,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2161,
1
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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 | [
{
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"state_before": "R : Type u_1\ninstβ : CommRing R\nf : R[X]\nβ’ IsOpenMap β(PrimeSpectrum.comap C)",
"tactic": "rintro U β¨... | [
82,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | EMetric.exists_forall_closedBall_subset_auxβ | [
{
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74,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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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\ninstβ : LinearOrderedRing G\nh : abs x β 1\nβ’ orderOf x β€ 2\n\ncase inr\nG : Type u\nA : Type v\nx y : G\na b : A\nn m : β\ninstβ : LinearOrderedRing G\nh : abs x = 1\nβ’ orderOf x β€ 2",
"state_before": "G : Type u\nA : Type v\nx ... | [
1096,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
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Mathlib/GroupTheory/DoubleCoset.lean | Doset.right_bot_eq_right_quot | [
{
"state_after": "G : Type u_1\ninstβΒΉ : Group G\nΞ± : Type ?u.70749\ninstβ : Mul Ξ±\nJ : Subgroup G\ng : G\nH : Subgroup G\nβ’ _root_.Quotient (setoid βH.toSubmonoid ββ₯) = _root_.Quotient (QuotientGroup.rightRel H)",
"state_before": "G : Type u_1\ninstβΒΉ : Group G\nΞ± : Type ?u.70749\ninstβ : Mul Ξ±\nJ : Subgro... | [
215,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
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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\ninstβ : DecidableEq Ξ±\nsβ : Multiset Ξ±\na : Ξ±\ns : Multiset Ξ±\nh : Β¬a β s\nβ’ βcard (ndinsert a s) = βcard s + 1",
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}
] | [
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 : βm < β΅β\nhb : βn < β΅β\nβ’ β(m ^ n) < β΅β",
"state_before": "Ξ± Ξ² : Type u\na b : Cardinal\nm n : β\nha : βm < β΅β\nhb : βn < β΅β\nβ’ βm ^ βn < β΅β",
"tactic": "rw [β 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\nΞ± : Type u\nΞ² : Type ?u.63411\ninstβ : StrictOrderedSemiring Ξ±\na b c d : Ξ±\nhn : 0 < a\nhm : 1 < b\nβ’ a = a * 1",
"state_before": "Ξ± : Type u\nΞ² : Type ?u.63411\ninstβ : StrictOrderedSemiring Ξ±\na b c d : Ξ±\nhn : 0 < a\nhm : 1 < b\nβ’ 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\ninstβ : BooleanAlgebra Ξ±\na b c d : Ξ±\nβ’ a β (b β c) = b β (a β c)",
"tactic": "simp_rw [β 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",
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"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 | [
{
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403,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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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\nsβ tβ : Finset Ξ±\nf : Ξ± β Ξ²\nn : β\ninstβ : DecidableEq Ξ±\ns t : Finset Ξ±\nβ’ card (s βͺ β
) + card (s β© β
) = card s + card β
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"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 lβ lββ : List (Sigma Ξ²)\ninstβ : DecidableEq Ξ±\na : Ξ±\nlβ : List (Sigma Ξ²)\nh : Β¬a β keys []\nβ’ dlookup a (kunion [] lβ) = dlookup a lβ\n\ncase cons\nΞ± : Type u\nΞ² : Ξ± β Type v\nl lβ lββ : List (Sigma Ξ²)\ninstβ : DecidableEq Ξ±\na : Ξ±\nheadβ : Sigma Ξ²\nta... | [
763,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
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] |
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\nvβ : ΞΉ β M\ninstββΆ : Ring R\ninstββ΅ : AddCommGroup M\ninstββ΄ : AddCommGroup M'\ninstβΒ³ : AddCommGroup M''\ninstβΒ² : ... | [
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\ninstβΒ³ : Ring k\ninstβΒ² : AddCommGroup V\ninstβΒΉ : Module k V\ninstβ : AffineSpace V P\nm n : β\ns : Simplex k P m\ne : Fin (n + 1) β Fin (m + 1)\nβ’ reindex (reindex s e.symm) e = s",
"tactic": "rw [β 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\nmβ : MeasurableSpace Ξ±\nΞΌβ Ξ½ : Measure Ξ±\nm : MeasurableSpace Ξ±\nf : Ξ± ββ ββ₯0β\nΞΌ : Measure Ξ±\nβ’ (β¨ (g : Ξ± ββ ββ₯0β) (_ : βg β€ fun a => βf a), lintegral g ΞΌ) = lintegral f ΞΌ",
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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'\ninstβΒ³ : Category J\nCβ : Type u\ninstβΒ² : Category Cβ\nX Y : Cβ\nC : Type u\ninstβΒΉ : Category C\ninstβ : HasFiniteCoproducts C\nT : C\nHT : IsTerminal T\ncβ : BinaryCofan T T\nhcβ : IsColimit cβ\nH : IsVanKampenColimit cβ\nβ’ 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": "Ξ±β : Type ?u.105347\nΞ² : Type ?u.105350\nΞ³ : Type ?u.105353\nΞΉβ : Sort ?u.105356\nΞΉ' : Sort ?u.105359\nΞΉβ : Sort ?u.105362\nΞΊ : ΞΉβ β Sort ?u.105367\nΞΊβ : ΞΉβ β Sort ?u.105372\nΞΊβ : ΞΉβ 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\nsβ sβ : Set (Set Ξ©)\ninstβ : MeasurableSpace Ξ©\nΞΌ : MeasureTheory.Measure Ξ©\nh : IndepSets sβ sβ\nt1 t2 : Set Ξ©\nht1 : t1 β sβ\nht2 : t2 β sβ\nβ’ ββΞΌ (t1 β© t2) = ββΞΌ t1 * ββΞΌ t2",
"state_before": "Ξ© : Type u_1\nΞΉ : Type ?u.432097\nsβ sβ : Set (Set Ξ©)\ninstβ... | [
151,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.isLocalRingHom_expand | [
{
"state_after": "R : Type u\ninstβΒΉ : CommRing R\ninstβ : IsDomain R\np : β\nhp : 0 < p\nf : R[X]\nhf1 : IsUnit (ββ(expand R p) f)\nβ’ IsUnit f",
"state_before": "R : Type u\ninstβΒΉ : CommRing R\ninstβ : IsDomain R\np : β\nhp : 0 < p\nβ’ IsLocalRingHom β(expand R p)",
"tactic": "refine' β¨fun f hf1 => _β©"... | [
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\ninstβΒΉ : Field F\ninstβ : Field K\nΟ : F β+* K\nx y z : K\nha : P.a β 0\nh3 : roots (map Ο P) = {x, y, z}\nβ’ x β y β§ x β z β§ y β z β 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\nMβ : ΞΉ β Type vβ\nMβ : Type vβ\nMβ : Type vβ\nM' : Type v'\ninstββ· : CommSemiring R\ninstββΆ : (i : ΞΉ) β AddCommMonoid (Mβ i)\ninstββ΅ : (i : Fin (Nat.succ n)) β AddCommMonoid (M i)\ninstββ΄ : AddCommMonoid Mβ\ninstβΒ³ : (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\ninstβΒΉ : PseudoMetricSpace Ξ±\ninstβ : PseudoMetricSpace Ξ²\nhβ h : Ξ± βα΅’ Ξ²\nx : Ξ²\nr : β\nβ’ βh β»ΒΉ' Metric.sphere x r = Metric.sphere (β(IsometryEquiv.symm h) x) r",
"tactic": "rw [β 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
] |
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