file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | Ideal.IsHomogeneous.iInf₂ | [] | [
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299,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.coconePointsIsoOfNatIso_hom_desc | [
{
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.mem_normalizedFactors_eq_of_associated | [
{
"state_after": "α : Type u_1\ninst✝³ : CancelCommMonoidWithZero α\ninst✝² : DecidableEq α\ninst✝¹ : NormalizationMonoid α\ninst✝ : UniqueFactorizationMonoid α\na b c : α\nha : a ∈ normalizedFactors c\nhb : b ∈ normalizedFactors c\nh : a ~ᵤ b\n⊢ a ∣ b ∧ b ∣ a",
"state_before": "α : Type u_1\ninst✝³ : Cance... | [
774,
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770,
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Mathlib/Algebra/Order/Interval.lean | Interval.length_sub_le | [
{
"state_after": "no goals",
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"tactic": "simpa [sub_eq_add_neg] using length_add_le s (-t)"
}
] | [
717,
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Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.Integrable.of_smul | [
{
"state_after": "no goals",
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362,
46
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360,
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Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.coeff_sub_eq_neg_right_of_lt | [
{
"state_after": "no goals",
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"tactic": "rwa [sub_eq_add_neg, coeff_add_eq_right_of_lt, coeff_neg]"
}
] | [
316,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_bot | [] | [
670,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
669,
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Mathlib/CategoryTheory/Sites/CoverLifting.lean | CategoryTheory.RanIsSheafOfCoverLifting.getSection_commute | [
{
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201,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
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Mathlib/Topology/Separation.lean | t1Space_iff_disjoint_pure_nhds | [] | [
512,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
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Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.prev | [] | [
147,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.T_add | [
{
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"tactic": "simp [T, single_mul_single]"
}
] | [
180,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
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Mathlib/Data/Fintype/Basic.lean | Set.toFinset_union | [
{
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705,
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703,
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Mathlib/Analysis/Calculus/FDerivMeasurable.lean | ContinuousLinearMap.measurable_apply₂ | [] | [
95,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/GroupPower/Lemmas.lean | zpow_bit1 | [
{
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] | [
266,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
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Mathlib/MeasureTheory/Decomposition/Lebesgue.lean | MeasureTheory.SignedMeasure.rnDeriv_add | [
{
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1177,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
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Mathlib/Algebra/Hom/Aut.lean | AddAut.one_def | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
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Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbs.mono_right | [] | [
82,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/Deriv/Linear.lean | ContinuousLinearMap.hasDerivAtFilter | [] | [
53,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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11
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycle_swap_mul_aux₂ | [
{
"state_after": "ι : Type ?u.676454\nα✝ : Type ?u.676457\nβ : Type ?u.676460\nf g : Perm α✝\nx y : α✝\ninst✝² : DecidableEq α✝\ninst✝¹ : Fintype α✝\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℤ\n⊢ ∀ {b x : α} {f : Perm α},\n ↑(swap x (↑f x) * f) b ≠ b → ↑(f ^ n) (↑f x) = b → ∃ i, ↑((swap x (↑f x) * f) ^ i) (↑... | [
495,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
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Mathlib/Data/Fintype/Card.lean | Function.Embedding.nonempty_of_card_le | [
{
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"tactic": "classical exact (truncOfCardLe h).nonempty"
},
{
"state_after": "no goals",
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798,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.vars_one | [] | [
369,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
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Mathlib/NumberTheory/FermatPsp.lean | FermatPsp.psp_from_prime_gt_p | [
{
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"tactic": "unfold psp_from_pri... | [
348,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
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Std/Data/List/Lemmas.lean | List.singleton_disjoint | [
{
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}
] | [
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] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
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Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.map_perm | [
{
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714,
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707,
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Mathlib/Analysis/Convex/Strict.lean | Set.Subsingleton.strictConvex | [] | [
128,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
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Mathlib/Algebra/Order/Field/Basic.lean | inv_pow_anti | [] | [
648,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/Holder.lean | holderOnWith_one | [
{
"state_after": "no goals",
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"tactic": "simp only [HolderOnWith, Li... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/FiniteType.lean | Algebra.FiniteType.isNoetherianRing | [
{
"state_after": "case intro\nR✝ : Type ?u.65970\nA : Type u\nB : Type ?u.65961\nM : Type ?u.65964\nN : Type ?u.65967\ninst✝¹² : CommRing R✝\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Algebra R✝ A\ninst✝⁹ : CommRing B\ninst✝⁸ : Algebra R✝ B\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R✝ M\ninst✝⁵ : AddCommGroup N\ninst✝⁴ :... | [
179,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Combinatorics/SimpleGraph/Clique.lean | SimpleGraph.cliqueFinset_eq_empty_iff | [
{
"state_after": "no goals",
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"tactic": "simp_rw [CliqueFree, eq_empty_iff_forall_not_mem, mem_cliqueFinset... | [
298,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
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Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.mkSpanSingleton_apply | [] | [
187,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
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Std/Data/Nat/Lemmas.lean | Nat.mod_eq_zero_of_dvd | [
{
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},
{
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724,
41
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src/lean/Init/Control/Lawful.lean | ReaderT.run_monadLift | [] | [
196,
73
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.suppPreservation_iff_liftpPreservation | [
{
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"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\n⊢ SuppPreser... | [
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24
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713,
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Mathlib/CategoryTheory/Functor/Flat.lean | CategoryTheory.cofiltered_of_hasFiniteLimits | [] | [
186,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.hasColimit_of_equivalence_comp | [
{
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"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Type u₂\nins... | [
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49
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1079,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_equiv_top | [] | [
956,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
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Mathlib/Topology/Covering.lean | IsCoveringMapOn.continuousOn | [] | [
104,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
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Mathlib/Data/Set/Finite.lean | Set.Finite.subset | [
{
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"tactic": "cases hs"
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{
... | [
763,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
760,
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Mathlib/Data/Multiset/Bind.lean | Multiset.mem_join | [
{
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},
{
"state_after": "no goals",
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Mathlib/Analysis/Calculus/FDeriv/Basic.lean | HasFDerivAt.continuousAt | [] | [
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42
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Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.int_cast_im | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_le_iff_coeff_zero | [
{
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"tactic": "simp only [degree, Finset.max, Finset.sup_le_iff, mem_support_iff, Ne.... | [
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36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Basic.lean | IsOpen.inter_frontier_eq | [
{
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"tactic": "rw [hs.frontier_eq, inter_diff_self]"
}
] | [
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39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
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Mathlib/Geometry/Manifold/ChartedSpace.lean | chartedSpaceSelf_atlas | [] | [
531,
10
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529,
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_basis_open | [] | [
91,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Chain.lean | chainClosure_empty | [
{
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"tactic": "have : Cha... | [
207,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_eq_iSup_iInf_of_nat' | [] | [
763,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
762,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mem_graph_iff | [
{
"state_after": "case mk\nα : Type u_1\nβ : Type ?u.1790\nγ : Type ?u.1793\nι : Type ?u.1796\nM : Type u_2\nM' : Type ?u.1802\nN : Type ?u.1805\nP : Type ?u.1808\nG : Type ?u.1811\nH : Type ?u.1814\nR : Type ?u.1817\nS : Type ?u.1820\ninst✝ : Zero M\nf : α →₀ M\nfst✝ : α\nsnd✝ : M\n⊢ (fst✝, snd✝) ∈ graph f ↔ ↑... | [
83,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Data/Complex/Exponential.lean | Real.exp_approx_succ | [
{
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1785,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1775,
1
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Mathlib/Algebra/GroupPower/Order.lean | min_lt_of_mul_lt_sq | [
{
"state_after": "no goals",
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305,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
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Mathlib/Algebra/Algebra/Tower.lean | Algebra.lsmul_coe | [] | [
57,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_le_of_le | [] | [
760,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
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Mathlib/Data/Set/Lattice.lean | Set.biUnion_and | [
{
"state_after": "no goals",
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810,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
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Mathlib/Analysis/Complex/Conformal.lean | isConformalMap_complex_linear | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℂ E\nz : ℂ\ng : ℂ →L[ℝ] E\nf : ℂ → E\nmap : ℂ →L[ℂ] E\nnonzero : map ≠ 0\nminor₁ : ‖↑map 1‖ ≠ 0\n⊢ IsConformalMap (restrictScalars ℝ map)",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup ... | [
67,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
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Mathlib/LinearAlgebra/Matrix/Dual.lean | Matrix.toLin_transpose | [
{
"state_after": "case a\nK : Type u_3\nV₁ : Type u_4\nV₂ : Type u_5\nι₁ : Type u_1\nι₂ : Type u_2\ninst✝⁸ : Field K\ninst✝⁷ : AddCommGroup V₁\ninst✝⁶ : Module K V₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module K V₂\ninst✝³ : Fintype ι₁\ninst✝² : Fintype ι₂\ninst✝¹ : DecidableEq ι₁\ninst✝ : DecidableEq ι₂\nB₁ : Ba... | [
47,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.ret_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\na : α\nf : α → WSeq β\n⊢ bind (ret a) f ~ʷ f a",
"tactic": "simp [bind]"
}
] | [
1743,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1743,
1
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Mathlib/Algebra/Group/UniqueProds.lean | UniqueMul.mulHom_image_iff | [
{
"state_after": "case refine'_1\nG : Type u_2\nH : Type u_1\ninst✝² : Mul G\ninst✝¹ : Mul H\nA B : Finset G\na0 b0 : G\ninst✝ : DecidableEq H\nf : G →ₙ* H\nhf : Function.Injective ↑f\nh : UniqueMul (Finset.image (↑f) A) (Finset.image (↑f) B) (↑f a0) (↑f b0)\n⊢ UniqueMul A B a0 b0\n\ncase refine'_2\nG : Type u_... | [
143,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Analysis/Complex/Basic.lean | Complex.dist_of_im_eq | [
{
"state_after": "no goals",
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"tactic": "rw [dist_eq_re_im, h, sub_self, zero_pow two_pos, add_zero, Real.sqrt_sq_eq_abs, Real.dist_eq]"
}
] | [
119,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/Computability/TuringMachine.lean | Turing.Tape.mk'_right | [] | [
564,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.nhdsWithin_basis_closed_eball | [] | [
645,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
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Mathlib/Algebra/Lie/OfAssociative.lean | LinearEquiv.lieConj_apply | [] | [
334,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
333,
1
] |
Mathlib/Topology/Inseparable.lean | SeparationQuotient.continuousWithinAt_lift₂ | [] | [
619,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
9
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | ciSup_pos | [] | [
861,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
860,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Real.isLittleO_one_exp_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx y z : ℝ\nl : Filter α\nf : α → ℝ\n⊢ ((fun x => 1) =o[l] fun x => exp (f x)) ↔ Tendsto f l atTop",
"tactic": "simp only [← exp_zero, isLittleO_exp_comp_exp_comp, sub_zero]"
}
] | [
393,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_sdiff_sup_sdiff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.31125\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\n⊢ z \\ (x \\ y ⊔ y \\ x) = (z \\ x ⊔ z ⊓ x ⊓ y) ⊓ (z \\ y ⊔ z ⊓ y ⊓ x)",
"tactic": "rw [sdiff_sup, sdiff_sdiff_right, sdiff_sdiff_right]"
},
{
"state_after": "no goals",... | [
411,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.rec_add_one | [] | [
385,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.cons_cons_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nL L₁ L₂ L₃ L₄ : List (α × Bool)\n⊢ ∀ {p : α × Bool}, Step (p :: L₁) (p :: L₂) ↔ Step L₁ L₂",
"tactic": "simp (config := { contextual := true }) [Step.cons_left_iff, iff_def, or_imp]"
}
] | [
188,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
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Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.rootMultiplicity_add | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\na : R\nhzero : p + q ≠ 0\n⊢ (X - ↑C a) ^ min (rootMultiplicity a p) (rootMultiplicity a q) ∣ p + q",
"state_before": "R : Type u\nS : Type v\nT : Type w\na✝ b : R\nn : ℕ\ninst✝ : CommRing R\np q : R[X]\na ... | [
395,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | LinearMap.splittingOfFinsuppSurjective_splits | [
{
"state_after": "R : Type u_1\nM : Type u_2\nN : Type ?u.770436\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\nα : Type u_3\nf : M →ₗ[R] α →₀ R\ns : Surjective ↑f\nx y : α\n⊢ ↑(↑(comp (comp f (splittingOfFinsuppSurjective f s)) (lsingle x)) 1)... | [
1229,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1221,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_mul | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b✝ c a b : α\n⊢ a * b = abs a * abs b ∨ a * b = -(abs a * abs b)",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedRing α\na✝ b✝ c a b : α\n⊢ abs (a * b) = abs a * abs b",
"tactic": "rw [abs_eq (mul_nonneg (abs_nonneg a) (abs_nonneg b))... | [
40,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_smul_vadd_smul_vadd_of_nonpos_of_nonneg | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.554527\nP : Type u_3\nP' : Type ?u.554533\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx : P\nv : V\nr₁ r₂ : R\nhr₁ : r₁ ≤ 0\nhr₂ : 0 ≤ r₂\n⊢ Wbtw R (r₁ • v +ᵥ x) x ... | [
799,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Order/Hom/Lattice.lean | SupHom.symm_dual_comp | [] | [
1396,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1393,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_comp | [
{
"state_after": "case h\nM : Type u_1\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_3\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\nx✝ : M\n⊢ ↑(MonoidHom.comp (lift f hg) (toMap f)) x✝ = ↑g x✝",
"state_bef... | [
1023,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
1
] |
Mathlib/GroupTheory/Submonoid/Inverses.lean | Submonoid.leftInvEquiv_mul | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝ : CommMonoid M\nS : Submonoid M\nhS : S ≤ IsUnit.submonoid M\nx : { x // x ∈ leftInv S }\n⊢ ↑(↑(leftInvEquiv S hS) x) * ↑x = 1",
"tactic": "simpa only [leftInvEquiv_apply, fromCommLeftInv] using fromLeftInv_mul S x"
}
] | [
198,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Finmap.lean | Finmap.not_mem_erase_self | [
{
"state_after": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : Finmap β\n⊢ a = a ∨ ¬a ∈ s",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\ns : Finmap β\n⊢ ¬a ∈ erase a s",
"tactic": "rw [mem_erase, not_and_or, not_not]"
},
{
"state_after": "case h\nα ... | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter_union_of_antitone | [] | [
606,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Analysis/Complex/UnitDisc/Basic.lean | Complex.UnitDisc.re_conj | [] | [
238,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Logic/Equiv/Option.lean | Equiv.optionSubtype_symm_apply_apply_none | [] | [
260,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Order/Lattice.lean | le_antisymm' | [] | [
71,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/RingTheory/Subring/Pointwise.lean | Subring.pointwise_smul_toSubsemiring | [] | [
74,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.coe_max | [] | [
581,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/Analysis/Calculus/FDerivAnalytic.lean | HasFPowerSeriesAt.hasFDerivAt | [] | [
49,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/GroupTheory/Coset.lean | leftCoset_eq_iff | [
{
"state_after": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\nx y : α\n⊢ (∀ (x_1 : α), x_1 ∈ x *l ↑s ↔ x_1 ∈ y *l ↑s) ↔ x⁻¹ * y ∈ s",
"state_before": "α : Type u_1\ninst✝ : Group α\ns : Subgroup α\nx y : α\n⊢ x *l ↑s = y *l ↑s ↔ x⁻¹ * y ∈ s",
"tactic": "rw [Set.ext_iff]"
},
{
"state_after": "... | [
283,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.coe_prod | [] | [
347,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.nonempty_iso_refl | [] | [
150,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_indicator | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.1768900\nγ : Type ?u.1768903\nδ : Type ?u.1768906\nm : MeasurableSpace α\nμ ν : Measure α\ns : Set α\nhs : MeasurableSet s\nf : α → ℝ≥0∞\nt : Set α\nht : MeasurableSet t\n⊢ ↑↑(withDensity μ (indicator s f)) t = ↑↑(withDensity (Measure.restrict μ s) f) t",
... | [
1640,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1636,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.teichmuller_coeff_pos | [] | [
120,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.id_comp | [] | [
246,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Init/CcLemmas.lean | ne_of_eq_of_ne | [] | [
119,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Algebra/Star/Basic.lean | star_neg | [] | [
296,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_add_left' | [] | [
742,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_ceil_atTop | [] | [
46,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.gcd_singleton | [] | [
179,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/Order/Pointwise.lean | LinearOrderedField.smul_Ioi | [
{
"state_after": "case h\nα : Type ?u.61362\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\nx : K\n⊢ x ∈ r • Ioi a ↔ x ∈ Ioi (r • a)",
"state_before": "α : Type ?u.61362\nK : Type u_1\ninst✝ : LinearOrderedField K\na b r : K\nhr : 0 < r\n⊢ r • Ioi a = Ioi (r • a)",
"tactic": "ext x"
... | [
254,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Nat.sum_four_squares_of_two_mul_sum_four_squares | [
{
"state_after": "m a b c d : ℤ\nh : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * m\nthis :\n ∀ (f : Fin 4 → ZMod 2),\n f 0 ^ 2 + f 1 ^ 2 + f 2 ^ 2 + f 3 ^ 2 = 0 →\n ∃ i, f i ^ 2 + f (↑(swap i 0) 1) ^ 2 = 0 ∧ f (↑(swap i 0) 2) ^ 2 + f (↑(swap i 0) 3) ^ 2 = 0\n⊢ ∃ w x y z, w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 = m",
... | [
143,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
9
] |
Mathlib/MeasureTheory/Function/UniformIntegrable.lean | MeasureTheory.Memℒp.snormEssSup_indicator_norm_ge_eq_zero | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.92822\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\np : ℝ≥0∞\nf : α → β\nhf : Memℒp f ⊤\nhmeas : StronglyMeasurable f\nhbdd : snormEssSup f μ < ⊤\n⊢ ∃ M, snormEssSup (Set.indicator {x | M ≤ ↑‖f x‖₊} f) μ = 0",
"state_before": "... | [
257,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Data/Finset/Basic.lean | Multiset.toFinset_bind_dedup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.453885\ninst✝¹ : DecidableEq α\ns t : Multiset α\ninst✝ : DecidableEq β\nm : Multiset α\nf : α → Multiset β\n⊢ toFinset (bind (dedup m) f) = toFinset (bind m f)",
"tactic": "simp_rw [toFinset, dedup_bind_dedup]"
}
] | [
3203,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3202,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.to_inf_right | [] | [
281,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_sub_self | [] | [
869,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
868,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.odd_iff_not_even | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ Odd n ↔ ¬Even n",
"tactic": "rw [not_even_iff, odd_iff]"
}
] | [
64,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
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