file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.disjoint_ndinsert_left | [
{
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}
] | [
126,
52
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124,
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Mathlib/Data/List/TFAE.lean | List.tfae_singleton | [
{
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}
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37,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Constructions.lean | Continuous.comp₂ | [] | [
417,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
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Mathlib/Topology/Instances/NNReal.lean | NNReal.summable_nat_add_iff | [
{
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"tactic": "rw [← summable_coe, ← summable_coe]"
},
{
"state_after": "no ... | [
215,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
8
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Mathlib/FieldTheory/Separable.lean | Polynomial.separable_gcd_left | [] | [
102,
57
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100,
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.domCongr_symm | [] | [
1761,
28
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1759,
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Mathlib/Data/Set/Image.lean | Set.compl_compl_image | [
{
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"tactic": "rw [← image_comp, compl_comp_compl, image_id]"
}
] | [
385,
48
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383,
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Mathlib/Data/List/Zip.lean | List.lt_length_left_of_zipWith | [
{
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearEquiv.antilipschitz | [] | [
1945,
46
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1943,
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Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_pow | [] | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
342,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_bot | [] | [
1536,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1535,
1
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Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bit0_val | [
{
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}
] | [
157,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.h_apply_fromCoset' | [] | [
277,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
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Mathlib/Algebra/Group/Basic.lean | mul_mul_div_cancel | [
{
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"tactic": "rw [mul_assoc, mul_div_cancel'_right]"
}
] | [
989,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
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Mathlib/Algebra/GroupPower/Basic.lean | one_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.9049\nM : Type u\nN : Type v\nG : Type w\nH : Type x\nA : Type y\nB : Type z\nR : Type u₁\nS : Type u₂\ninst✝¹ : Monoid M\ninst✝ : AddMonoid A\na : A\n⊢ 1 • a = a",
"tactic": "rw [succ_nsmul, zero_nsmul, add_zero]"
}
] | [
82,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Algebra/Hom/Group.lean | MonoidWithZeroHom.comp_apply | [] | [
1130,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1129,
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Mathlib/Data/Set/Finite.lean | Set.infinite_of_injOn_mapsTo | [] | [
1363,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1361,
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Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean | MeasureTheory.integrable_comp_mul_right_iff | [
{
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"tactic": "simpa only [mul_comm] using integrable_comp_mul_left_iff g hR"
}
] | [
173,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
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Mathlib/Data/Complex/Module.lean | rank_real_of_complex | [
{
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"state_before": "E : Type u_1\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℂ E\n⊢ Cardinal.lift (Module.rank ℝ E) = Cardinal.lift (2 * Module.rank ℂ E)",
... | [
240,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.coinduction | [] | [
422,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
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] |
Mathlib/Combinatorics/SimpleGraph/DegreeSum.lean | SimpleGraph.dart_fst_fiber_card_eq_degree | [
{
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"tactic": "simpa only [dart_fst_fiber, Finset.card_univ, card_ne... | [
75,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.trace_comp_comm' | [
{
"state_after": "R : Type u_1\ninst✝⁹ : CommRing R\nM : Type u_2\ninst✝⁸ : AddCommGroup M\ninst✝⁷ : Module R M\nN : Type u_3\ninst✝⁶ : AddCommGroup N\ninst✝⁵ : Module R N\nι : Type ?u.726554\ninst✝⁴ : Module.Free R M\ninst✝³ : Module.Finite R M\ninst✝² : Module.Free R N\ninst✝¹ : Module.Finite R N\ninst✝ : Non... | [
284,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
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Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.WF.combine | [] | [
251,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
247,
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Mathlib/Data/Set/Finite.lean | Set.card_fintypeInsertOfNotMem | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\na : α\ns : Set α\ninst✝ : Fintype ↑s\nh : ¬a ∈ s\n⊢ Finset.card { val := a ::ₘ (toFinset s).val, nodup := (_ : Multiset.Nodup (a ::ₘ (toFinset s).val)) } =\n Fintype.card ↑s + 1",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Ty... | [
1204,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1199,
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Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearEquiv.unitsEquivAut_symm_apply | [] | [
2383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2382,
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Mathlib/Order/Hom/CompleteLattice.lean | sInfHom.cancel_left | [
{
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494,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
492,
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.id_apply | [] | [
735,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
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Mathlib/RingTheory/Algebraic.lean | IsIntegralClosure.exists_smul_eq_mul | [
{
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335,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
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Mathlib/Data/Rat/Defs.lean | Rat.mkRat_eq_div | [
{
"state_after": "a b c : ℚ\nn : ℤ\nd : ℕ\n⊢ (if h : d = 0 then 0 else normalize n d) = ↑n / ↑d",
"state_before": "a b c : ℚ\nn : ℤ\nd : ℕ\n⊢ mkRat n d = ↑n / ↑d",
"tactic": "simp [mkRat]"
},
{
"state_after": "case pos\na b c : ℚ\nn : ℤ\nd : ℕ\nh : d = 0\n⊢ (if h : d = 0 then 0 else normalize n ... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
550,
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Mathlib/Data/Int/GCD.lean | Nat.xgcd_aux_rec | [
{
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64,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.mem_withConstants | [] | [
755,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
754,
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Mathlib/Deprecated/Subfield.lean | IsSubfield.pow_mem | [
{
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"state_before": "F ... | [
55,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Real/Sign.lean | Real.sign_of_neg | [
{
"state_after": "no goals",
"state_before": "r : ℝ\nhr : r < 0\n⊢ sign r = -1",
"tactic": "rw [sign, if_pos hr]"
}
] | [
39,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
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] |
Mathlib/Data/Bool/Basic.lean | Bool.not_false' | [] | [
79,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Set/Image.lean | Set.range_eq_empty | [] | [
753,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
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] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.card_add | [] | [
911,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
910,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.dart_edge_eq_mk'_iff | [
{
"state_after": "case mk\nι : Sort ?u.98474\n𝕜 : Type ?u.98477\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v w : V\ne : Sym2 V\np : V × V\nh : Adj G p.fst p.snd\n⊢ ∀ {p_1 : V × V},\n Dart.edge { toProd := p, is_adj := h } = Quotient.mk (Sym2.Rel.setoid V) p_1 ↔\n ... | [
782,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
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Mathlib/GroupTheory/GroupAction/SubMulAction.lean | SubMulAction.val_smul_of_tower | [] | [
261,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
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Mathlib/Order/Filter/Cofinite.lean | Filter.mem_cofinite | [] | [
44,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivary_id_iff | [] | [
300,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
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] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_injective | [
{
"state_after": "no goals",
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"tactic": "rw [... | [
823,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
822,
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] |
Mathlib/Data/List/BigOperators/Basic.lean | List.headI_le_sum | [] | [
608,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.iff_comp_neg | [
{
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343,
71
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Mathlib/Data/Sym/Basic.lean | Sym.cons_erase | [] | [
225,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Combinatorics/SimpleGraph/Density.lean | Rel.swap_mem_interedges_iff | [
{
"state_after": "𝕜 : Type ?u.102463\nι : Type ?u.102466\nκ : Type ?u.102469\nα : Type u_1\nβ : Type ?u.102475\nr : α → α → Prop\ninst✝ : DecidableRel r\ns s₁ s₂ t t₁ t₂ : Finset α\na b : α\nhr : Symmetric r\nx : α × α\n⊢ (Prod.swap x).fst ∈ s ∧ (Prod.swap x).snd ∈ t ∧ r (Prod.swap x).snd (Prod.swap x).fst ↔\n... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.carrier_eq_coe | [] | [
464,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
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Mathlib/Analysis/InnerProductSpace/l2Space.lean | OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single | [
{
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254,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
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Mathlib/CategoryTheory/Limits/Shapes/WidePullbacks.lean | CategoryTheory.Limits.hasWidePullbacks_shrink | [] | [
555,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
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Mathlib/Topology/Algebra/OpenSubgroup.lean | OpenSubgroup.toSubgroup_prod | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_comp_rTensor | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1273862\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1273868\ninst✝¹² : Semiring R''\nM : Type u_2\nN : Type u_4\nP : Type u_3\nQ : Type u_5\nS : Type ?u.1273886\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ni... | [
1119,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1117,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.coe_inv | [] | [
491,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderiv_sub_const | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.523964\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
595,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Tactic/NormNum/Prime.lean | Mathlib.Meta.NormNum.MinFacHelper.one_lt | [
{
"state_after": "n k : ℕ\nh : MinFacHelper n k\nthis : 2 < minFac n\n⊢ 1 < n",
"state_before": "n k : ℕ\nh : MinFacHelper n k\n⊢ 1 < n",
"tactic": "have : 2 < minFac n := h.1.trans_le h.2.2"
},
{
"state_after": "case inl\nk : ℕ\nh : MinFacHelper 0 k\nthis : 2 < minFac 0\n⊢ 1 < 0\n\ncase inr\nn ... | [
60,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Combinatorics/HalesJewett.lean | Combinatorics.Line.apply_none | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nι : Type u_2\nl : Line α ι\nx : α\ni : ι\nh : idxFun l i = none\n⊢ (fun x i => Option.getD (idxFun l i) x) x i = x",
"tactic": "simp only [Option.getD_none, h, l.apply]"
}
] | [
186,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Finset/Slice.lean | Set.Sized.subsingleton | [] | [
82,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
11
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_eq | [
{
"state_after": "α : Type u\ninst✝ : DivisionRing α\nx : α\nh : x ≠ 1\nn : ℕ\nthis : x - 1 ≠ 0\n⊢ ∑ i in range n, x ^ i = (x ^ n - 1) / (x - 1)",
"state_before": "α : Type u\ninst✝ : DivisionRing α\nx : α\nh : x ≠ 1\nn : ℕ\n⊢ ∑ i in range n, x ^ i = (x ^ n - 1) / (x - 1)",
"tactic": "have : x - 1 ≠ 0 :... | [
269,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/ContinuousFunction/StoneWeierstrass.lean | ContinuousMap.inf_mem_subalgebra_closure | [
{
"state_after": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ C(X, ℝ)\nf g : { x // x ∈ A }\n⊢ 2⁻¹ • (↑f + ↑g - Abs.abs (↑f - ↑g)) ∈ Subalgebra.topologicalClosure A",
"state_before": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\nA : Subalgebra ℝ ... | [
132,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | fderiv_add_const | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.231390\ninst✝³ : NormedAddCommGroup G\ninst✝² : Normed... | [
249,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.transpose_mem_iff | [
{
"state_after": "no goals",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : Fintype l\ninst✝ : CommRing R\nA : Matrix (l ⊕ l) (l ⊕ l) R\nhA : Aᵀ ∈ symplecticGroup l R\n⊢ A ∈ symplecticGroup l R",
"tactic": "simpa using transpose_mem hA"
}
] | [
178,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.card_le_mul_card_image | [] | [
296,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.mem_bind | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nq : Semiquot α\nf : α → Semiquot β\nb : β\n⊢ b ∈ bind q f ↔ ∃ a _h, b ∈ f a",
"state_before": "α : Type u_1\nβ : Type u_2\nq : Semiquot α\nf : α → Semiquot β\nb : β\n⊢ b ∈ bind q f ↔ ∃ a, a ∈ q ∧ b ∈ f a",
"tactic": "simp_rw [← exists_prop]"
},
{
"st... | [
144,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearEquiv.toSpanNonzeroSingleton_coord | [] | [
321,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/NumberTheory/RamificationInertia.lean | Ideal.inertiaDeg_algebraMap | [
{
"state_after": "R : Type u\ninst✝⁴ : CommRing R\nS : Type v\ninst✝³ : CommRing S\nf : R →+* S\np : Ideal R\nP : Ideal S\ninst✝² : Algebra R S\ninst✝¹ : Algebra (R ⧸ p) (S ⧸ P)\ninst✝ : IsScalarTower R (R ⧸ p) (S ⧸ P)\nhp : IsMaximal p\n✝ : Nontrivial (S ⧸ P)\n⊢ inertiaDeg (algebraMap R S) p P = finrank (R ⧸ p... | [
222,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.comp_assoc | [] | [
1137,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.extension_comp_coe | [] | [
573,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Algebra/Field/Basic.lean | one_add_div | [] | [
47,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_mul_apply | [] | [
1183,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1182,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_unit_singleton | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.635187\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E\ninst✝ : CompleteSpace { x // x ∈ K }\nv : E\nhv : ‖v‖ = 1\nw : E\n⊢ ↑(↑(orthog... | [
608,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
605,
1
] |
Std/Data/List/Basic.lean | List.scanl_eq_scanlTR | [
{
"state_after": "case h.h.h.h\nα : Type u_2\nf : Type u_1\nn : α → f → α\nl : α\n⊢ scanl n l = scanlTR n l",
"state_before": "⊢ @scanl = @scanlTR",
"tactic": "funext α f n l"
},
{
"state_after": "no goals",
"state_before": "case h.h.h.h\nα : Type u_2\nf : Type u_1\nn : α → f → α\nl : α\n⊢ s... | [
645,
48
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
644,
10
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.congr_arg | [] | [
194,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
11
] |
Std/Data/List/Lemmas.lean | List.get_of_append_proof | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl₁ : List α\na : α\nl₂ : List α\nn : Nat\nl : List α\neq : l = l₁ ++ a :: l₂\nh : length l₁ = n\n⊢ length l₁ < length (l₁ ++ a :: l₂)",
"tactic": "simp_arith"
}
] | [
610,
90
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
609,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | mem_integralClosure_iff_mem_FG | [] | [
562,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.HasFiniteIntegral.mono' | [] | [
151,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Order/Basic.lean | Pi.sdiff_def | [] | [
909,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_pow | [] | [
299,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Algebra/Hom/Freiman.lean | FreimanHom.coe_mk | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/Compare.lean | Eq.cmp_eq_eq' | [] | [
281,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.range_add | [
{
"state_after": "α : Type ?u.108255\nβ : Type ?u.108258\nγ : Type ?u.108261\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na✝ : α\nb✝ c : β\na b : ℕ\n⊢ (range (a + b)).val = (range a).val ∪ (map (addLeftEmbedding a) (range b)).val",
"state_before": "α : Type ?u.108255\nβ : Type ?u.108258\... | [
581,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_eq_toReal_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.33209\nβ : Type ?u.33212\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y : ℝ≥0∞\nhx : x ≠ ⊤\nhy : y ≠ ⊤\n⊢ ENNReal.toReal x = ENNReal.toReal y ↔ x = y",
"tactic": "simp only [ENNReal.toReal, NNReal.coe_eq, toNNReal_eq_toNNReal_iff' hx hy]"
}
] | [
395,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Equicontinuous.comp | [] | [
199,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Symmetric.lean | ModuleCat.MonoidalCategory.hexagon_forward | [
{
"state_after": "case H\nR : Type u\ninst✝ : CommRing R\nX Y Z : ModuleCat R\n⊢ ∀ (x : ↑X) (y : ↑Y) (z : ↑Z),\n ↑((α_ X Y Z).hom ≫ (braiding X (Y ⊗ Z)).hom ≫ (α_ Y Z X).hom) ((x ⊗ₜ[R] y) ⊗ₜ[R] z) =\n ↑(((braiding X Y).hom ⊗ 𝟙 Z) ≫ (α_ Y X Z).hom ≫ (𝟙 Y ⊗ (braiding X Z).hom)) ((x ⊗ₜ[R] y) ⊗ₜ[R] z)",
... | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Std/Data/String/Lemmas.lean | String.Pos.ne_of_gt | [] | [
123,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
123,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.lt_of_div_lt_div | [] | [
629,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Algebra/Group/Prod.lean | MulHom.fst_comp_prod | [] | [
360,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.swap_swap_eq | [] | [
355,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Algebra/Order/Floor.lean | abs_sub_round_eq_min | [
{
"state_after": "F : Type ?u.259084\nα : Type u_1\nβ : Type ?u.259090\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nx : α\n⊢ abs (x - ↑(if fract x < 1 - fract x then ⌊x⌋ else ⌈x⌉)) = if fract x < 1 - fract x then fract x else 1 - fract x",
"state_before": "F : Type ?u.259084\nα : Type u_1\nβ : Type ?... | [
1408,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Std/Data/Int/DivMod.lean | Int.fdiv_add_fmod | [] | [
317,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
316,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | UniformContinuous.nndist | [] | [
1841,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1839,
11
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_mul | [] | [
449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | gauge_lt_one_eq_self_of_open | [
{
"state_after": "𝕜 : Type ?u.194308\nE : Type u_1\nF : Type ?u.194314\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\na : ℝ\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousSMul ℝ E\nhs₁ : Convex ℝ s\nhs₀ : 0 ∈ s\nhs₂ : IsOpen s\n⊢ s ⊆ {x | gauge s x < 1}",
"state_before": "𝕜 : Type ?u.194308\... | [
358,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.prod_eq_one_iff | [
{
"state_after": "ι : Type ?u.6108\nα : Type ?u.6111\nM : Type u_1\nN : Type ?u.6117\nP : Type ?u.6120\nM₀ : Type ?u.6123\nG : Type ?u.6126\nR : Type ?u.6129\ninst✝ : CanonicallyOrderedMonoid M\nl : List M\nh : ∀ (x : M), x ∈ l → x = 1\n⊢ ℕ\n\nι : Type ?u.6108\nα : Type ?u.6111\nM : Type u_1\nN : Type ?u.6117\n... | [
61,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_nonempty | [] | [
492,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.intersecting_empty | [] | [
60,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Order/Group/Bounds.lean | IsLUB.exists_between_sub_self | [] | [
31,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.mono | [] | [
125,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_and | [] | [
1324,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1323,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.restrict_subset | [] | [
445,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
] |
Mathlib/Topology/Bases.lean | TopologicalSpace.IsTopologicalBasis.open_iff_eq_sUnion | [] | [
203,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/RingTheory/Adjoin/Tower.lean | fg_of_fg_of_fg | [] | [
171,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Analysis/Convex/Independent.lean | Function.Injective.convexIndependent_iff_set | [] | [
122,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
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