file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.cg_closure_singleton | [] | [
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Mathlib/CategoryTheory/Functor/Category.lean | CategoryTheory.NatTrans.naturality_app | [] | [
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Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.ext_iff | [] | [
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Mathlib/Topology/MetricSpace/Basic.lean | closedBall_pi' | [
{
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Mathlib/ModelTheory/Definability.lean | FirstOrder.Language.DefinableSet.coe_compl | [] | [
367,
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Mathlib/Topology/Algebra/Order/MonotoneConvergence.lean | tendsto_iff_tendsto_subseq_of_monotone | [
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Mathlib/Algebra/GeomSum.lean | Nat.geom_sum_Ico_le | [
{
"state_after": "case zero\nα : Type u\nβ : Type ?u.223090\nb : ℕ\nhb : 2 ≤ b\na : ℕ\n⊢ ∑ i in Ico 1 zero, a / b ^ i ≤ a / (b - 1)\n\ncase succ\nα : Type u\nβ : Type ?u.223090\nb : ℕ\nhb : 2 ≤ b\na n : ℕ\n⊢ ∑ i in Ico 1 (succ n), a / b ^ i ≤ a / (b - 1)",
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433,
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Mathlib/Algebra/Tropical/BigOperators.lean | Multiset.trop_sum | [
{
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Mathlib/Analysis/Convex/Segment.lean | image_openSegment | [
{
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Mathlib/Algebra/MonoidAlgebra/Support.lean | MonoidAlgebra.support_single_mul_eq_image | [
{
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Nontrivial.le_infsep | [] | [
413,
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411,
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Mathlib/Analysis/Asymptotics/SuperpolynomialDecay.lean | Asymptotics.SuperpolynomialDecay.mul_polynomial | [] | [
141,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
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Mathlib/Algebra/Associated.lean | Associated.isUnit | [
{
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] | [
629,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
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Std/Data/Int/Lemmas.lean | Int.ofNat_nonneg | [] | [
604,
54
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_add_const_Iic | [
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] | [
279,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_of_ge | [
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481,
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Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.multiset_prod_X_sub_C_nextCoeff | [
{
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254,
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Mathlib/Algebra/Group/OrderSynonym.lean | toDual_inv | [] | [
124,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_ne_zero | [
{
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993,
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousOn.const_cpow | [] | [
153,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/Order/CompleteLattice.lean | iInf_extend_top | [] | [
1490,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1488,
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Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.div_add_mod | [] | [
125,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
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Std/Data/List/Basic.lean | List.bind_eq_bindTR | [
{
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"state_after": "case h.h.h.h\nα : Type u_2\nβ : Type u_1\nas : List α\nf : α → List β\n⊢ List.bind ... | [
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Mathlib/Topology/Basic.lean | interior_eq_iff_isOpen | [] | [
306,
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Mathlib/Data/List/Perm.lean | List.Perm.inter | [] | [
1018,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Std/Data/List/Lemmas.lean | List.length_singleton | [] | [
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Mathlib/Data/Finset/Sups.lean | Finset.infs_infs_infs_comm | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
389,
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Mathlib/Data/Setoid/Basic.lean | Setoid.ker_apply_mk_out | [] | [
109,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cosh_add_sinh | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh x + sinh x = exp x",
"tactic": "rw [← mul_right_inj' (two_ne_zero' ℂ), mul_add, two_cosh, two_sinh, add_add_sub_cancel, two_mul]"
}
] | [
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727,
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Mathlib/Analysis/Normed/Group/AddCircle.lean | AddCircle.norm_coe_eq_abs_iff | [
{
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},
{
"state_after": "p x : ℝ\nhp : p ≠ 0\n⊢ ∀ (p : ℝ), 0 < p → abs... | [
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhds_top' | [] | [
156,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.coe_pow | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/WithBot.lean | WithBot.map_comm | [] | [
165,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingSeminorm.ne_zero_iff | [
{
"state_after": "no goals",
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"tactic": "simp [eq_zero_iff]"
}
] | [
120,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.ext | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Interval.lean | NonemptyInterval.map₂_pure | [] | [
212,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
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Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.of_surjective | [] | [
115,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
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Mathlib/Data/Multiset/Basic.lean | Multiset.le_union_right | [] | [
1703,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1702,
1
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Mathlib/Algebra/Support.lean | Set.image_inter_mulSupport_eq | [
{
"state_after": "no goals",
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"tactic": "rw [mulSupport_comp_eq_preimage f g, image_inter_preimage]"
}
] | [
453,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
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Mathlib/Order/Ideal.lean | Order.Ideal.principal_le_iff | [] | [
302,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Filter.Eventually.isBigO | [] | [
536,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
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Mathlib/Topology/Order.lean | coinduced_mono | [] | [
428,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mul_mk'_one_eq_mk' | [
{
"state_after": "no goals",
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"tactic": "rw [mul_mk'_eq_mk'_of... | [
863,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
862,
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Mathlib/Analysis/Convex/Cone/Dual.lean | innerDualCone_union | [] | [
98,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/LocallyFinite.lean | Finset.mem_Iio | [] | [
425,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Combinatorics/SimpleGraph/IncMatrix.lean | SimpleGraph.incMatrix_mul_transpose | [
{
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Mathlib/Data/List/Zip.lean | List.unzip_revzip | [] | [
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Mathlib/Order/Interval.lean | NonemptyInterval.ext_iff | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/Count.lean | Nat.lt_of_count_lt_count | [] | [
129,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Formula.isAtomic_graph | [] | [
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36
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Mathlib/Analysis/Convex/Cone/Basic.lean | Convex.toCone_eq_sInf | [] | [
684,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_biInf_comap | [
{
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.smul_const | [] | [
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42
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Mathlib/Data/Sym/Basic.lean | Sym.sound | [] | [
200,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
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Std/Data/RBMap/Lemmas.lean | Std.RBNode.Ordered.lowerBound?_least | [
{
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301,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
298,
1
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Mathlib/Order/Heyting/Basic.lean | le_himp_iff_left | [
{
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"tactic": "rw [le_himp_iff, inf_idem]"
}
] | [
335,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
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Mathlib/Data/Set/Image.lean | Set.range_quotient_lift | [] | [
975,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
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Mathlib/LinearAlgebra/Trace.lean | LinearMap.IsProj.trace | [
{
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296,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.mulLeftRight_apply | [] | [
1134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_eq | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.326493\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q p : MvPolynomial σ R\n⊢ (Finset.sup (support p) fun s => sum s fun x e => e) = Finset.sup (support p) fun m => ↑Multiset.card (↑toMultiset m)",
"state_before": "R : Typ... | [
601,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
597,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nil_append_stream | [] | [
523,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.coe_mul | [] | [
364,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/Analysis/Convex/Segment.lean | Ioo_subset_openSegment | [] | [
509,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid.dual_iff | [] | [
1092,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1091,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_filter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.333912\nγ : Type ?u.333915\np✝ q✝ : α → Prop\ninst✝³ : DecidablePred p✝\ninst✝² : DecidablePred q✝\ns : Finset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\n⊢ _root_.Disjoint (filter p s) (filter q s) ↔ ∀ (x : α)... | [
2768,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2766,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_open_of_generateFrom | [] | [
1056,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1052,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.zero_lf_neg_iff | [
{
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"tactic": "rw [lf_neg_iff, neg_zero]"
}
] | [
1384,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1384,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_cons | [
{
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"state_before": "ctx : Context\nk : Nat\nv : Var\np : Poly\n⊢ denote ctx ((k, v) :: p) = k * Var.denote ctx v + denote ctx p",
"tactic": "match p with\n| [] => simp\n| _ :: m => simp [denote_cons]"
},
{
"state_after": "no goals",
"state_before": "ctx : Contex... | [
307,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
304,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.mem_edgeFinset | [] | [
898,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace.lean | AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nX : PresheafedSpace C\n⊢ Functor.op (IsOpenMap.functor (_ : IsOpenMap ((CategoryTheory.forget TopCat).map (Opens.inclusion ⊤)))) ⋙ X.presheaf =\n (Opens.inclusionTopIso ↑X).inv _* X.presheaf",
"state_before": "C : Type u_1\ninst✝ : Category C\nX : Presh... | [
426,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/UniqueGluing.lean | TopCat.Presheaf.isGluing_iff_eq_res | [
{
"state_after": "case mp\nC : Type u\ninst✝¹ : Category C\ninst✝ : ConcreteCategory C\nX : TopCat\nF : Presheaf (Type v) X\nι : Type v\nU : ι → Opens ↑X\nsf : piOpens F U\ns : F.obj (iSup U).op\nh : IsGluing F U ((piOpensIsoSectionsFamily F U).hom sf) s\n⊢ res F U s = sf\n\ncase mpr\nC : Type u\ninst✝¹ : Categ... | [
143,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Data/Set/Intervals/Instances.lean | Set.Ioc.coe_le_one | [] | [
281,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_and_distrib_left | [
{
"state_after": "no goals",
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"tactic": "simp only [Filter.Frequently, not_and, eventually_imp_distrib_left, not_imp]"
}
] | [
1376,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1374,
1
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Mathlib/Algebra/Lie/Basic.lean | LieEquiv.trans_apply | [] | [
652,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_sub_left | [
{
"state_after": "no goals",
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652,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.regular_of_isMulLeftInvariant | [
{
"state_after": "G : Type u_1\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : T2Space G\ninst✝⁵ : TopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : SecondCountableTopology G\nμ : Measure G\ninst✝¹ : SigmaFinite μ\ninst✝ : IsMulLeftInvariant μ\nK : Set G\nhK : IsCompact K\... | [
716,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_transpose | [
{
"state_after": "m : Type ?u.1055285\nn : Type u_1\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nM : Matrix n n R\n⊢ ∑ σ : Perm n, ↑↑(↑sign σ) * ∏ i : n, Mᵀ (↑σ i) i = ∑ σ : Perm n, ↑↑(↑sign σ) * ∏ i : n, M (↑σ i) i",
"state_before"... | [
239,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.top_mul_bot | [] | [
897,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
9
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.induction | [
{
"state_after": "α : Type u_1\nβ : Type ?u.3290795\nι : Type ?u.3290798\nE : Type u_2\nF : Type ?u.3290804\n𝕜 : Type ?u.3290807\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf✝ : α → E\np : ℝ≥0∞\nμ : Measure α\n_i : Fact (1 ≤ p)\nhp_ne_top : p ≠ ⊤\nP : { x // x ∈ Lp E p } → Prop\nh_ind :\n ∀ (c ... | [
978,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.21450\nι : Sort ?u.21453\nf✝ f₁ f₂ : Filter α\ng✝ g₁ g₂ : Set α → Filter β\nf : Filter α\ng h : Set α → Filter β\n⊢ (Filter.lift f fun x => g x ⊓ h x) = Filter.lift f g ⊓ Filter.lift f h",
"tactic": "simp only [Filter.... | [
189,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.leftMoves_ofLists | [] | [
169,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
1
] |
Mathlib/Data/Rat/Order.lean | Rat.num_nonneg_iff_zero_le | [] | [
245,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.one_ne_zero | [] | [
293,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
11
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.inv_eq_bot_iff | [] | [
219,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Algebra/Associated.lean | Associates.exists_rep | [] | [
790,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Data/Prod/PProd.lean | PProd.exists | [] | [
36,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
35,
1
] |
Mathlib/Data/Complex/Module.lean | Complex.real_algHom_eq_id_or_conj | [
{
"state_after": "case refine'_1\nf : ℂ →ₐ[ℝ] ℂ\nh : ↑f I = I\n⊢ ↑f I = ↑(AlgHom.id ℝ ℂ) I\n\ncase refine'_2\nf : ℂ →ₐ[ℝ] ℂ\nh : ↑f I = -I\n⊢ ↑f I = ↑↑conjAe I",
"state_before": "f : ℂ →ₐ[ℝ] ℂ\n⊢ f = AlgHom.id ℝ ℂ ∨ f = ↑conjAe",
"tactic": "refine'\n (eq_or_eq_neg_of_sq_eq_sq (f I) I <| by rw [← map_... | [
319,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.neg_right_iff | [] | [
1268,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1266,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Symmetric.lean | ModuleCat.MonoidalCategory.braiding_hom_apply | [] | [
84,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Computability/Ackermann.lean | ack_strictMono_left | [] | [
221,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.principal_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.231867\nι : Sort x\na : α\ns : Set α\n⊢ s ∈ 𝓟 {a} ↔ s ∈ pure a",
"tactic": "simp only [mem_pure, mem_principal, singleton_subset_iff]"
}
] | [
1987,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1986,
1
] |
Mathlib/Algebra/Group/Opposite.lean | AddMonoidHom.mul_op_ext | [] | [
663,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
658,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Order.lean | isLUB_hasSum | [] | [
89,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Logic/Nonempty.lean | Classical.nonempty_pi | [] | [
167,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.exists_fundamental_sequence | [
{
"state_after": "α : Type ?u.70717\nr : α → α → Prop\na : Ordinal\nh : ∃ o f, IsFundamentalSequence a o f\n⊢ ∃ f, IsFundamentalSequence a (ord (cof a)) f\n\ncase h\nα : Type ?u.70717\nr : α → α → Prop\na : Ordinal\n⊢ ∃ o f, IsFundamentalSequence a o f",
"state_before": "α : Type ?u.70717\nr : α → α → Prop\... | [
646,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.map_comp_obj | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Topology/Order/Basic.lean | eventually_ge_of_tendsto_gt | [] | [
377,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | mul_right_inj' | [] | [
175,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Algebra/Associated.lean | Associated.eq_zero_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.208063\nγ : Type ?u.208066\nδ : Type ?u.208069\ninst✝ : MonoidWithZero α\na b : α\nh : a ~ᵤ b\nha : a = 0\nu : αˣ\nhu : a * ↑u = b\n⊢ b = 0",
"state_before": "α : Type u_1\nβ : Type ?u.208063\nγ : Type ?u.208066\nδ : Type ?u.208069\ninst✝ : MonoidWithZero α\na b :... | [
585,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
580,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.span_of_finite | [] | [
386,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
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