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/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_of_ne | [] | [
1388,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1386,
1
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Mathlib/Topology/SubsetProperties.lean | IsPreirreducible.open_subset | [] | [
1980,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1977,
1
] |
Mathlib/Order/Max.lean | Prod.isMax_iff | [] | [
460,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.one_le_pow | [
{
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"state_before": "n m : ℕ\nh : 0 < m\n⊢ 1 ≤ m ^ n",
"tactic": "rw [← one_pow n]"
},
{
"state_after": "no goals",
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"tactic": "exact Nat.pow_le_pow_of_le_left h n"
}
] | [
61,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Group/Units.lean | Units.mul_inv | [] | [
269,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
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Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_subsingleton_apply | [
{
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... | [
146,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
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Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimit_toDual_iff | [
{
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}
] | [
265,
34
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264,
1
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Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.acc_zero | [] | [
117,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | norm_add_sq | [
{
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1034,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.op_norm_zero_iff | [
{
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396,
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391,
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Mathlib/Algebra/Order/Floor.lean | Int.floorRing_floor_eq | [] | [
636,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_single | [] | [
1789,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1787,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.natDegree_map_eq_of_injective | [] | [
338,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
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Mathlib/Combinatorics/Quiver/Symmetric.lean | Quiver.reverse_reverse | [
{
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}
] | [
67,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
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Mathlib/Algebra/Order/Pi.lean | Function.const_le_one_of_le_one | [] | [
131,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
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Mathlib/Computability/Ackermann.lean | ack_injective_right | [] | [
155,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
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Mathlib/Topology/Bornology/Constructions.lean | Bornology.cobounded_prod | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
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Mathlib/Algebra/Free.lean | FreeSemigroup.map_pure | [] | [
598,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
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Mathlib/LinearAlgebra/AffineSpace/Independent.lean | Affine.Simplex.face_centroid_eq_iff | [
{
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963,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.measureUnivNNReal_pos | [
{
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3144,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3142,
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Mathlib/Data/Finset/Lattice.lean | Finset.iInf_union | [] | [
1954,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1952,
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Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.mk_list_dProd | [
{
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"tactic": "match l... | [
411,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
406,
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Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.exists_eq_mk | [] | [
122,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
11
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Mathlib/ModelTheory/ElementaryMaps.lean | FirstOrder.Language.ElementarySubstructure.coe_top | [] | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/ModelTheory/Order.lean | FirstOrder.Language.realize_noTopOrder_iff | [
{
"state_after": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝ : LE M\n⊢ (∀ (a : M), ∃ a_1, ¬Fin.snoc (Fin.snoc default a) a_1 1 ≤ Fin.snoc (Fin.snoc default a) a_1 0) ↔ NoTopOrder M",
"state_before": "L : Language\nα : Type w\nM : Type w'\nn : ℕ\ninst✝ : LE M\n⊢ M ⊨ noTopOrderSentence Language.order... | [
240,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
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Mathlib/Algebra/Associated.lean | associated_one_of_associated_mul_one | [
{
"state_after": "no goals",
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"tactic": "simpa [mul_assoc] using h"
}
] | [
449,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.sphere_isEmpty_of_subsingleton | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.33233\nι : Type ?u.33236\ninst✝¹ : PseudoMetricSpace α\nx y z : α\nδ ε ε₁ ε₂ : ℝ\ns : Set α\ninst✝ : Subsingleton α\nhε : ε ≠ 0\n⊢ IsEmpty ↑∅",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.33233\nι : Type ?u.33236\ninst✝¹ : PseudoMetricSpace α\nx... | [
506,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.le_degrees_add | [
{
"state_after": "case a\nR : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.45634\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q✝ p q : MvPolynomial σ R\nh : Multiset.Disjoint (degrees p) (degrees q)\n⊢ ∀ (b : σ →₀ ℕ), b ∈ support p → ↑toMultiset b ≤ degrees (p + q)",
"state_before": "R : ... | [
215,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.toMatrix₂_comp | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.1586479\nR₂ : Type ?u.1586482\nM : Type ?u.1586485\nM₁ : Type u_2\nM₂ : Type u_3\nM₁' : Type u_4\nM₂' : Type ?u.1586497\nn : Type u_7\nm : Type u_5\nn' : Type u_6\nm' : Type ?u.1586509\nι : Type ?u.1586512\ninst✝¹⁶ : CommRing R\ninst✝¹⁵ : AddCommMonoid M₁\ninst✝¹⁴ : ... | [
471,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_map_equiv | [
{
"state_after": "G : Type u_1\nG' : Type ?u.254283\ninst✝⁴ : Group G\ninst✝³ : Group G'\nA : Type ?u.254292\ninst✝² : AddGroup A\nH K✝ : Subgroup G\nk : Set G\nN : Type u_2\ninst✝¹ : Group N\nP : Type ?u.254319\ninst✝ : Group P\nf : G ≃* N\nK : Subgroup G\nx : N\n⊢ ↑f.symm x ∈ ↑K ↔ ↑(MulEquiv.symm f) x ∈ K",
... | [
1459,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1457,
1
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Mathlib/LinearAlgebra/FiniteDimensional.lean | Subalgebra.bot_eq_top_iff_rank_eq_one | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\nF : Type u_2\nE : Type u_1\ninst✝³ : Field F\ninst✝² : Ring E\ninst✝¹ : Algebra F E\ninst✝ : Nontrivial E\n⊢ ⊥ = ⊤ ↔ Module.rank F E = 1",
"tactic": "rw [← rank_top, Subalgebra.rank_eq_one_iff, eq_comm]"
}
] | [
1422,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1419,
1
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Mathlib/Analysis/Quaternion.lean | Quaternion.coeComplex_add | [
{
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"tactic": "ext <;> simp"
}
] | [
136,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Nat/Choose/Multinomial.lean | Nat.multinomial_insert | [
{
"state_after": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : DecidableEq α\nh : ¬a ∈ s\n⊢ multinomial (insert a s) f = (f a + Finset.sum s f)! / ((f a)! * (f a + Finset.sum s f - f a)!) * multinomial s f",
"state_before": "α : Type u_1\ns : Finset α\nf : α → ℕ\na b : α\nn : ℕ\ninst✝ : De... | [
88,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.ext_iff_of_biUnion_eq_univ | [
{
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1903,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1901,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.map_map | [
{
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660,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Init/Logic.lean | if_ctx_congr | [] | [
370,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Data/List/BigOperators/Basic.lean | List.length_pos_of_prod_lt_one | [] | [
207,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
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Mathlib/Algebra/Hom/Units.lean | IsUnit.div_eq_iff | [
{
"state_after": "no goals",
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"tactic": "rw [div_eq_mul_inv, h.mul_inv_eq_iff_eq_mul]"
}
] | [
412,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
11
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_Ico | [
{
"state_after": "no goals",
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"tactic": "simp only [sum_Ico_eq_sub _ hmn, geom_sum_eq hx, div_sub_div_same, sub_sub_sub_cancel_right]"
}
] | [
357,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_closure | [
{
"state_after": "no goals",
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"tactic": "simp_rw [cthickening, infEdist_closure]"
}
] | [
1241,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/Data/Multiset/Dedup.lean | Multiset.Nodup.le_nsmul_iff_le | [
{
"state_after": "no goals",
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"tactic": "classical\n rw [← h.le_dedup_iff_le, Iff.comm, ← h.le_dedup_iff_le]\n simp [hn]"
},
{
"state_after": "α : Type u_1\ns t : Multiset α\nn : ℕ\nh : Nodup ... | [
154,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/List/Sigma.lean | List.dlookup_dedupKeys | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\n⊢ dlookup a (dedupKeys []) = dlookup a []\n\ncase cons\nα : Type u\nβ : α → Type v\nl l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\na : α\nl_hd : Sigma β\ntail✝ : List (Sigma β)\nl_ih : dlookup a (de... | [
660,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
653,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.support_of_subset | [] | [
146,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.classes_inj | [
{
"state_after": "no goals",
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"tactic": "simp only [rel_iff_exists_classes, exists_prop, h]"
}
] | [
112,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Finsupp.linearEquivFunOnFinite_symm_single | [] | [
119,
35
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_congr_set | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.right_isBigO_sub | [] | [
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Mathlib/Data/List/Permutation.lean | List.mem_foldr_permutationsAux2 | [
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.neg | [] | [
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Mathlib/Order/Heyting/Basic.lean | sup_hnot_self | [] | [
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_neg | [] | [
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Mathlib/Computability/Primrec.lean | Primrec.of_equiv_symm | [
{
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Mathlib/Data/Finsupp/Lex.lean | Finsupp.lex_lt_of_lt_of_preorder | [] | [
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Mathlib/RingTheory/AlgebraicIndependent.lean | AlgebraicIndependent.linearIndependent | [
{
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Mathlib/Analysis/Convex/Basic.lean | convex_halfspace_lt | [] | [
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Mathlib/Algebra/Order/Ring/Defs.lean | StrictAnti.mul_const_of_neg | [] | [
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Mathlib/Algebra/Opposites.lean | MulOpposite.op_bijective | [] | [
141,
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Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.colimitPresheafObjIsoComponentwiseLimit_inv_ι_app | [
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Mathlib/CategoryTheory/Simple.lean | CategoryTheory.mono_to_simple_zero_of_not_iso | [
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41
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigOWith_zero | [
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Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.coe_equivMapOfInjective_apply | [] | [
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Mathlib/Data/Set/Ncard.lean | Set.ncard_congr | [
{
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382,
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Mathlib/Data/Finset/Basic.lean | Finset.cons_induction_on | [] | [
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25
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Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.comp_right | [] | [
78,
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Mathlib/Data/Matrix/Basic.lean | Matrix.conjTransposeLinearEquiv_symm | [] | [
2303,
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Mathlib/Analysis/Calculus/Inverse.lean | HasStrictFDerivAt.localInverse_def | [] | [
627,
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625,
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Mathlib/Probability/ProbabilityMassFunction/Basic.lean | Pmf.ext | [] | [
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20
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Mathlib/Analysis/Calculus/ContDiffDef.lean | hasFTaylorSeriesUpTo_zero_iff | [
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Mathlib/NumberTheory/ClassNumber/AdmissibleAbsoluteValue.lean | AbsoluteValue.IsAdmissible.exists_approx | [
{
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Mathlib/Order/Atoms.lean | isSimpleOrder_iff_isCoatom_bot | [] | [
673,
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Mathlib/RingTheory/Localization/AtPrime.lean | IsLocalization.AtPrime.isUnit_mk'_iff | [] | [
162,
78
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Mathlib/Analysis/Normed/Group/Pointwise.lean | singleton_div_ball | [
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Mathlib/Analysis/Calculus/Dslope.lean | ContinuousOn.of_dslope | [] | [
106,
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Mathlib/Data/Finset/Sups.lean | Finset.infs_subset | [] | [
263,
16
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262,
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Mathlib/Data/Finset/Prod.lean | Finset.product_biUnion | [
{
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.closure_subset_thickening | [
{
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Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasDerivAt | [] | [
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71
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_sub | [
{
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88
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Mathlib/Order/Filter/Basic.lean | Filter.Eventually.comap | [] | [
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Mathlib/RingTheory/Polynomial/Basic.lean | MvPolynomial.mem_ideal_of_coeff_mem_ideal | [
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Mathlib/Analysis/Normed/Order/Lattice.lean | norm_inf_sub_inf_le_add_norm | [
{
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43
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_tendsto | [] | [
271,
41
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269,
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Mathlib/Data/Finset/Sum.lean | Finset.map_inl_disjUnion_map_inr | [] | [
66,
6
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Mathlib/Data/Set/Finite.lean | Set.iUnion_iInter_of_antitone | [] | [
1533,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.prod_of_support_subset | [
{
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Mathlib/Algebra/Parity.lean | Even.pow_pos_iff | [
{
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Mathlib/CategoryTheory/Monoidal/Opposite.lean | CategoryTheory.MonoidalOpposite.unop_inj_iff | [] | [
65,
10
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Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.charFn_inj | [] | [
124,
43
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_mem_nhds | [] | [
1013,
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1012,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometry.ediam_range | [] | [
194,
25
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Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_max | [
{
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}
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27
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Mathlib/RingTheory/Subring/Basic.lean | RingHom.map_closure | [] | [
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Mathlib/Data/Rat/Lemmas.lean | Rat.mul_self_den | [
{
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},
{
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Mathlib/Order/ModularLattice.lean | sup_inf_assoc_of_le | [] | [
211,
69
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.enumOrd_range | [
{
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31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2204,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_mul | [] | [
213,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Std/Data/Int/DivMod.lean | Int.add_emod_self | [
{
"state_after": "a b : Int\nthis : (a + b * 1) % b = a % b\n⊢ (a + b) % b = a % b",
"state_before": "a b : Int\n⊢ (a + b) % b = a % b",
"tactic": "have := add_mul_emod_self_left a b 1"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nthis : (a + b * 1) % b = a % b\n⊢ (a + b) % b ... | [
415,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
414,
9
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.isometry | [] | [
628,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
11
] |
Mathlib/Data/List/Destutter.lean | List.destutter_cons' | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.not_linearIndependent_of_infinite | [
{
"state_after": "K : Type u\nV : Type v\ninst✝⁵ : DivisionRing K\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module K V\nV₂ : Type v'\ninst✝² : AddCommGroup V₂\ninst✝¹ : Module K V₂\nι : Type w\ninf : Infinite ι\ninst✝ : FiniteDimensional K V\nv : ι → V\nh_lin_indep : LinearIndependent K v\n⊢ False",
"state_before"... | [
314,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
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