file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Std/Data/List/Init/Lemmas.lean | List.tail!_cons | [] | [
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56
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Mathlib/Data/List/Basic.lean | List.enumFrom_append | [
{
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Mathlib/Data/Set/Pointwise/Basic.lean | Group.card_pow_eq_card_pow_card_univ_aux | [
{
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"state_before": "F : Typ... | [
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68
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1350,
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Mathlib/Topology/Homotopy/HSpaces.lean | Path.delayReflLeft_zero | [
{
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"state_before": "X : Type u\ninst✝ : TopologicalSpace X\nx y : X\nγ : Path x y\n⊢ delayReflLeft 0 γ = trans (refl x) γ",
"tactic": "simp only [delayReflLeft, delayReflRight_zero, trans_symm, refl_symm, Path.symm_symm]"
}
] | [
282,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
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Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzWith.subtype_val | [] | [
208,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Hom/Bounded.lean | TopHom.coe_copy | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
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Mathlib/Topology/Connected.lean | isPreconnected_of_forall_pair | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nι : Type ?u.2516\nπ : ι → Type ?u.2521\ninst✝ : TopologicalSpace α\ns t u v : Set α\nH : ∀ (x : α), x ∈ ∅ → ∀ (y : α), y ∈ ∅ → ∃ t, t ⊆ ∅ ∧ x ∈ t ∧ y ∈ t ∧ IsPreconnected t\n⊢ IsPreconnected ∅\n\ncase inr.intro\nα : Type u\nβ : Type v\nι : Type ?u.2516\nπ : ι ... | [
126,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.uniformity_basis_dist_le | [] | [
799,
77
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797,
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Mathlib/Algebra/Order/Group/Defs.lean | inv_lt_inv_iff | [
{
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"state_before": "α : Type u\ninst✝³ : Group ... | [
389,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
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Mathlib/LinearAlgebra/Matrix/Circulant.lean | Matrix.Fin.circulant_mul_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.36269\nm : Type ?u.36272\nn : Type ?u.36275\nR : Type ?u.36278\ninst✝¹ : CommSemigroup α\ninst✝ : AddCommMonoid α\n⊢ ∀ (v w : Fin 0 → α), circulant v ⬝ circulant w = circulant w ⬝ circulant v",
"tactic": "simp [Injective]"
}
] | [
158,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
1
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Mathlib/CategoryTheory/Preadditive/FunctorCategory.lean | CategoryTheory.NatTrans.app_zero | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/Deprecated/Ring.lean | IsRingHom.map_sub | [
{
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"tactic": "simp [sub_eq_add_neg, hf.map_add, hf.map_neg]"
}
] | [
119,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.pow_eq_prod_const | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
1452,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1452,
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Mathlib/Data/List/Infix.lean | List.eq_of_prefix_of_length_eq | [] | [
123,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
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Std/Data/List/Lemmas.lean | List.forall_mem_nil | [] | [
215,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
215,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.lintegral_smul | [] | [
1050,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1049,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | span_lt_top_of_card_lt_finrank | [] | [
363,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
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Mathlib/Data/Set/Basic.lean | Set.Subsingleton.strictMonoOn | [] | [
2685,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2684,
11
] |
Mathlib/Dynamics/PeriodicPts.lean | Function.IsPeriodicPt.right_of_add | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1334\nf fa : α → α\nfb : β → β\nx y : α\nm n : ℕ\nhn : IsPeriodicPt f (m + n) x\nhm : IsPeriodicPt f n x\n⊢ IsPeriodicPt f m x",
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113,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/WithZero.lean | inv_le_one₀ | [] | [
151,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
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Mathlib/Data/Stream/Init.lean | Stream'.cons_append_stream | [] | [
528,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/Data/List/Cycle.lean | Cycle.mem_map | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
735,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
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Mathlib/Algebra/Order/Ring/Defs.lean | lt_mul_of_lt_one_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.88483\ninst✝ : StrictOrderedRing α\na b c : α\nha : a < 0\nh : b < 1\n⊢ a < a * b",
"tactic": "simpa only [mul_one] using mul_lt_mul_of_neg_left h ha"
}
] | [
714,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
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Mathlib/Order/Lattice.lean | Pi.sup_apply | [] | [
1009,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
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Mathlib/Data/Finset/Basic.lean | Finset.Subset.antisymm_iff | [] | [
389,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.div_self | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na : R\na0 : a ≠ 0\n⊢ a / a = 1",
"tactic": "simpa only [one_mul] using mul_div_cancel 1 a0"
}
] | [
91,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/GroupTheory/Perm/List.lean | List.mem_of_formPerm_ne_self | [
{
"state_after": "α : Type u_1\nβ : Type ?u.815968\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ : α\nl : List α\nx : α\nh : ↑(formPerm l) x ≠ x\n⊢ x ∈ {y | ↑(formPerm l) y ≠ y}",
"state_before": "α : Type u_1\nβ : Type ?u.815968\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ : α\nl : List α\nx : α\nh : ↑(formPerm l) x ... | [
407,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.comp_id | [] | [
293,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
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Mathlib/Data/Real/EReal.lean | EReal.neg_lt_neg_iff | [] | [
800,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
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Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.balance' | [] | [
1340,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1335,
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Mathlib/Init/Logic.lean | ExistsUnique.elim | [] | [
239,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
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Mathlib/Order/Monotone/Basic.lean | monotone_id | [] | [
511,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/LiminfLimsup.lean | Filter.isCobounded_bot | [
{
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"tactic": "simp [IsCobounded]"
}
] | [
216,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
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] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_comp_of_ker_eq_bot | [
{
"state_after": "no goals",
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1722,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1721,
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Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists | [
{
"state_after": "case mp\nC : Type u\ninst✝⁶ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝⁵ : Category D\ninst✝⁴ : ConcreteCategory D\ninst✝³ : PreservesLimits (forget D)\ninst✝² : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (... | [
266,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
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Mathlib/Data/Multiset/Bind.lean | Multiset.mem_product | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.62033\nδ : Type ?u.62036\na✝ : α\nb✝ : β\ns✝ : Multiset α\nt✝ : Multiset β\ns : Multiset α\nt : Multiset β\na : α\nb : β\n⊢ (a, b) ∈ product s t ↔ (a, b).fst ∈ s ∧ (a, b).snd ∈ t",
"tactic": "simp [product, and_left_co... | [
292,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.pi_top | [
{
"state_after": "no goals",
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1842,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1841,
1
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Mathlib/Analysis/Calculus/Deriv/Add.lean | deriv_neg'' | [] | [
273,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Sum/Order.lean | Sum.not_inl_lt_inr | [] | [
158,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/List/MinMax.lean | List.maximum_mem | [] | [
306,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_add_add_self | [
{
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307,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
306,
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Mathlib/Order/CompleteBooleanAlgebra.lean | iInf_sup_of_monotone | [] | [
234,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
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Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.norm_image_sub_le_of_bound | [
{
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228,
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198,
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Mathlib/Data/Real/EReal.lean | EReal.sign_mul_abs | [
{
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"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "⊢ ↑(↑sign ⊤) * ↑(EReal.abs ⊤) = ⊤",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ ↑(↑sign ↑x) * ↑(E... | [
1144,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
19
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Mathlib/Order/SuccPred/Basic.lean | Order.pred_injective | [] | [
830,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
830,
1
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Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_nonpos | [] | [
1219,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Order/SuccPred/Relation.lean | transGen_of_pred_of_gt | [] | [
117,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Data/Finset/Sort.lean | Finset.sort_singleton | [] | [
77,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.mem_inf | [] | [
303,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Std/Data/Int/Lemmas.lean | Int.le_refl | [] | [
609,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
608,
19
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousIdeal.lean | HomogeneousIdeal.coe_inf | [] | [
360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Analysis/ODE/PicardLindelof.lean | exists_isPicardLindelof_const_of_contDiffOn_nhds | [
{
"state_after": "case intro.intro.intro\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : ProperSpace E\nv : E → E\nt₀ : ℝ\nx₀ : E\ns : Set E\nhv : ContDiffOn ℝ 1 v s\nhs : s ∈ 𝓝 x₀\nL : ℝ≥0\ns' : Set E\nhs' : s' ∈ 𝓝 x₀\nhlip : LipschitzOnWith L v s'\n⊢ ∃ ε, ε > 0 ∧ ∃ L R C, IsP... | [
435,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.spanExt_inv_app_left | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nX Y Z X' Y' Z' : C\niX : X ≅ X'\niY : Y ≅ Y'\niZ : Z ≅ Z'\nf : X ⟶ Y\ng : X ⟶ Z\nf' : X' ⟶ Y'\ng' : X' ⟶ Z'\nwf : iX.hom ≫ f' = f ≫ iY.hom\nwg : iX.hom ≫ g' = g ≫ iZ.hom\n⊢ (spanExt iX iY iZ wf wg... | [
491,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
] |
Mathlib/RingTheory/FreeCommRing.lean | FreeCommRing.isSupported_of | [
{
"state_after": "α : Type u\nβ : Type v\nf : α → β\np : α\ns : Set α\nhps : IsSupported (of p) s\nthis : DecidablePred s\n⊢ p ∈ s",
"state_before": "α : Type u\nβ : Type v\nf : α → β\np : α\ns : Set α\nhps : IsSupported (of p) s\n⊢ p ∈ s",
"tactic": "haveI := Classical.decPred s"
},
{
"state_af... | [
268,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/GroupTheory/Nilpotent.lean | normalizerCondition_of_isNilpotent | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nh : Group.IsNilpotent G\n⊢ ∀ (H : Subgroup G), normalizer H = H → H = ⊤",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nH : Subgroup G\ninst✝ : Normal H\nh : Group.IsNilpotent G\n⊢ NormalizerCondition G",
"tactic": "r... | [
850,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Std/Data/Rat/Lemmas.lean | Rat.zero_mkRat | [
{
"state_after": "n : Nat\n⊢ (if h : n = 0 then 0 else 0) = 0",
"state_before": "n : Nat\n⊢ mkRat 0 n = 0",
"tactic": "simp [mkRat_def]"
},
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ (if h : n = 0 then 0 else 0) = 0",
"tactic": "apply ite_self"
}
] | [
97,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
97,
9
] |
Mathlib/Algebra/Group/Commute.lean | mul_inv_cancel_comm | [] | [
412,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/CategoryTheory/NatTrans.lean | CategoryTheory.NatTrans.vcomp_app | [] | [
101,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | IsLinearMap.with_bound | [] | [
84,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/Polynomial/Opposites.lean | Polynomial.opRingEquiv_symm_C_mul_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nr : Rᵐᵒᵖ\nn : ℕ\n⊢ ↑(RingEquiv.symm (opRingEquiv R)) (↑C r * X ^ n) = op (↑C (unop r) * X ^ n)",
"tactic": "rw [C_mul_X_pow_eq_monomial, opRingEquiv_symm_monomial, C_mul_X_pow_eq_monomial]"
}
] | [
90,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.nhds_coe_units | [] | [
99,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph'.relIso_coe | [] | [
173,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.ae_of_ae_map | [] | [
2714,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2712,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | mulRothNumber_map_mul_left | [
{
"state_after": "case refine'_1\nF : Type ?u.143344\nα : Type u_1\nβ : Type ?u.143350\n𝕜 : Type ?u.143353\nE : Type ?u.143356\ninst✝¹ : DecidableEq α\ninst✝ : CancelCommMonoid α\ns : Finset α\na : α\n⊢ ↑mulRothNumber (map (mulLeftEmbedding a) s) ≤ ↑mulRothNumber s\n\ncase refine'_2\nF : Type ?u.143344\nα : Ty... | [
439,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Std/Data/List/Init/Lemmas.lean | List.mapM_append | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 → Type u_2\nα : Type u_3\nβ : Type u_1\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : α → m β\nl₁ l₂ : List α\n⊢ mapM f (l₁ ++ l₂) = do\n let __do_lift ← mapM f l₁\n let __do_lift_1 ← mapM f l₂\n pure (__do_lift ++ __do_lift_1)",
"tactic... | [
224,
96
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
223,
9
] |
Mathlib/Combinatorics/SimpleGraph/Trails.lean | SimpleGraph.Walk.IsEulerian.even_degree_iff | [
{
"state_after": "case h.e'_1.h.e'_3\nV : Type u_1\nG : SimpleGraph V\ninst✝² : DecidableEq V\nx u v : V\np : Walk G u v\nht : IsEulerian p\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\n⊢ degree G x = List.countp (fun e => decide (x ∈ e)) (edges p)",
"state_before": "V : Type u_1\nG : SimpleGraph V\ninst... | [
145,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Analysis/Convex/Uniform.lean | exists_forall_sphere_dist_add_le_two_sub | [] | [
58,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.mk_one_eq_algebraMap | [] | [
1025,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1024,
1
] |
Mathlib/Topology/Algebra/FilterBasis.lean | GroupFilterBasis.nhds_eq | [
{
"state_after": "case h₀\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nx₀ : G\n⊢ pure ≤ N B\n\ncase h₁\nG : Type u\ninst✝ : Group G\nB✝ B : GroupFilterBasis G\nx₀ : G\n⊢ ∀ (a : G) (s : Set G), s ∈ N B a → ∃ t, t ∈ N B a ∧ t ⊆ s ∧ ∀ (a' : G), a' ∈ t → s ∈ N B a'",
"state_before": "G : Type u\nins... | [
203,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.alephIdx.init | [] | [
115,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Topology/ContinuousOn.lean | principal_subtype | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.190164\nβ : Type ?u.190167\nγ : Type ?u.190170\nδ : Type ?u.190173\ninst✝ : TopologicalSpace α✝\nα : Type u_1\ns : Set α\nt : Set ↑s\n⊢ 𝓟 t = comap Subtype.val (𝓟 (Subtype.val '' t))",
"tactic": "rw [comap_principal, preimage_image_eq _ Subtyp... | [
396,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | isCoprime_of_irreducible_dvd | [
{
"state_after": "R : Type u\nM : Type v\ninst✝³ : CommRing R\ninst✝² : IsDomain R\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : GCDMonoid R\nx y : R\nnonzero : ¬(x = 0 ∧ y = 0)\nH : ∀ (z : R), Irreducible z → z ∣ x → ¬z ∣ y\n⊢ ∀ (z : R), z ∈ nonunits R → z ≠ 0 → z ∣ x → ¬z ∣ y",
"state_before": "R : Type u\nM ... | [
418,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Probability/CondCount.lean | ProbabilityTheory.condCount_add_compl_eq | [
{
"state_after": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t✝ u✝ u t : Set Ω\nhs : Set.Finite s\nthis :\n ↑↑(condCount s) t =\n ↑↑(condCount (s ∩ u)) t * ↑↑(condCount (s ∩ u ∪ s ∩ uᶜ)) (s ∩ u) +\n ↑↑(condCount (s ∩ uᶜ)) t * ↑↑(condCount (s ∩ u ∪ s ∩ uᶜ)) (s ∩ uᶜ)\... | [
204,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.OpenNhdsOf.mem | [] | [
443,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
11
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.coe_id | [] | [
161,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Logic/Small/Basic.lean | small_subset | [] | [
104,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/CategoryTheory/EssentialImage.lean | CategoryTheory.Functor.essImage.ofNatIso | [] | [
69,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.add_mul_succ | [
{
"state_after": "case H₁\na b c : Ordinal\nba : b + a = a\n⊢ (a + b) * succ 0 = a * succ 0 + b\n\ncase H₂\na b c : Ordinal\nba : b + a = a\n⊢ ∀ (o : Ordinal), (a + b) * succ o = a * succ o + b → (a + b) * succ (succ o) = a * succ (succ o) + b\n\ncase H₃\na b c : Ordinal\nba : b + a = a\n⊢ ∀ (o : Ordinal),\n ... | [
2488,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2480,
1
] |
Mathlib/GroupTheory/GroupAction/Quotient.lean | Subgroup.quotientCentralizerEmbedding_apply | [] | [
389,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Matrix/Basic.lean | Equiv.mapMatrix_trans | [] | [
1393,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMaxOn.bicomp_mono | [] | [
393,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.eq_zero_of_add_eq_zero_right | [
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ 0 + m = 0 → 0 = 0",
"tactic": "simp [Nat.zero_add]"
},
{
"state_after": "n m : Nat\nh : succ (n + m) = 0\n⊢ n + 1 = 0",
"state_before": "n m : Nat\nh : n + 1 + m = 0\n⊢ n + 1 = 0",
"tactic": "rw [add_one, succ_add] at h"
},
{
... | [
22,
25
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
18,
11
] |
Mathlib/Data/Set/Basic.lean | Antitone.inter | [] | [
2899,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2897,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.dist_map | [] | [
630,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
629,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_le | [] | [
208,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.18111\nδ : Type ?u.18114\na : α\ns t : Multiset α\nf✝ g : α → Multiset β\nf : α → β\n⊢ (bind 0 fun x => {f x}) = map f 0",
"tactic": "rw [zero_bind, map_zero]"
},
{
"state_after": "no goals",
"state_before"... | [
139,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_mul | [] | [
739,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.reindex_refl | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.368486\nR : Type u_2\nR₂ : Type ?u.368492\nK : Type ?u.368495\nM : Type u_3\nM' : Type ?u.368501\nM'' : Type ?u.368504\nV : Type u\nV' : Type ?u.368509\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCo... | [
442,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
441,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_anti_mono_ideal | [] | [
186,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.sq_mul_squarefree_of_pos | [
{
"state_after": "n : ℕ\nhn : 0 < n\nS : Finset ℕ := Finset.filter (fun s => s ∣ n ∧ ∃ x, s = x ^ 2) (Finset.range (n + 1))\n⊢ ∃ a b, 0 < a ∧ 0 < b ∧ b ^ 2 * a = n ∧ Squarefree a",
"state_before": "n : ℕ\nhn : 0 < n\n⊢ ∃ a b, 0 < a ∧ 0 < b ∧ b ^ 2 * a = n ∧ Squarefree a",
"tactic": "set S := (Finset.ran... | [
352,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.measurePreserving_finTwoArrow | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.6010588\nι' : Type ?u.6010591\nα✝ : ι → Type ?u.6010596\ninst✝¹ : Fintype ι\nm✝ : (i : ι) → OuterMeasure (α✝ i)\nα : Type u\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : SigmaFinite μ\n⊢ MeasurePreserving ↑MeasurableEquiv.finTwoArrow",
"tactic":... | [
818,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | Monotone.csInf_image_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.97518\nι : Sort ?u.97521\ninst✝¹ : Preorder α\ninst✝ : ConditionallyCompleteLattice β\nf : α → β\nh_mono : Monotone f\ns : Set α\nc : α\nhcs : c ∈ s\nh_bdd : BddBelow s\nf' : αᵒᵈ → βᵒᵈ := f\n⊢ sInf (f '' s) ≤ f c",
"state_before": "α : Type u_1\nβ : ... | [
1260,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1256,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.span_mul_span' | [
{
"state_after": "R : Type u\nι : Type ?u.222969\ninst✝ : CommSemiring R\nI J K L : Ideal R\nS T : Set R\n⊢ Submodule.span R S * Submodule.span R T = Submodule.span R (S * T)",
"state_before": "R : Type u\nι : Type ?u.222969\ninst✝ : CommSemiring R\nI J K L : Ideal R\nS T : Set R\n⊢ span S * span T = span (... | [
524,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
522,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.comp_apply | [] | [
191,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sum_mapDomain_index_addMonoidHom | [] | [
596,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/RingTheory/TensorProduct.lean | TensorProduct.AlgebraTensorModule.curry_injective | [] | [
109,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
8
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.fst_prodExtendRight | [
{
"state_after": "α₁ : Type u_1\nβ₁ : Type u_2\ninst✝ : DecidableEq α₁\na : α₁\ne : Perm β₁\nab : α₁ × β₁\n⊢ (↑{ toFun := fun ab => if ab.fst = a then (a, ↑e ab.snd) else ab,\n invFun := fun ab => if ab.fst = a then (a, ↑e.symm ab.snd) else ab,\n left_inv :=\n (_ :\n ... | [
851,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/Topology/Basic.lean | Filter.HasBasis.lift'_closure_eq_self | [] | [
590,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/Real/CauSeq.lean | CauSeq.mul_not_equiv_zero | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrderedField α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf g : CauSeq β abv\nhf : ¬f ≈ 0\nhg : ¬g ≈ 0\nthis : LimZero (f * g - 0)\nhlz : LimZero (f * g)\n⊢ False",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝² : LinearOrder... | [
556,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.mk_coordChange | [
{
"state_after": "ι : Type ?u.53743\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.53754\nZ : Type u_3\ninst✝³ : TopologicalSpace B\ninst✝² : TopologicalSpace F\nproj : Z → B\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace (TotalSpace E)\ne : Trivialization F proj\nx✝ : Z\ne' : Trivialization F TotalSpace.... | [
674,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
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