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/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_surjective | [] | [
737,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.image_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_4\nβ : Type u_3\nγ : Type u_2\ninst✝² : DecidableEq β\nf✝ g✝ : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\nβ' : Type u_1\ninst✝¹ : DecidableEq β'\ninst✝ : DecidableEq γ\nf : β → γ\ng : α → β\nf' : α → β'\ng' : β' → γ\nh_comm : ∀ (a : α), f (g a... | [
427,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\nh : K ⊆ L\nD : ComponentCompl G K\n⊢ hom h C = D ↔ ∃ x, x ∈ ↑C ∧ x ∈ ↑D",
"state_before": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\nC : ComponentCompl G L\nh : K ⊆ L\nD : ComponentCompl G K\n⊢ hom h C = D ↔ ¬D... | [
207,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.swap_inj | [] | [
210,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Data/List/Rotate.lean | List.nthLe_cyclicPermutations | [
{
"state_after": "case inl\nα : Type u\nl l' : List α\nn : ℕ\nhn : n < length (cyclicPermutations [])\n⊢ nthLe (cyclicPermutations []) n hn = rotate [] n\n\ncase inr\nα : Type u\nl✝ l' l : List α\nn : ℕ\nhn : n < length (cyclicPermutations l)\nh : l ≠ []\n⊢ nthLe (cyclicPermutations l) n hn = rotate l n",
"... | [
607,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.coeff_map | [] | [
1689,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1688,
1
] |
Mathlib/Data/Set/Sups.lean | Set.Nonempty.of_infs_right | [] | [
283,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Analysis/Convex/Exposed.lean | IsExposed.mono | [
{
"state_after": "case intro\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : OrderedRing 𝕜\ninst✝² : AddCommMonoid E\ninst✝¹ : TopologicalSpace E\ninst✝ : Module 𝕜 E\nl : E →L[𝕜] 𝕜\nA B C : Set E\nX : Finset E\nx : E\nhC : IsExposed 𝕜 A C\nhBA : B ⊆ A\nhCB : C ⊆ B\nw : E\nhw : w ∈ C\n⊢... | [
113,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
11
] |
Mathlib/Combinatorics/SimpleGraph/Finsubgraph.lean | SimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom | [
{
"state_after": "case intro\nV : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Finite W\nh : (G' : Subgraph G) → Set.Finite G'.verts → Subgraph.coe G' →g F\nval✝ : Fintype W\n⊢ Nonempty (G →g F)",
"state_before": "V : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Fin... | [
156,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Data/PFun.lean | PFun.coe_preimage | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.45105\nδ : Type ?u.45108\nε : Type ?u.45111\nι : Type ?u.45114\nf✝ : α →. β\nf : α → β\ns : Set β\nx✝ : α\n⊢ x✝ ∈ preimage (↑f) s ↔ x✝ ∈ f ⁻¹' s",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.45105\nδ : Type ?u.45108\nε : Type ?u.... | [
457,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
] |
Mathlib/Algebra/ContinuedFractions/TerminatedStable.lean | GeneralizedContinuedFraction.numerators_stable_of_terminated | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\ng : GeneralizedContinuedFraction K\nn m : ℕ\ninst✝ : DivisionRing K\nn_le_m : n ≤ m\nterminated_at_n : TerminatedAt g n\n⊢ numerators g m = numerators g n",
"tactic": "simp only [num_eq_conts_a, continuants_stable_of_terminated n_le_m terminate... | [
80,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Topology/Separation.lean | disjoint_nhds_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T2Space α\nx y : α\nhd : Disjoint (𝓝 x) (𝓝 y)\nhe : x = y\n⊢ False",
"tactic": "simp [he, nhds_neBot.ne] at hd"
}
] | [
888,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_pred_iterate_of_not_isMin | [] | [
984,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
982,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.singleton_smoothManifoldWithCorners | [] | [
734,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.Ordered.insert | [
{
"state_after": "α✝ : Type u_1\ncmp : α✝ → α✝ → Ordering\nt : RBNode α✝\nv : α✝\nh : Ordered cmp t\n⊢ Ordered cmp\n (match isRed t with\n | red => setBlack (ins cmp v t)\n | black => ins cmp v t)",
"state_before": "α✝ : Type u_1\ncmp : α✝ → α✝ → Ordering\nt : RBNode α✝\nv : α✝\nh : Ordered cmp t\n... | [
117,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
116,
11
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.edges_takeUntil_subset | [] | [
1159,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.mem_inv_pointwise_smul_iff₀ | [] | [
324,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.prob_compl_eq_one_sub | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.707839\nγ : Type ?u.707842\nδ : Type ?u.707845\nι : Type ?u.707848\nR : Type ?u.707851\nR' : Type ?u.707854\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β\ninst✝¹ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set... | [
3250,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3249,
1
] |
Mathlib/Tactic/NormNum/IsCoprime.lean | Tactic.NormNum.int_not_isCoprime_helper | [
{
"state_after": "x y : ℤ\nd : ℕ\nhd : Int.gcd x y = d\nh : Nat.beq d 1 = false\n⊢ ¬d = 1",
"state_before": "x y : ℤ\nd : ℕ\nhd : Int.gcd x y = d\nh : Nat.beq d 1 = false\n⊢ ¬IsCoprime x y",
"tactic": "rw [Int.isCoprime_iff_gcd_eq_one, hd]"
},
{
"state_after": "no goals",
"state_before": "x ... | [
26,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.Step.cons_not | [] | [
125,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/Order/SupIndep.lean | Finset.SupIndep.attach | [
{
"state_after": "α : Type u_1\nβ : Type ?u.16631\nι : Type u_2\nι' : Type ?u.16637\ninst✝¹ : Lattice α\ninst✝ : OrderBot α\ns t✝ : Finset ι\nf : ι → α\ni✝ : ι\nhs : SupIndep s f\nt : Finset { x // x ∈ s }\na✝¹ : t ⊆ Finset.attach s\ni : { x // x ∈ s }\na✝ : i ∈ Finset.attach s\nhi : ¬i ∈ t\n⊢ Disjoint ((f ∘ Su... | [
141,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Computability/Reduce.lean | OneOneReducible.of_equiv_symm | [
{
"state_after": "case h.e'_5\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\ne : α ≃ β\nq : β → Prop\nh : Computable ↑e.symm\n⊢ q = (q ∘ ↑e) ∘ ↑e.symm",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\ne : α ≃ β\nq : β → Prop\nh : Compu... | [
118,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Std/Data/String/Lemmas.lean | String.next_of_valid | [] | [
258,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
257,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.mod_modEq | [] | [
105,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Data/List/Perm.lean | List.filter_append_perm | [
{
"state_after": "case nil\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\np : α → Bool\n⊢ filter p [] ++ filter (fun x => decide ¬p x = true) [] ~ []\n\ncase cons\nα : Type uu\nβ : Type vv\nl₁ l₂ : List α\np : α → Bool\nx : α\nl : List α\nih : filter p l ++ filter (fun x => decide ¬p x = true) l ~ l\n⊢ filter p (x ... | [
287,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.val_lt_iff | [] | [
420,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Topology/PathConnected.lean | mem_pathComponent_self | [] | [
904,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/MeasureTheory/Decomposition/RadonNikodym.lean | MeasureTheory.Measure.absolutelyContinuous_iff_withDensity_rnDeriv_eq | [] | [
70,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
src/lean/Init/Data/List/BasicAux.lean | List.append_cancel_right_eq | [
{
"state_after": "case a\nα : Type u_1\nas bs cs : List α\n⊢ as ++ bs = cs ++ bs ↔ as = cs",
"state_before": "α : Type u_1\nas bs cs : List α\n⊢ (as ++ bs = cs ++ bs) = (as = cs)",
"tactic": "apply propext"
},
{
"state_after": "case a.mp\nα : Type u_1\nas bs cs : List α\n⊢ as ++ bs = cs ++ bs → ... | [
158,
28
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
155,
9
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_eq_one_or_self | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.2284\nι : Type ?u.2287\nM : Type u_2\nN : Type ?u.2293\ninst✝¹ : One M\ninst✝ : One N\ns✝ t : Set α\nf✝ g : α → M\na✝ : α\ns : Set α\nf : α → M\na : α\nh : a ∈ s\n⊢ mulIndicator s f a = 1 ∨ mulIndicator s f a = f a\n\ncase neg\nα : Type u_1\nβ : Type ?u.2284... | [
97,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/RingTheory/FiniteType.lean | RingHom.FiniteType.comp_surjective | [
{
"state_after": "A : Type u_1\nB : Type u_2\nC : Type u_3\ninst✝² : CommRing A\ninst✝¹ : CommRing B\ninst✝ : CommRing C\nf : A →+* B\ng : B →+* C\nhf : FiniteType f\nhg : Surjective ↑g\nx✝ : Algebra A B := toAlgebra f\n⊢ FiniteType (comp g f)",
"state_before": "A : Type u_1\nB : Type u_2\nC : Type u_3\nins... | [
228,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.add_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\nx✝ : a₁ ≡ b₁ [PMOD p]\nm : ℤ\nhm : b₁ - a₁ = m • p\n⊢ (∃ b, b₁ + b₂ - (a₁ + a₂) = ↑(Equiv.addLeft m).symm.symm b • p) ↔ a₂ ≡ b₂ [PMOD p]",
"tactic": "simp [add_sub_add_comm, hm, add... | [
192,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.add_cons | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.45497\nγ : Type ?u.45500\na : α\ns t : Multiset α\n⊢ s + a ::ₘ t = a ::ₘ (s + t)",
"tactic": "rw [add_comm, cons_add, add_comm]"
}
] | [
679,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
678,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | isCyclic_of_orderOf_eq_card | [
{
"state_after": "no goals",
"state_before": "α : Type u\na : α\ninst✝¹ : Group α\ninst✝ : Fintype α\nx : α\nhx : orderOf x = Fintype.card α\n⊢ IsCyclic α",
"tactic": "classical\n use x\n simp_rw [← SetLike.mem_coe, ← Set.eq_univ_iff_forall]\n rw [← Fintype.card_congr (Equiv.Set.univ α), orderOf_eq_c... | [
112,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Order/SymmDiff.lean | compl_symmDiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.87749\nα : Type u_1\nβ : Type ?u.87755\nπ : ι → Type ?u.87760\ninst✝ : BooleanAlgebra α\na b c d : α\n⊢ (a ∆ b)ᶜ = a ⇔ b",
"tactic": "simp_rw [symmDiff, compl_sup_distrib, compl_sdiff, bihimp, inf_comm]"
}
] | [
738,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Data/Finsupp/Defs.lean | Finsupp.induction₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.320386\nγ : Type ?u.320389\nι : Type ?u.320392\nM : Type u_2\nM' : Type ?u.320398\nN : Type ?u.320401\nP : Type ?u.320404\nG : Type ?u.320407\nH : Type ?u.320410\nR : Type ?u.320413\nS : Type ?u.320416\ninst✝ : AddZeroClass M\np : (α →₀... | [
1112,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.bitwise'_zero | [
{
"state_after": "f : Bool → Bool → Bool\n⊢ (bif f false true then 0 else 0) = 0",
"state_before": "f : Bool → Bool → Bool\n⊢ bitwise' f 0 0 = 0",
"tactic": "rw [bitwise'_zero_left]"
},
{
"state_after": "no goals",
"state_before": "f : Bool → Bool → Bool\n⊢ (bif f false true then 0 else 0) =... | [
423,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Tactic/Congr!.lean | Lean.MVarId.rel_of_eq_and_refl | [] | [
582,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
581,
1
] |
Mathlib/Algebra/Order/AbsoluteValue.lean | AbsoluteValue.le_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_1\ninst✝¹ : Ring R\ninst✝ : OrderedRing S\nabv : AbsoluteValue R S\na b : R\n⊢ ↑abv a ≤ ↑abv (a - b) + ↑abv b",
"tactic": "simpa using abv.add_le (a - b) b"
}
] | [
223,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
11
] |
Mathlib/Combinatorics/SimpleGraph/Ends/Defs.lean | SimpleGraph.ComponentCompl.supp_injective | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nK L L' M : Set V\n⊢ ∀ (v w : ↑(Kᶜ)),\n supp (connectedComponentMk (induce (Kᶜ) G) v) = supp (connectedComponentMk (induce (Kᶜ) G) w) →\n connectedComponentMk (induce (Kᶜ) G) v = connectedComponentMk (induce (Kᶜ) G) w",
"state_before": "V : Type u\nG :... | [
54,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/MonoidAlgebra/NoZeroDivisors.lean | AddMonoidAlgebra.Left.exists_add_of_mem_support_single_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝¹ : Semiring R\ninst✝ : AddLeftCancelSemigroup A\ng : AddMonoidAlgebra R A\na x : A\nhx : x ∈ (single a 1 * g).support\n⊢ ∃ b, b ∈ g.support ∧ a + b = x",
"tactic": "rwa [support_single_mul _ _ (fun y => by rw [one_mul] : ∀ y... | [
77,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Std/Data/Int/DivMod.lean | Int.ediv_eq_iff_eq_mul_right | [] | [
761,
66
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
759,
11
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_diff_Ioc_same | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43968\ninst✝ : PartialOrder α\na b c : α\nh : a ≤ b\n⊢ Icc a b \\ Ioc a b = {a}",
"tactic": "rw [← Icc_diff_left, diff_diff_cancel_left (singleton_subset_iff.2 <| left_mem_Icc.2 h)]"
}
] | [
826,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.foldr_swap | [] | [
1422,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
] |
Mathlib/Analysis/InnerProductSpace/Orthogonal.lean | Submodule.IsOrtho.mono_left | [] | [
291,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_plift_down | [] | [
234,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeFinset_subset_edgeFinset | [
{
"state_after": "no goals",
"state_before": "ι : Sort ?u.107664\n𝕜 : Type ?u.107667\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\nG₁ G₂ : SimpleGraph V\ninst✝² : Fintype ↑(edgeSet G)\ninst✝¹ : Fintype ↑(edgeSet G₁)\ninst✝ : Fintype ↑(edgeSet G₂)\n... | [
908,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.mem_ℒ1_toReal_of_lintegral_ne_top | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1070083\nγ : Type ?u.1070086\nδ : Type ?u.1070089\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf : α → ℝ≥0∞\nhfm : AEMeasurable f\nhfi : (∫⁻ (x : α), f x ∂μ) ≠ ⊤\n⊢ AEStronglyMeasurab... | [
990,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
985,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/FiniteProducts.lean | CategoryTheory.Limits.hasFiniteProducts_of_hasProducts | [] | [
62,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.one_snd | [] | [
258,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.dist_pointReflection_self | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nV : Type u_2\nV₁ : Type ?u.2089423\nV₂ : Type ?u.2089426\nV₃ : Type ?u.2089429\nV₄ : Type ?u.2089432\nP₁ : Type ?u.2089435\nP : Type u_1\nP₂ : Type ?u.2089441\nP₃ : Type ?u.2089444\nP₄ : Type ?u.2089447\ninst✝²¹ : NormedField 𝕜\ninst✝²⁰ : Seminor... | [
816,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
814,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.nhds_zero_basis_Iic | [] | [
205,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Std/Data/Int/Lemmas.lean | Int.lt_add_of_le_of_pos | [] | [
844,
53
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
843,
11
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_comm | [] | [
783,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | closedBall_one_mul_singleton | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx y : E\n⊢ closedBall 1 δ * {x} = closedBall x δ",
"tactic": "simp"
}
] | [
192,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Std/Data/Int/Lemmas.lean | Int.add_le_of_le_neg_add | [
{
"state_after": "a b c : Int\nh✝ : b ≤ -a + c\nh : a + b ≤ a + (-a + c)\n⊢ a + b ≤ c",
"state_before": "a b c : Int\nh : b ≤ -a + c\n⊢ a + b ≤ c",
"tactic": "have h := Int.add_le_add_left h a"
},
{
"state_after": "no goals",
"state_before": "a b c : Int\nh✝ : b ≤ -a + c\nh : a + b ≤ a + (-a... | [
952,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
950,
11
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.Admissible.one_lt_sumInv | [
{
"state_after": "pqr : Multiset ℕ+\n⊢ (∃ q r, A' q r = pqr) ∨ (∃ r, D' r = pqr) ∨ E' 3 = pqr ∨ E' 4 = pqr ∨ E' 5 = pqr → 1 < sumInv pqr",
"state_before": "pqr : Multiset ℕ+\n⊢ Admissible pqr → 1 < sumInv pqr",
"tactic": "rw [Admissible]"
},
{
"state_after": "case inl.intro.intro\npqr : Multiset... | [
173,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | exists_one_lt_mul_of_lt' | [
{
"state_after": "case intro\nα : Type u\ninst✝³ : MulOneClass α\ninst✝² : Preorder α\ninst✝¹ : ContravariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : ExistsMulOfLE α\na c : α\nh : a < a * c\n⊢ ∃ c_1, 1 < c_1 ∧ a * c_1 = a * c",
"state_before": "α : Type u\ninst✝³ : MulOneClass α\ninst✝... | [
62,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/PSeries.lean | Finset.le_sum_condensed' | [
{
"state_after": "case zero\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n → f n ≤ f m\n⊢ ∑ k in Ico 1 (2 ^ Nat.zero), f k ≤ ∑ k in range Nat.zero, 2 ^ k • f (2 ^ k)\n\ncase succ\nM : Type u_1\ninst✝ : OrderedAddCommMonoid M\nf : ℕ → M\nhf : ∀ ⦃m n : ℕ⦄, 0 < m → m ≤ n ... | [
63,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Topology/NhdsSet.lean | mem_nhdsSet_iff_exists | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9322\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ s ∈ 𝓝ˢ t ↔ ∃ U, IsOpen U ∧ t ⊆ U ∧ U ⊆ s",
"tactic": "rw [← subset_interior_iff_mem_nhdsSet, subset_interior_iff]"
}
] | [
71,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.constantCoeff_invOfUnit | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\nφ : PowerSeries R\nu : Rˣ\n⊢ ↑(constantCoeff R) (invOfUnit φ u) = ↑u⁻¹",
"tactic": "rw [← coeff_zero_eq_constantCoeff_apply, coeff_invOfUnit, if_pos rfl]"
}
] | [
1928,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1926,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_comap_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.260618\nι : Sort x\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Filter β\nm✝ : α → β\nm' : β → γ\ns : Set α\nt : Set β\nf : Filter β\nm : α → β\ninj : Injective m\nlarge : range m ∈ f\nS : Set α\n⊢ S ∈ comap m f ↔ m '' S ∈ f",
... | [
2307,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2305,
1
] |
Mathlib/LinearAlgebra/Alternating.lean | AlternatingMap.curryLeft_same | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1320421\ninst✝¹⁹ : Semiring R\nM : Type ?u.1320427\ninst✝¹⁸ : AddCommMonoid M\ninst✝¹⁷ : Module R M\nN : Type ?u.1320459\ninst✝¹⁶ : AddCommMonoid N\ninst✝¹⁵ : Module R N\nP : Type ?u.1320489\ninst✝¹⁴ : AddCommMonoid P\ninst✝¹³ : Module R P\nM' : Type... | [
1290,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1288,
1
] |
Mathlib/Topology/ContinuousFunction/CocompactMap.lean | CocompactMap.ext | [] | [
95,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_ssubset_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.93993\nγ : Type ?u.93996\ns✝ t : Set α\ninst✝¹ : Fintype α\ns : Set α\ninst✝ : Fintype ↑s\n⊢ toFinset s ⊂ Finset.univ ↔ s ⊂ univ",
"tactic": "rw [← coe_ssubset, coe_toFinset, coe_univ]"
}
] | [
765,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
764,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.toFun_equiv_empty | [] | [
1002,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_subset_smul_left | [] | [
1365,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
] |
Mathlib/Topology/List.lean | Vector.continuous_insertNth | [] | [
215,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Topology/Constructions.lean | continuous_update | [] | [
1251,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Algebra/Star/Basic.lean | semiconjBy_star_star_star | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Semigroup R\ninst✝ : StarSemigroup R\nx y z : R\n⊢ SemiconjBy (star x) (star z) (star y) ↔ SemiconjBy x y z",
"tactic": "simp_rw [SemiconjBy, ← star_mul, star_inj, eq_comm]"
}
] | [
152,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.subset_sInter | [] | [
1062,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1061,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.exp_nat_mul | [
{
"state_after": "no goals",
"state_before": "x✝ y x : ℂ\n⊢ exp (↑0 * x) = exp x ^ 0",
"tactic": "rw [Nat.cast_zero, zero_mul, exp_zero, pow_zero]"
},
{
"state_after": "no goals",
"state_before": "x✝ y x : ℂ\nn : ℕ\n⊢ exp (↑(Nat.succ n) * x) = exp x ^ Nat.succ n",
"tactic": "rw [pow_succ... | [
542,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Algebra/GeomSum.lean | mul_neg_geom_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Ring α\nx : α\nn : ℕ\n⊢ op ((1 - x) * ∑ i in range n, x ^ i) = op (1 - x ^ n)",
"tactic": "simpa using geom_sum_mul_neg (op x) n"
}
] | [
237,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_mul_right | [
{
"state_after": "no goals",
"state_before": "n k m : ℕ\n⊢ dist (n * k) (m * k) = dist n m * k",
"tactic": "rw [dist.def, dist.def, right_distrib, tsub_mul n, tsub_mul m]"
}
] | [
104,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_one' | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np : K[X]\n⊢ RatFunc.mk p 1 = { toFractionRing := ↑(algebraMap K[X] (FractionRing K[X])) p }",
"tactic": "rw [← IsLocalization.mk'_one (M := K[X]⁰) (FractionRing K[X]) p, ← mk_coe_def, Submonoid.coe_one]"
... | [
237,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | integrableOn_Ici_iff_integrableOn_Ioi' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.3648470\nE : Type u_2\nF : Type ?u.3648476\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : PartialOrder α\ninst✝ : MeasurableSingletonClass α\nf : α → E\nμ : MeasureTheory.Measure α\na b : α\nhb : ↑↑μ {b} ≠ ⊤\n⊢ Int... | [
666,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.neg_le | [
{
"state_after": "no goals",
"state_before": "a b : EReal\n⊢ -a ≤ b ↔ -b ≤ a",
"tactic": "rw [← neg_le_neg_iff, neg_neg]"
}
] | [
804,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
803,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | MulOpposite.norm_unop | [] | [
2614,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2613,
1
] |
Mathlib/Order/CompactlyGenerated.lean | complementedLattice_of_sSup_atoms_eq_top | [] | [
620,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
] |
Mathlib/Data/Int/Interval.lean | Int.card_fintype_Ioc_of_le | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\nh : a ≤ b\n⊢ ↑(Fintype.card ↑(Set.Ioc a b)) = b - a",
"tactic": "rw [card_fintype_Ioc, toNat_sub_of_le h]"
}
] | [
175,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/EpiMono.lean | CategoryTheory.IsSplitMono.id | [] | [
110,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/FieldTheory/Minpoly/Field.lean | minpoly.one | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\nB : Type u_2\ninst✝³ : Field A\ninst✝² : Ring B\ninst✝¹ : Algebra A B\nx : B\ninst✝ : Nontrivial B\n⊢ minpoly A 1 = X - 1",
"tactic": "simpa only [RingHom.map_one, C_1, sub_eq_add_neg] using eq_X_sub_C B (1 : A)"
}
] | [
232,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_pure | [] | [
1876,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1873,
1
] |
Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na✝ b : R\nn : ℕ\ninst✝¹ : Field R\np q : R[X]\nK : Type u_1\ninst✝ : Field K\nf : K[X]\na : K\nhf' : eval a (↑derivative f) ≠ 0\n⊢ ¬X - ↑C a ∣ f /ₘ (X - ↑C a)",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na✝ b : R\nn : ℕ\... | [
540,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_left_neg | [
{
"state_after": "no goals",
"state_before": "a b c : ℚ\nn : ℤ\nd : ℕ\nh : d ≠ 0\n⊢ -(n /. ↑d) + n /. ↑d = 0",
"tactic": "simp [h, mkRat_add_mkRat]"
}
] | [
227,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
11
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.norm_integral_le_of_norm_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12172012\n𝕜 : Type ?u.12172015\nE : Type u_1\nF : Type ?u.12172021\nA : Type ?u.12172024\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b : ℝ\nf g✝ : ℝ → E\nμ : MeasureTheory.Measure ℝ\ng : ℝ → ℝ\nh : ∀ᵐ (t : ℝ)... | [
563,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
8
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | HasFDerivAt.arctan | [] | [
174,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.comap_op_pow | [] | [
537,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/RingTheory/DedekindDomain/Basic.lean | Ring.DimensionLEOne.not_lt_lt | [] | [
80,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_map_comap | [] | [
1463,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1462,
1
] |
src/lean/Init/Data/Nat/Div.lean | Nat.mod_one | [
{
"state_after": "x : Nat\nh : x % 1 < 1\n⊢ x % 1 = 0",
"state_before": "x : Nat\n⊢ x % 1 = 0",
"tactic": "have h : x % 1 < 1 := mod_lt x (by decide)"
},
{
"state_after": "x : Nat\nh : x % 1 < 1\nthis : ∀ (y : Nat), y < 1 → y = 0\n⊢ x % 1 = 0",
"state_before": "x : Nat\nh : x % 1 < 1\n⊢ x % ... | [
164,
17
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
157,
1
] |
Mathlib/Analysis/Calculus/Conformal/InnerProduct.lean | conformalFactorAt_inner_eq_mul_inner' | [] | [
58,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.inv_image_trans_target | [] | [
850,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Topology/Algebra/ValuedField.lean | Valued.continuous_valuation | [
{
"state_after": "K : Type u_2\ninst✝² : DivisionRing K\nΓ₀ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\n⊢ ∀ (x : K), ContinuousAt (↑v) x",
"state_before": "K : Type u_2\ninst✝² : DivisionRing K\nΓ₀ : Type u_1\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\n... | [
130,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.mk_zero_smul | [] | [
283,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.polynomial_mem_ideal_of_coeff_mem_ideal | [] | [
520,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Std/Data/Int/DivMod.lean | Int.ofNat_mod_ofNat | [] | [
237,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
237,
1
] |
Mathlib/Algebra/CharP/Two.lean | CharTwo.multiset_sum_mul_self | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nι : Type ?u.17742\ninst✝¹ : CommSemiring R\ninst✝ : CharP R 2\nl : Multiset R\n⊢ Multiset.sum l * Multiset.sum l = Multiset.sum (Multiset.map (fun x => x * x) l)",
"tactic": "simp_rw [← pow_two, multiset_sum_sq]"
}
] | [
112,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.isCompact_of_isClosed_bounded | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nX : Type ?u.526468\nι : Type ?u.526471\ninst✝¹ : PseudoMetricSpace α\nx : α\nt : Set α\nr : ℝ\ninst✝ : ProperSpace α\nhc : IsClosed ∅\nhb : Bounded ∅\n⊢ IsCompact ∅\n\ncase inr.intro\nα : Type u\nβ : Type v\nX : Type ?u.526468\nι : Type ?u.526471\ninst✝¹ : Pse... | [
2517,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2512,
1
] |
Mathlib/Data/Rat/Lemmas.lean | Rat.add_num_den' | [
{
"state_after": "q r : ℚ\ns : ℚ := (q.num * ↑r.den + r.num * ↑q.den) /. (↑q.den * ↑r.den)\n⊢ (q + r).num * ↑q.den * ↑r.den = (q.num * ↑r.den + r.num * ↑q.den) * ↑(q + r).den",
"state_before": "q r : ℚ\n⊢ (q + r).num * ↑q.den * ↑r.den = (q.num * ↑r.den + r.num * ↑q.den) * ↑(q + r).den",
"tactic": "let s... | [
167,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
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