file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Finset/MulAntidiagonal.lean | Set.IsWf.min_mul | [
{
"state_after": "α : Type u_1\ns t : Set α\ninst✝ : LinearOrderedCancelCommMonoid α\nhs : IsWf s\nht : IsWf t\nhsn : Set.Nonempty s\nhtn : Set.Nonempty t\n⊢ min hs hsn * min ht htn ≤ min (_ : IsWf (s * t)) (_ : Set.Nonempty (s * t))",
"state_before": "α : Type u_1\ns t : Set α\ninst✝ : LinearOrderedCancelC... | [
48,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Topology/Instances/EReal.lean | EReal.embedding_coe | [
{
"state_after": "α : Type ?u.1666\ninst✝ : TopologicalSpace α\n⊢ OrdConnected (Ioo ⊥ ⊤)",
"state_before": "α : Type ?u.1666\ninst✝ : TopologicalSpace α\n⊢ OrdConnected (range Real.toEReal)",
"tactic": "rw [range_coe_eq_Ioo]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.1666\... | [
58,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.IsPwo.mono | [] | [
405,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
8
] |
Mathlib/Logic/Unique.lean | Option.subsingleton_iff_isEmpty | [] | [
268,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.degree_map | [
{
"state_after": "case pos\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝² : Semiring R\ninst✝¹ : Semiring S\ninst✝ : Nontrivial S\nP : R[X]\nhmo : Monic P\nf : R →+* S\nhP : P = 0\n⊢ degree (Polynomial.map f P) = degree P\n\ncase neg\nR : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝² :... | [
321,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
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Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.aeval_eq | [
{
"state_after": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf p : R[X]\nx : R\n⊢ ↑(algebraMap R (AdjoinRoot f)) x = ↑(mk f) (↑C x)",
"state_before": "R : Type u\nS : Type v\nK : Type w\ninst✝ : CommRing R\nf p : R[X]\nx : R\n⊢ ↑(aeval (root f)) (↑C x) = ↑(mk f) (↑C x)",
"tactic": "rw [aeva... | [
236,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.nat_cast_def | [] | [
274,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.IsCompactElement.exists_finset_of_le_iSup | [
{
"state_after": "ι✝ : Sort ?u.10018\nα : Type u_1\ninst✝ : CompleteLattice α\nf✝ : ι✝ → α\nk : α\nhk : IsCompactElement k\nι : Type u_2\nf : ι → α\nh : k ≤ ⨆ (i : ι), f i\ng : Finset ι → α := fun s => ⨆ (i : ι) (_ : i ∈ s), f i\n⊢ ∃ s, k ≤ ⨆ (i : ι) (_ : i ∈ s), f i",
"state_before": "ι✝ : Sort ?u.10018\nα... | [
170,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | SeminormFamily.basisSets_smul | [
{
"state_after": "case intro.intro.intro\n𝕜 : Type u_2\n𝕜₂ : Type ?u.63334\n𝕝 : Type ?u.63337\n𝕝₂ : Type ?u.63340\nE : Type u_1\nF : Type ?u.63346\nG : Type ?u.63349\nι : Type u_3\nι' : Type ?u.63355\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\ninst✝ : ... | [
167,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.nat_cast_le | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"tactic": "rw [← Cardinal.ord_nat, ← Cardinal.ord_nat, Cardinal.ord_le_ord, Cardinal.natCast_le]"
}
] | [
2306,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2305,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.add_right_comm | [
{
"state_after": "no goals",
"state_before": "n m k : Nat\n⊢ n + m + k = n + k + m",
"tactic": "rw [Nat.add_assoc, Nat.add_comm m k, ← Nat.add_assoc]"
}
] | [
146,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
145,
11
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.coe_max | [] | [
140,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.singleton_bind | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.11036\nδ : Type ?u.11039\na : α\ns t : Multiset α\nf g : α → Multiset β\n⊢ bind {a} f = f a",
"tactic": "simp [bind]"
}
] | [
115,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.algebraMap_ofSubsemiring | [] | [
515,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.congr_arg | [] | [
697,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.splits_codomain | [
{
"state_after": "case a\nk✝ : Type u\ninst✝³ : Field k✝\nk : Type u_1\nK : Type u_2\ninst✝² : Field k\ninst✝¹ : IsAlgClosed k\ninst✝ : Field K\nf : K →+* k\np : K[X]\n⊢ Splits f p ↔ Splits (RingHom.id k) (map f p)",
"state_before": "k✝ : Type u\ninst✝³ : Field k✝\nk : Type u_1\nK : Type u_2\ninst✝² : Field... | [
65,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Data/Finset/PiInduction.lean | Finset.induction_on_pi | [] | [
82,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.mem_iff_ultrafilter | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type ?u.37751\nf : Filter α\ns : Set α\na : α\nH : ∀ (g : Ultrafilter α), ↑g ≤ f → s ∈ g\nhf : ¬s ∈ f\n⊢ False",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.37751\nf : Filter α\ns : Set α\na : α\n⊢ s ∈ f ↔ ∀ (g : Ultrafilter α), ↑g ≤ f → s ∈ g",
"ta... | [
438,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_pow | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nea₁ b : ℕ\na₂ xa₁ : R\n⊢ (xa₁ ^ ea₁ * a₂) ^ b = xa₁ ^ (ea₁ * b) * a₂ ^ b",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nea₁ b ... | [
697,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.trans_right | [] | [
502,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.toSubsemiring_injective | [
{
"state_after": "no goals",
"state_before": "R' : Type u'\nR : Type u\nA : Type v\nB : Type w\nC : Type w'\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Algebra R A\ninst✝³ : Semiring B\ninst✝² : Algebra R B\ninst✝¹ : Semiring C\ninst✝ : Algebra R C\nS T : Subalgebra R A\nh : S.toSubsemiring = T.... | [
81,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.degree_map_eq_of_leadingCoeff_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q r : R[X]\ninst✝ : Semiring S\nf✝ f : R →+* S\nhf : ↑f (leadingCoeff p) ≠ 0\nhp0 : p ≠ 0\n⊢ degree p ≤ degree (map f p)",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n ... | [
879,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.reaches₁_fwd | [
{
"state_after": "case intro.intro\nσ : Type u_1\nf : σ → Option σ\na b c : σ\nh₁ : Reaches₁ f a c\nh₂ : b ∈ f a\nb' : σ\nhab : b' ∈ f a\nhbc : ReflTransGen (fun a b => b ∈ f a) b' c\n⊢ Reaches f b c",
"state_before": "σ : Type u_1\nf : σ → Option σ\na b c : σ\nh₁ : Reaches₁ f a c\nh₂ : b ∈ f a\n⊢ Reaches f... | [
771,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Std/Data/Int/Lemmas.lean | Int.natAbs_sub_le | [
{
"state_after": "a b : Int\n⊢ natAbs (a - b) ≤ natAbs a + natAbs (-b)",
"state_before": "a b : Int\n⊢ natAbs (a - b) ≤ natAbs a + natAbs b",
"tactic": "rw [← Int.natAbs_neg b]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ natAbs (a - b) ≤ natAbs a + natAbs (-b)",
"tacti... | [
1352,
47
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1351,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | CompleteLattice.Independent.subtype_ne_bot_le_rank | [
{
"state_after": "K : Type u\nV✝ V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.220324\nR : Type u\ninst✝⁸ : Ring R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nM' : Type v'\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : Module R M'\nM₁ : Type v\n... | [
462,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.IsTheta.div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.44608\nE : Type ?u.44611\nF : Type ?u.44614\nG : Type ?u.44617\nE' : Type ?u.44620\nF' : Type ?u.44623\nG' : Type ?u.44626\nE'' : Type ?u.44629\nF'' : Type ?u.44632\nG'' : Type ?u.44635\nR : Type ?u.44638\nR' : Type ?u.44641\n𝕜 : Type ... | [
245,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.IsPath.nil | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu : V\n⊢ IsPath Walk.nil",
"tactic": "constructor <;> simp"
}
] | [
965,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
965,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelHom.coe_fn_injective | [] | [
127,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/NhdsSet.lean | nhdsSet_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12597\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns t s₁ s₂ t₁ t₂ : Set α\nx : α\n⊢ 𝓝ˢ univ = ⊤",
"tactic": "rw [isOpen_univ.nhdsSet_eq, principal_univ]"
}
] | [
118,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Order/SymmDiff.lean | sup_sdiff_symmDiff | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.59418\nα : Type u_1\nβ : Type ?u.59424\nπ : ι → Type ?u.59429\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\n⊢ (a ⊔ b) \\ (a ⊓ b) = a ∆ b",
"tactic": "rw [symmDiff_eq_sup_sdiff_inf]"
}
] | [
398,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_mem_eq_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.372476\nγ : Type ?u.372479\np q : α → Prop\ninst✝³ : DecidablePred p\ninst✝² : DecidablePred q\ninst✝¹ : DecidableEq α\ns t : Finset α\ninst✝ : (i : α) → Decidable (i ∈ t)\ni : α\n⊢ i ∈ filter (fun i => i ∈ t) s ↔ i ∈ s ∩ t",
"tacti... | [
2822,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2820,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.mem_iff' | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.17778\nγ : Type ?u.17781\na b c w✝ : α\nh : Quotient.mk (Rel.setoid α) (b, c) = Quotient.mk (Rel.setoid α) (a, w✝)\n⊢ a = b ∨ a = c",
"state_before": "α : Type u_1\nβ : Type ?u.17778\nγ : Type ?u.17781\na b c : α\n⊢ Sym2.Mem a (Quotient.mk (Rel.setoid ... | [
301,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Order/Bounds/Basic.lean | lowerBounds_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝¹ : Preorder α\ninst✝ : Preorder β\ns✝ t : Set α\na✝ b a : α\ns : Set α\n⊢ lowerBounds (insert a s) = Iic a ∩ lowerBounds s",
"tactic": "rw [insert_eq, lowerBounds_union, lowerBounds_singleton]"
}
] | [
979,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
977,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.rotateR_node | [] | [
280,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombination_filter_of_ne | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.369441\ns₂ : Finset ι₂\nw : ι → k\np : ι → P\npred : ι → Prop\ninst✝ : DecidablePred pred\nh : ... | [
572,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.map_add | [] | [
956,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.coe_neg | [] | [
256,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
11
] |
Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.radius_eq_top_iff_summable_norm | [
{
"state_after": "case mp\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.244081\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\np✝ : FormalM... | [
326,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/Fin/Tuple/Reflection.lean | FinVec.etaExpand_eq | [] | [
92,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
src/lean/Init/Core.lean | Squash.ind | [] | [
1590,
13
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1589,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.dropUntil_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v' w' : V\np : Walk G v' w'\nh : u ∈ support (Walk.copy p (_ : v' = v') (_ : w' = w'))\n⊢ u ∈ support p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG... | [
1130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1126,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.HeapNode.WellFormed.rank_eq | [] | [
431,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
428,
9
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.le_sub_of_add_le_left | [] | [
1161,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.ext_iff | [] | [
82,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/ContinuousFunction/Ordered.lean | ContinuousMap.inf'_apply | [] | [
141,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.exists_finset_toPouFun_eventuallyEq | [
{
"state_after": "case intro.intro\nι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\nx : X\nU : Set X\nhU : U ∈ 𝓝 x\nhf : Set.Finite {i | Set.Nonempty ((fun i => support ↑(toFun s f i)) i ∩ U)}\n⊢ ∃ t, toPouFun f i =ᶠ[𝓝 x] ↑(toFun s f i) * ↑(∏ j in Finset.filter (f... | [
423,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_eq_self_of_subset_right | [] | [
813,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
812,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | div_mul_le_div_mul_of_div_le_div | [
{
"state_after": "ι : Type ?u.107585\nα : Type u_1\nβ : Type ?u.107591\ninst✝ : LinearOrderedSemifield α\na b c d e : α\nm n : ℤ\nh : a / b ≤ c / d\nhe : 0 ≤ e\n⊢ a / b * (1 / e) ≤ c / d * (1 / e)",
"state_before": "ι : Type ?u.107585\nα : Type u_1\nβ : Type ?u.107591\ninst✝ : LinearOrderedSemifield α\na b ... | [
564,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
561,
1
] |
Std/Data/Int/Lemmas.lean | Int.neg_le_sub_right_of_le_add | [] | [
1025,
59
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1024,
11
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.pow_mono | [
{
"state_after": "case zero\nR : Type u\nι : Type ?u.295460\ninst✝ : CommSemiring R\nI✝ J✝ K L I J : Ideal R\ne : I ≤ J\n⊢ I ^ Nat.zero ≤ J ^ Nat.zero\n\ncase succ\nR : Type u\nι : Type ?u.295460\ninst✝ : CommSemiring R\nI✝ J✝ K L I J : Ideal R\ne : I ≤ J\nn✝ : ℕ\nhn : I ^ n✝ ≤ J ^ n✝\n⊢ I ^ Nat.succ n✝ ≤ J ^ N... | [
803,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
799,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_finset_bUnion_disjoint | [] | [
785,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_nonpos_of_nonpos_of_nonneg | [
{
"state_after": "a b : Int\nha : a ≤ 0\nhb : 0 ≤ b\nh : a * b ≤ 0 * b\n⊢ a * b ≤ 0",
"state_before": "a b : Int\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a * b ≤ 0",
"tactic": "have h : a * b ≤ 0 * b := Int.mul_le_mul_of_nonneg_right ha hb"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nha : ... | [
1186,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1183,
11
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_apply | [
{
"state_after": "case h₀\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.154448\nι : Type ?u.154451\nM : Type u_3\nM' : Type ?u.154457\nN : Type ?u.154460\nP : Type ?u.154463\nG : Type ?u.154466\nH : Type ?u.154469\nR : Type ?u.154472\nS : Type ?u.154475\ninst✝ : AddCommMonoid M\nv v₁ v₂ : α →₀ M\nf : α → β\nhf : Inj... | [
458,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Analysis/Normed/Group/InfiniteSum.lean | nnnorm_tsum_le | [] | [
158,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/List/Basic.lean | List.concat_eq_reverse_cons | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.26992\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : List α\n⊢ concat l a = reverse (a :: reverse l)",
"tactic": "simp only [concat_eq_append, reverse_cons, reverse_reverse]"
}
] | [
642,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Analysis/Normed/Field/Basic.lean | mulRight_bound | [
{
"state_after": "α : Type u_1\nβ : Type ?u.44527\nγ : Type ?u.44530\nι : Type ?u.44533\ninst✝ : NonUnitalSeminormedRing α\nx y : α\n⊢ ‖↑(AddMonoidHom.mulRight x) y‖ ≤ ‖y‖ * ‖x‖",
"state_before": "α : Type u_1\nβ : Type ?u.44527\nγ : Type ?u.44530\nι : Type ?u.44533\ninst✝ : NonUnitalSeminormedRing α\nx y :... | [
234,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.abs_tendsto_atTop_iff | [] | [
105,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.sInf_glb | [
{
"state_after": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\nS : Set (LieSubalgebra R L)\nh : ∀ (K K' : LieSubalgebra R L), ↑K ≤ ↑K' ↔ K ≤ ... | [
511,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_of_neg | [] | [
231,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberPrebundle.isOpen_source | [
{
"state_after": "ι : Type ?u.57301\nB : Type u_1\nF : Type u_2\nX : Type ?u.57310\ninst✝³ : TopologicalSpace X\nE : B → Type u_3\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\ninst✝ : (x : B) → TopologicalSpace (E x)\na : FiberPrebundle F E\ne✝ e e' : Pretrivialization F TotalSpace.proj\nx✝ : e' ∈ ... | [
821,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/Data/List/Basic.lean | List.length_enum | [] | [
3819,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3818,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.isPrimitiveClassified_of_coprime_of_zero_left | [
{
"state_after": "y z : ℤ\nh : PythagoreanTriple 0 y z\nhc : Int.gcd 0 y = 1\n⊢ IsPrimitiveClassified h",
"state_before": "x y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhx : x = 0\n⊢ IsPrimitiveClassified h",
"tactic": "subst x"
},
{
"state_after": "y z : ℤ\nh : PythagoreanTriple... | [
252,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Order/Height.lean | Set.chainHeight_add_le_chainHeight_add | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LT α\ninst✝ : LT β\ns✝ t✝ : Set α\nl : List α\na : α\ns : Set α\nt : Set β\nn m : ℕ\nH : ∀ (l : List α), l ∈ subchain s → ∃ l', l' ∈ subchain t ∧ length l + n ≤ length l' + m\n⊢ chainHeight s + ↑n ≤ chainHeight t + ↑m",
"state_before": "α : Type u_1\nβ ... | [
187,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_le_rpow_of_exponent_le | [
{
"state_after": "x y z : ℝ\nhx : 1 ≤ x\nhyz : y ≤ z\n⊢ exp (log x * y) ≤ exp (log x * z)",
"state_before": "x y z : ℝ\nhx : 1 ≤ x\nhyz : y ≤ z\n⊢ x ^ y ≤ x ^ z",
"tactic": "repeat' rw [rpow_def_of_pos (lt_of_lt_of_le zero_lt_one hx)]"
},
{
"state_after": "x y z : ℝ\nhx : 1 ≤ x\nhyz : y ≤ z\n⊢ l... | [
477,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Analysis/Calculus/Deriv/AffineMap.lean | AffineMap.hasDerivAtFilter | [
{
"state_after": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 →ᵃ[𝕜] E\na b : E\nL : Filter 𝕜\ns : Set 𝕜\nx : 𝕜\n⊢ HasDerivAtFilter (↑f.linear + fun x => ↑f 0) (↑f.linear 1) x L",
"state_before": "𝕜 : Type u_1\ninst✝² ... | [
38,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_le' | [] | [
766,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Data/List/OfFn.lean | List.get?_ofFn | [
{
"state_after": "α : Type u\nn : ℕ\nf : Fin n → α\ni : ℕ\nh : i < length (ofFn f)\n⊢ some (f (↑(Fin.cast (_ : length (ofFn f) = n)) { val := i, isLt := h })) = ofFnNthVal f i",
"state_before": "α : Type u\nn : ℕ\nf : Fin n → α\ni : ℕ\nh : i < length (ofFn f)\n⊢ get? (ofFn f) i = ofFnNthVal f i",
"tacti... | [
69,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\nh : mirror p = 0\n⊢ p = 0",
"tactic": "rw [← p.mirror_mirror, h, mirror_zero]"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\nh : p = 0\n⊢ mirror p = 0"... | [
148,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.forall_image | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.62593\ninst✝ : DecidableEq β\nf g : α → β\ns : Finset α\nt : Finset β\na : α\nb c : β\np : β → Prop\n⊢ (∀ (b : β), b ∈ image f s → p b) ↔ ∀ (a : α), a ∈ s → p (f a)",
"tactic": "simp only [mem_image, forall_exists_inde... | [
336,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Order/Heyting/Hom.lean | BiheytingHom.toFun_eq_coe_aux | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
517,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinite_of_infinitesimal_inv | [
{
"state_after": "case inl\nx : ℝ*\nh0 : x ≠ 0\nhi : Infinitesimal x⁻¹\nhn : x < 0\n⊢ Infinite x\n\ncase inr\nx : ℝ*\nh0 : x ≠ 0\nhi : Infinitesimal x⁻¹\nhp : x > 0\n⊢ Infinite x",
"state_before": "x : ℝ*\nh0 : x ≠ 0\nhi : Infinitesimal x⁻¹\n⊢ Infinite x",
"tactic": "cases' lt_or_gt_of_ne h0 with hn hp"... | [
763,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
759,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.binaryRec_eq | [
{
"state_after": "C : ℕ → Sort u\nz : C 0\nf : (b : Bool) → (n : ℕ) → C n → C (bit b n)\nh : f false 0 z = z\nb : Bool\nn : ℕ\n⊢ (if n0 : bit b n = 0 then Eq.mpr (_ : C (bit b n) = C 0) z\n else\n let n' := div2 (bit b n);\n let_fun _x := (_ : bit (bodd (bit b n)) (div2 (bit b n)) = bit b n);\n ... | [
383,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousOn.cpow | [] | [
149,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/GroupTheory/Torsion.lean | IsTorsionFree.not_torsion | [
{
"state_after": "case intro\nG : Type u_1\nH : Type ?u.211777\ninst✝ : Group G\nhN : Nontrivial G\ntfG : IsTorsionFree G\nx : G\nhx : x ≠ 1\n⊢ ∃ g, ¬IsOfFinOrder g",
"state_before": "G : Type u_1\nH : Type ?u.211777\ninst✝ : Group G\nhN : Nontrivial G\ntfG : IsTorsionFree G\n⊢ ∃ g, ¬IsOfFinOrder g",
"t... | [
397,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/CategoryTheory/Triangulated/Pretriangulated.lean | CategoryTheory.Pretriangulated.comp_dist_triangle_mor_zero₂₃ | [] | [
146,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/Order/Basic.lean | pi_Ici_mem_nhds | [] | [
1469,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.tails_eq_iterate | [] | [
682,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
681,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.monomial_natDegree_leadingCoeff_eq_self | [
{
"state_after": "case intro.intro\nR : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝ : Semiring R\nq : R[X]\nι : Type ?u.661802\nn : ℕ\na : R\nh : card (support (↑(monomial n) a)) ≤ 1\n⊢ ↑(monomial (natDegree (↑(monomial n) a))) (leadingCoeff (↑(monomial n) a)) = ↑(monomial n) a",
"state_before": "R : ... | [
964,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Analysis/Convex/Combination.lean | Finset.centerMass_smul | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nE : Type u_1\nF : Type ?u.34119\nι : Type u_3\nι' : Type ?u.34125\nα : Type ?u.34128\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Module R F\ni... | [
81,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Order/Field/Power.lean | Odd.zpow_nonpos_iff | [
{
"state_after": "case intro\nα : Type u_1\ninst✝ : LinearOrderedField α\na b c d : α\nn k : ℤ\nhk : n = 2 * k + 1\n⊢ a ^ n ≤ 0 ↔ a ≤ 0",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nhn : Odd n\n⊢ a ^ n ≤ 0 ↔ a ≤ 0",
"tactic": "cases' hn with k hk"
},
{
"state... | [
198,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Data/Nat/Factors.lean | Nat.factors_one | [
{
"state_after": "no goals",
"state_before": "⊢ factors 1 = []",
"tactic": "rw [factors]"
}
] | [
52,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.Functor.hext | [] | [
202,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.dvd_iff_mod_eq_zero | [] | [
727,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
726,
1
] |
Mathlib/Topology/LocalAtTarget.lean | isOpen_iff_inter_of_iSup_eq_top | [
{
"state_after": "case mp\nα : Type ?u.13206\nβ : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns✝ : Set β\nι : Type ?u.13225\nU : ι → Opens β\nhU : iSup U = ⊤\ns : Set β\n⊢ IsOpen s → ∀ (i : ι), IsOpen (s ∩ ↑(U i))\n\ncase mpr\nα : Type ?u.13206\nβ : Type u_1\ninst✝¹ : Topologic... | [
90,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.comap_id | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.9782\nN : Type ?u.9785\nP : Type u_1\ninst✝² : MulOneClass M\ninst✝¹ : MulOneClass N\ninst✝ : MulOneClass P\nS✝ : Submonoid M\nF : Type ?u.9809\nmc : MonoidHomClass F M N\nS : Submonoid P\n⊢ ∀ (x : P), x ∈ comap (MonoidHom.id P) S ↔ x ∈ S",
"tact... | [
213,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/Hom/Open.lean | ContinuousOpenMap.coe_id | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.induction_on''' | [] | [
430,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/CategoryTheory/Abelian/Exact.lean | CategoryTheory.Abelian.Exact.op | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nh : Exact f g\n⊢ g.op ≫ f.op = 0 ∧ kernel.ι f.op ≫ cokernel.π g.op = 0",
"state_before": "C : Type u₁\ninst✝¹ : Category C\ninst✝ : Abelian C\nX Y Z : C\nf : X ⟶ Y\ng : Y ⟶ Z\nh : Exact f g\n⊢ Exact g.op ... | [
303,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x = 0 ∨ y ≠ 0\n⊢ ‖y‖ / (‖y‖ / ‖x‖) = ‖x‖",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x = 0 ∨ y ≠ ... | [
228,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | isPiSystem_prod | [] | [
156,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.lim_const | [] | [
364,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.normalClosure_closure_eq_normalClosure | [] | [
2526,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2524,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_comp_mul_deriv'' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1940354\n𝕜 : Type ?u.1940357\nE : Type ?u.1940360\nF : Type ?u.1940363\nA : Type ?u.1940366\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nf✝¹ : ℝ → E\ng' g✝ φ : ℝ → ℝ\nf✝ f'✝ : ℝ → E\na b : ℝ\nf f' g : ℝ → ℝ\nhf ... | [
1480,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1476,
1
] |
Mathlib/Order/MinMax.lean | max_le_iff | [] | [
52,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_range_of_tendsto_cofinite_uniformity | [
{
"state_after": "case intro.intro\nα : Type u\nβ : Type v\nX : Type ?u.494672\nι : Type ?u.494675\ninst✝ : PseudoMetricSpace α\nx : α\ns✝ t : Set α\nr : ℝ\nf : β → α\nhf : Tendsto (Prod.map f f) (Filter.cofinite ×ˢ Filter.cofinite) (𝓤 α)\ns : Set β\nhsf : Set.Finite s\nhs1 : ∀ (x : β × β), x ∈ sᶜ ×ˢ sᶜ → Prod... | [
2430,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2423,
1
] |
Mathlib/Algebra/GradedMonoid.lean | List.dProd_monoid | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nR : Type u_3\nα : Type u_1\ninst✝¹ : AddMonoid ι\ninst✝ : Monoid R\nl : List α\nfι : α → ι\nfA : α → R\n⊢ dProd l fι fA = prod (map fA l)",
"tactic": "match l with\n| [] =>\n rw [List.dProd_nil, List.map_nil, List.prod_nil]\n rfl\n| head::tai... | [
478,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
470,
1
] |
Mathlib/RingTheory/DedekindDomain/Dvr.lean | IsLocalization.AtPrime.discreteValuationRing_of_dedekind_domain | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.45003\nA : Type u_1\nK : Type ?u.45009\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : IsDomain A\ninst✝⁵ : Field K\ninst✝⁴ : IsDedekindDomain A\nP : Ideal A\nhP : P ≠ ⊥\npP : Ideal.IsPrime P\nAₘ : Type u_2\ninst✝³ : CommRing Aₘ\ninst✝² : IsDomai... | [
146,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Algebra.mul_smul_comm | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type ?u.319925\ninst✝⁵ : CommSemiring R\ninst✝⁴ : CommSemiring S\ninst✝³ : Semiring A\ninst✝² : Algebra R A\ninst✝¹ : Semiring B\ninst✝ : Algebra R B\ns : R\nx y : A\n⊢ x * s • y = s • (x * y)",
"tactic": "rw [smul_def... | [
393,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
11
] |
Mathlib/Data/Set/Basic.lean | Set.union_nonempty | [] | [
508,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/Order/Bounds/Basic.lean | subset_lowerBounds_upperBounds | [] | [
258,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
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