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/Order/Filter/Basic.lean | Filter.map_top | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.249964\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 : α → β\n⊢ map f ⊤ = 𝓟 (range f)",
"tactic": "rw [← principal_univ, map_principal, image_univ]"
}
] | [
2178,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2177,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.top_mul_top | [] | [
710,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.snd_surjective | [] | [
146,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/Algebra/UniformGroup.lean | group_separationRel | [
{
"state_after": "α : Type u_1\nβ : Type ?u.178136\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : UniformGroup α\nx y : α\nthis : Embedding fun a => a * (y / x)\n⊢ ((x, y) ∈ ⋂ (U : Set α) (_ : U ∈ 𝓝 1), (fun x => x.snd / x.fst) ⁻¹' U) ↔\n x / y ∈ (fun a => a * (y / x)) ⁻¹' closure ((fun a => a * (y / x... | [
379,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_le_map_iff_slope_le_slope_left | [] | [
224,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearMap.ker_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.1248475\nR₂ : Type u_3\nR₃ : Type ?u.1248481\nR₄ : Type ?u.1248484\nS : Type ?u.1248487\nK : Type ?u.1248490\nK₂ : Type ?u.1248493\nM : Type u_1\nM' : Type ?u.1248499\nM₁ : Type ?u.1248502\nM₂ : Type u_4\nM₃ : Type ?u.1248508\nM₄ : Typ... | [
1399,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.mul | [] | [
1588,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_swap' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nx y : α\nH : x = y\n⊢ ↑sign (swap x y) = if x = y then 1 else -1",
"tactic": "simp [H, swap_self]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ ... | [
584,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Std/Logic.lean | And.imp_left | [] | [
152,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
152,
1
] |
Mathlib/Algebra/Order/WithZero.lean | div_le_iff₀ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d x y z : α\ninst✝ : LinearOrderedCommGroupWithZero α\nhc : c ≠ 0\n⊢ a / c ≤ b ↔ a ≤ b * c",
"tactic": "rw [div_eq_mul_inv, mul_inv_le_iff₀ hc]"
}
] | [
253,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
252,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.not_infinite_of_exists_st | [] | [
293,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | mem_tangentCone_of_openSegment_subset | [
{
"state_after": "𝕜 : Type ?u.89534\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type ?u.89540\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type ?u.89635\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_1\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nx✝ y✝ : E\ns✝... | [
243,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.two_le_iff | [
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ 2 ≤ 0 ↔ 0 ≠ 0 ∧ 0 ≠ 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\n⊢ 2 ≤ 1 ↔ 1 ≠ 0 ∧ 1 ≠ 1",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "m n✝ k l n : ℕ\n⊢ 2 ... | [
168,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Logic/Equiv/Functor.lean | Bifunctor.mapEquiv_apply | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/BoxIntegral/Box/Basic.lean | BoxIntegral.Box.le_def | [] | [
153,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/RingTheory/ChainOfDivisors.lean | DivisorChain.exists_chain_of_prime_pow | [
{
"state_after": "case refine'_1\nM : Type u_1\ninst✝ : CancelCommMonoidWithZero M\np : Associates M\nn : ℕ\nhn : n ≠ 0\nhp : Prime p\n⊢ (fun i => p ^ ↑i) 1 = p\n\ncase refine'_2\nM : Type u_1\ninst✝ : CancelCommMonoidWithZero M\np : Associates M\nn✝ : ℕ\nhn : n✝ ≠ 0\nhp : Prime p\nn m : Fin (n✝ + 1)\nh : n < m... | [
85,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_insert_of_eq_one_if_not_mem | [
{
"state_after": "case pos\nι : Type ?u.267066\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf g : α → β\ninst✝¹ : CommMonoid β\ninst✝ : DecidableEq α\nh : ¬a ∈ s → f a = 1\nhm : a ∈ s\n⊢ ∏ x in insert a s, f x = ∏ x in s, f x\n\ncase neg\nι : Type ?u.267066\nβ : Type u\nα : Type v\nγ : Type w... | [
332,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Topology/Algebra/Module/CharacterSpace.lean | WeakDual.CharacterSpace.coe_coe | [] | [
72,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
11
] |
Std/Data/Int/Lemmas.lean | Int.le_of_add_le_add_left | [
{
"state_after": "a b c : Int\nh : a + b ≤ a + c\nthis : -a + (a + b) ≤ -a + (a + c)\n⊢ b ≤ c",
"state_before": "a b c : Int\nh : a + b ≤ a + c\n⊢ b ≤ c",
"tactic": "have : -a + (a + b) ≤ -a + (a + c) := Int.add_le_add_left h _"
},
{
"state_after": "a b c : Int\nh : a + b ≤ a + c\nthis : b ≤ c\n... | [
766,
13
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
763,
11
] |
Mathlib/Data/Finset/Lattice.lean | Finset.induction_on_min_value | [] | [
1685,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1683,
1
] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.lipschitz | [
{
"state_after": "V : Type ?u.232658\nV₁ : Type u_1\nV₂ : Type u_2\nV₃ : Type ?u.232667\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : SeminormedAddCommGroup V₁\ninst✝¹ : SeminormedAddCommGroup V₂\ninst✝ : SeminormedAddCommGroup V₃\nf g : NormedAddGroupHom V₁ V₂\nx y : V₁\n⊢ ‖↑f (x - y)‖ ≤ ↑{ val := ‖f‖, property... | [
265,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.Bicone.toCocone_pt | [] | [
131,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean | CategoryTheory.Limits.has_colimits_of_finite_and_filtered | [] | [
90,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/LinearAlgebra/Matrix/Reindex.lean | Matrix.reindexLinearEquiv_apply | [] | [
55,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Data/Finsupp/Interval.lean | Finsupp.card_Iio | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝¹ : CanonicallyOrderedAddMonoid α\ninst✝ : LocallyFiniteOrder α\nf : ι →₀ α\n⊢ card (Iio f) = ∏ i in f.support, card (Iic (↑f i)) - 1",
"tactic": "rw [card_Iio_eq_card_Iic_sub_one, card_Iic]"
}
] | [
143,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.pullbackConeOfRightIso_snd | [] | [
1701,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1701,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.map_id | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.169501\nm inst✝³ : MeasurableSpace α\ninst✝² : MeasurableSpace β\nM : Type u_2\ninst✝¹ : AddCommMonoid M\ninst✝ : TopologicalSpace M\nv : VectorMeasure α M\ni : Set α\nhi : MeasurableSet i\n⊢ ↑(map v id) i = ↑v i",
"tactic": "rw [ma... | [
594,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | Filter.EventuallyEq.contDiffWithinAt_iff | [] | [
471,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.eventually_sub_nonneg | [] | [
1772,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1770,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.map_mem_map | [] | [
802,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Std/Data/List/Init/Lemmas.lean | List.take_length | [] | [
149,
97
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
149,
9
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | real_inner_self_nonpos | [] | [
627,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
626,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.surjective_of_right_cancellable_Prop | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\nγ : Sort ?u.7146\nf : α → β\nh : (fun y => ∃ x, f x = y) = fun x => True\n⊢ Surjective f",
"state_before": "α : Sort u_1\nβ : Sort u_2\nγ : Sort ?u.7146\nf : α → β\nh : ∀ (g₁ g₂ : β → Prop), g₁ ∘ f = g₂ ∘ f → g₁ = g₂\n⊢ Surjective f",
"tactic": "specialize h... | [
238,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
235,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.apply_coe_mem_map | [] | [
721,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
720,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | UniformSpace.Completion.continuous_coe | [] | [
450,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | DistribMulActionHom.coe_toLinearMap | [] | [
661,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | piiUnionInter_mono_left | [] | [
468,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.biUnion_subset_biUnion_left | [] | [
878,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_vert_isIso | [] | [
877,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
] |
Mathlib/Data/Quot.lean | Quotient.liftOn₂_mk | [] | [
338,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.eqToIso_trans | [
{
"state_after": "case w\nC : Type u₁\ninst✝ : Category C\nX Y Z : C\np : X = Y\nq : Y = Z\n⊢ (eqToIso p ≪≫ eqToIso q).hom = (eqToIso (_ : X = Z)).hom",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y Z : C\np : X = Y\nq : Y = Z\n⊢ eqToIso p ≪≫ eqToIso q = eqToIso (_ : X = Z)",
"tactic": "ext"
}... | [
145,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_zero_apply | [] | [
50,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.diam_range | [
{
"state_after": "ι : Type ?u.61000\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nf : α → β\nhf : Isometry f\n⊢ Metric.diam (f '' univ) = Metric.diam univ",
"state_before": "ι : Type ?u.61000\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\... | [
231,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | NormedCommGroup.nhds_basis_norm_lt | [
{
"state_after": "𝓕 : Type ?u.128861\n𝕜 : Type ?u.128864\nα : Type ?u.128867\nι : Type ?u.128870\nκ : Type ?u.128873\nE : Type u_1\nF : Type ?u.128879\nG : Type ?u.128882\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nx : E\n⊢ H... | [
766,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_neg_atTop_atBot | [] | [
848,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
847,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_biUnion_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.539269\ninst✝ : DecidableEq β\ns✝ s₁ s₂ : Finset α\nt✝ t₁ t₂ : α → Finset β\ns : Finset β\nt : Finset α\nf : α → Finset β\n⊢ _root_.Disjoint s (Finset.biUnion t f) ↔ ∀ (i : α), i ∈ t → _root_.Disjoint s (f i)",
"tactic... | [
3683,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3681,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.mem_of_get_eq | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nh✝ : Terminates s\na : α\nh : get s = a\n⊢ a ∈ s",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Computation α\nh : Terminates s\na : α\n⊢ get s = a → a ∈ s",
"tactic": "intro h"
},
{
"state_after": "α : Type u\n... | [
472,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/Convex/Segment.lean | openSegment_eq_image' | [
{
"state_after": "case h.e'_3.h\n𝕜 : Type u_2\nE : Type u_1\nF : Type ?u.80863\nG : Type ?u.80866\nι : Type ?u.80869\nπ : ι → Type ?u.80874\ninst✝⁵ : OrderedRing 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : AddCommGroup F\ninst✝² : AddCommGroup G\ninst✝¹ : Module 𝕜 E\ninst✝ : Module 𝕜 F\nx y : E\na✝¹ : 𝕜\na✝ : a✝¹... | [
221,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/List/Zip.lean | List.unzip_swap | [
{
"state_after": "α : Type u\nβ : Type u_1\nγ : Type ?u.85279\nδ : Type ?u.85282\nε : Type ?u.85285\nl : List (α × β)\n⊢ (map (Prod.fst ∘ Prod.swap) l, map (Prod.snd ∘ Prod.swap) l) = Prod.swap (map Prod.fst l, map Prod.snd l)",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.85279\nδ : Type ?u.85282... | [
225,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.sub_top | [] | [
846,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
845,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1SCLM_congr_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.794201\nG : Type ?u.794204\n𝕜 : Type ?u.794207\np : ℝ≥0∞\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace ℝ E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedSpace ℝ F\ninst✝⁵ : NormedAddCommGroup F'\nin... | [
910,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.not_rotate | [] | [
412,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.map_add_atTop_eq_nat | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.342691\nι' : Type ?u.342694\nα : Type ?u.342697\nβ : Type ?u.342700\nγ : Type ?u.342703\nk a : ℕ\nh : a ≥ k\n⊢ a ≤ (fun a => a - k) a + k",
"tactic": "rw [tsub_add_cancel_of_le h]"
}
] | [
1641,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1639,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.eq_of_src | [] | [
86,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Convex/Star.lean | starConvex_iInter | [] | [
120,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.edist_le_of_le | [] | [
120,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.mem_center_iff | [] | [
801,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Algebra/Field/Basic.lean | add_div | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.34\nK : Type ?u.37\ninst✝ : DivisionSemiring α\na✝ b✝ c✝ d a b c : α\n⊢ (a + b) / c = a / c + b / c",
"tactic": "simp_rw [div_eq_mul_inv, add_mul]"
}
] | [
32,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.LiftRelAux.swap | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : α → β → Prop\nC : Computation α → Computation β → Prop\na : α ⊕ Computation α\nb : β ⊕ Computation β\n⊢ LiftRelAux (Function.swap R) (Function.swap C) b a = LiftRelAux R C a b",
"tactic": "cases' a with a ca <;> cases'... | [
1276,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Geometry/Euclidean/Inversion.lean | EuclideanGeometry.dist_inversion_inversion | [
{
"state_after": "V : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\na b c d x y z : P\nR✝ : ℝ\nhx : x ≠ c\nhy : y ≠ c\nR : ℝ\n⊢ dist ((R / dist x c) ^ 2 • (x -ᵥ c) +ᵥ c) ((R / dist y c) ^ 2 • (y -ᵥ c) +ᵥ c) =\n R ^ ... | [
114,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Order/Cover.lean | apply_wcovby_apply_iff | [] | [
134,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.compSL_apply | [] | [
943,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
942,
1
] |
Mathlib/Data/List/Join.lean | List.join_filter_ne_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.2829\ninst✝ : DecidablePred fun l => l ≠ []\nL : List (List α)\n⊢ join (filter (fun l => decide (l ≠ [])) L) = join L",
"tactic": "simp [join_filter_isEmpty_eq_false, ← isEmpty_iff_eq_nil]"
}
] | [
65,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Topology/Category/TopCat/Basic.lean | TopCat.openEmbedding_iff_comp_isIso | [] | [
165,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.Chain.eq_nil_of_well_founded | [] | [
1036,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1035,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos (-x) = cos x",
"tactic": "simp [cos, sub_eq_add_neg, exp_neg, add_comm]"
}
] | [
857,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | LaurentPolynomial.T_zero | [] | [
174,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.toEnd_neg | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Left.inv_le_one_iff | [
{
"state_after": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na b c d : α\n⊢ a * a⁻¹ ≤ a * 1 ↔ 1 ≤ a",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LE α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1... | [
103,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/ZMod/Coprime.lean | ZMod.eq_zero_iff_gcd_ne_one | [
{
"state_after": "no goals",
"state_before": "a : ℤ\np : ℕ\npp : Fact (Nat.Prime p)\n⊢ ↑a = 0 ↔ Int.gcd a ↑p ≠ 1",
"tactic": "rw [Ne, Int.gcd_comm, Int.gcd_eq_one_iff_coprime,\n (Nat.prime_iff_prime_int.1 pp.1).coprime_iff_not_dvd, Classical.not_not,\n int_cast_zmod_eq_zero_iff_dvd]"
}
] | [
30,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.ι_comp_lift | [
{
"state_after": "case h\nR : Type u_3\ninst✝² : CommSemiring R\nX : Type u_1\nA : Type u_2\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nf : X → A\nx✝ : X\n⊢ (↑(↑(lift R) f) ∘ ι R) x✝ = f x✝",
"state_before": "R : Type u_3\ninst✝² : CommSemiring R\nX : Type u_1\nA : Type u_2\ninst✝¹ : Semiring A\ninst✝ : Alge... | [
343,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.gc_ideal | [] | [
137,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Std/Data/Option/Lemmas.lean | Option.eq_none_iff_forall_not_mem | [
{
"state_after": "α✝ : Type u_1\no : Option α✝\ne : o = none\na : α✝\nh : a ∈ none\n⊢ False",
"state_before": "α✝ : Type u_1\no : Option α✝\ne : o = none\na : α✝\nh : a ∈ o\n⊢ False",
"tactic": "rw [e] at h"
},
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\no : Option α✝\ne : o... | [
49,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
48,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_inv | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\nf : ℝ → ℝ\nμ ν : MeasureTheory.Measure ℝ\ninst✝ : IsLocallyFiniteMeasure μ\nc d : ℝ\nh : ∀ (x : ℝ), x ∈ [[a, b]] → f x ≠ 0\nhf : ContinuousOn f [[a, b]]\n⊢ IntervalIntegrable (fun x => (f x)⁻¹) μ a b",
"tactic": "simpa only [one_div] using in... | [
203,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.le | [] | [
159,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
11
] |
Mathlib/Topology/MetricSpace/PartitionOfUnity.lean | EMetric.exists_continuous_real_forall_closedBall_subset | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nX : Type u_1\ninst✝ : EMetricSpace X\nK U : ι → Set X\nhK : ∀ (i : ι), IsClosed (K i)\nhU : ∀ (i : ι), IsOpen (U i)\nhKU : ∀ (i : ι), K i ⊆ U i\nhfin : LocallyFinite K\n⊢ ∃ δ, (∀ (x : X), 0 < ↑δ x) ∧ ∀ (i : ι) (x : X), x ∈ K i → closedBall x (ENNRe... | [
95,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.prod_mono | [] | [
867,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.diagram_left | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
src/lean/Init/Prelude.lean | Nat.ble_succ_eq_true | [] | [
1686,
53
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1684,
1
] |
Mathlib/CategoryTheory/Types.lean | CategoryTheory.uliftFunctor_map | [] | [
211,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | coe_nndist | [] | [
313,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.nat_succ | [] | [
1431,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1430,
11
] |
Mathlib/Algebra/Order/Kleene.lean | add_eq_sup | [] | [
137,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Order/WithBot.lean | WithBot.lt_iff_exists_coe_btwn | [] | [
530,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
524,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | iSup_nhds_le_uniformity | [] | [
926,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
925,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_eq_empty | [] | [
1483,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1482,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.mem_source | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.23235\nB : Type u_2\nF : Type u_3\nE : B → Type ?u.23246\nZ : Type u_1\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\n⊢ ... | [
360,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.closure_union | [] | [
728,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Algebra/Order/Module.lean | smul_add_smul_le_smul_add_smul | [
{
"state_after": "case intro\nk : Type u_2\nM : Type u_1\nN : Type ?u.53981\ninst✝⁴ : OrderedRing k\ninst✝³ : OrderedAddCommGroup M\ninst✝² : Module k M\ninst✝¹ : OrderedSMul k M\na✝ b✝ : M\nc✝ : k\ninst✝ : ContravariantClass M M (fun x x_1 => x + x_1) fun x x_1 => x ≤ x_1\na : k\nc d : M\nhcd : c ≤ d\nb : k\nh... | [
125,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Data/Int/Parity.lean | Int.even_iff_not_odd | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\n⊢ Even n ↔ ¬Odd n",
"tactic": "rw [not_odd_iff, even_iff]"
}
] | [
56,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | Matrix.J_inv | [
{
"state_after": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : CommRing R\ninst✝ : Fintype l\n⊢ J l R ⬝ (-J l R) = 1",
"state_before": "l : Type u_1\nR : Type u_2\ninst✝² : DecidableEq l\ninst✝¹ : CommRing R\ninst✝ : Fintype l\n⊢ (J l R)⁻¹ = -J l R",
"tactic": "refine' Matrix.inv_eq_righ... | [
65,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.measurableSet_exists_tendsto | [
{
"state_after": "case pos\nα : Type ?u.327871\ninst✝⁷ : TopologicalSpace α\nι : Type u_2\nγ : Type u_1\ntγ : TopologicalSpace γ\ninst✝⁶ : PolishSpace γ\ninst✝⁵ : MeasurableSpace γ\nhγb : BorelSpace γ\nβ : Type u_3\ntβ : TopologicalSpace β\ninst✝⁴ : T2Space β\ninst✝³ : MeasurableSpace β\ninst✝² : BorelSpace β\n... | [
706,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.MemBaseSet.exists_common_compl | [
{
"state_after": "case inr\nι : Type u_1\ninst✝ : Fintype ι\nI J : Box ι\nc c₁ c₂ : ℝ≥0\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I\nl l₁ l₂ : IntegrationParams\nh₁ : MemBaseSet l I c₁ r₁ π₁\nh₂ : MemBaseSet l I c₂ r₂ π₂\nhU : TaggedPrepartition.iUnion π₁ = TaggedPrepartition.iUnion π₂\nH ... | [
385,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_uniformity_isClosed | [] | [
1005,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1003,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | coplanar_iff_finrank_le_two | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.343704\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\ns : Set P\ninst✝ : FiniteDimensional k { x // x ∈ vectorSpan k s }\nh : Coplanar k s ↔ Module.rank k { x // x ∈ vectorSpan k s } ≤ 2\n⊢... | [
629,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/Computability/Partrec.lean | Computable.list_get? | [] | [
354,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Topology/Sheaves/SheafCondition/Sites.lean | TopCat.Sheaf.hom_ext | [
{
"state_after": "case a\nC : Type u\ninst✝ : Category C\nX : TopCat\nι : Type ?u.35577\nB : ι → Opens ↑X\nF : Presheaf C X\nF' : Sheaf C X\nh : Opens.IsBasis (Set.range B)\nα β : F ⟶ F'.val\nhe : ∀ (i : ι), α.app (B i).op = β.app (B i).op\n⊢ ↑(restrictHomEquivHom F F' h).symm α = ↑(restrictHomEquivHom F F' h).... | [
228,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.map_comap_of_surjective | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.121899\nR : Type ?u.121902\nR' : Type ?u.121905\nms : Set (OuterMeasure α)\nm✝ : OuterMeasure α\nβ : Type u_1\nf : α → β\nhf : Surjective f\nm : OuterMeasure β\ns : Set β\n⊢ ↑(↑(map f) (↑(comap f) m)) s = ↑m s",
"tactic": "rw [map_... | [
613,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
611,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_symm_trans_trans | [] | [
608,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
606,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | IsBaseChange.iff_lift_unique | [
{
"state_after": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : AddCommMonoid N\ninst✝¹⁴ : CommRing R\ninst✝¹³ : CommRing S\ninst✝¹² : Algebra R S\ninst✝¹¹ : Module R M\ninst✝¹⁰ : Module R N\ninst✝⁹ : Module S N\ninst✝⁸ : IsScalarTower R S N\nf : M →ₗ[R] N\nh✝ : IsBas... | [
310,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
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