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/Topology/UniformSpace/UniformConvergence.lean | UniformContinuousOn.tendstoUniformly | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : UniformSpace β\nF✝ : ι → α → β\nf : α → β\ns s' : Set α\nx✝ : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace γ\nx : α\nU : Set α\nhU : U ∈ 𝓝 x\nF : α → β → γ\nhF ... | [
390,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
386,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.monomial_zero_eq_C | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\n⊢ ↑(monomial R 0) = ↑(C R)",
"tactic": "rw [monomial, Finsupp.single_zero, MvPowerSeries.monomial_zero_eq_C, C]"
}
] | [
1405,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1404,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Ioi | [] | [
1230,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1229,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.BlockTriangular.inv_toBlock | [] | [
277,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Topology/SubsetProperties.lean | Inducing.isCompact_iff | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.93052\nπ : ι → Type ?u.93057\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns✝ t : Set α\nf : α → β\nhf : Inducing f\ns : Set α\nhs : IsCompact (f '' s)\nF : Filter α\nF_ne_bot : NeBot F\nF_le : F ≤ 𝓟 s\n⊢ ∃ a, a ∈ s ∧ ClusterPt a F",
"state_... | [
883,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
878,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.nodal_empty | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝ : Field F\nι : Type u_2\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\n⊢ nodal ∅ v = 1",
"tactic": "rfl"
}
] | [
497,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Data/Real/Sqrt.lean | NNReal.continuous_sqrt | [] | [
125,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitePos_of_tendsto_top | [
{
"state_after": "f : ℕ → ℝ\nhf : Tendsto f atTop atTop\nr : ℝ\nhf' : ∀ (b : ℝ), ∃ i, ∀ (a : ℕ), i ≤ a → b ≤ f a\ni : ℕ\nhi : ∀ (a : ℕ), i ≤ a → r + 1 ≤ f a\nhi' : ∀ (a : ℕ), f a < r + 1 → a < i\n⊢ {a | f a ≤ r} ⊆ {a | a ≤ i}",
"state_before": "f : ℕ → ℝ\nhf : Tendsto f atTop atTop\nr : ℝ\nhf' : ∀ (b : ℝ), ... | [
590,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Set/Sups.lean | Set.image_subset_sups_left | [] | [
98,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.floor_eq_on_Ico' | [] | [
793,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.singleton_inj | [] | [
710,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/List/Indexes.lean | List.foldlIdxM_eq_foldlM_enum | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u\nβ✝ : Type v\nm : Type u → Type v\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nα : Type u_1\nβ : Type u\nf : ℕ → β → α → m β\nb : β\nas : List α\n⊢ foldlIdxM f b as = List.foldlM (fun b p => f p.fst b p.snd) b (enum as)",
"tactic": "rw [foldlIdxM, f... | [
291,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.Theory.SemanticallyEquivalent.trans | [
{
"state_after": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ ψ θ : BoundedFormula L α n\nh1 : SemanticallyEquivalent T φ ψ\nh2 : SemanticallyEquivalent T ψ θ\nM : ModelType T\nv : α → ↑M\nxs : Fin n → ↑M\nh1' : BoundedFormula.Realize (φ ⇔ ψ) v xs\n⊢ BoundedFormula.Realize (φ ⇔ θ) v xs",
"state_before"... | [
443,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_mul_lt_iff_lt_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : CommGroup α\ninst✝¹ : LT 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⊢ c⁻¹ * a < b ↔ a < b * c",
"tactic": "rw [inv_mul_lt_iff_lt_mul, mul_comm]"
}
] | [
553,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
553,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.TM2.step_supports | [
{
"state_after": "K : Type u_1\ninst✝¹ : DecidableEq K\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : Inhabited Λ\nM : Λ → Stmt₂\nS : Finset Λ\nss : Supports M S\nl₁ : Λ\nv : σ\nT : (k : K) → List (Γ k)\nc' : Cfg₂\nh₁ : c' ∈ step M { l := some l₁, var := v, stk := T }\nh₂ : SupportsStmt S (M l₁)\n⊢ c'.l... | [
2264,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2252,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.neg_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nR₁ : Type ?u.2123585\nR₂ : Type ?u.2123588\nR₃ : Type ?u.2123591\nR₄ : Type ?u.2123594\nS : Type ?u.2123597\nK : Type ?u.2123600\nK₂ : Type ?u.2123603\nM : Type u_1\nM' : Type ?u.2123609\nM₁ : Type ?u.2123612\nM₂ : Type ?u.2123615\nM₃ : Type ?u.212... | [
2279,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2279,
1
] |
Std/Logic.lean | forall₃_congr | [] | [
391,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
389,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.take_spec | [
{
"state_after": "case nil\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu v w u✝ : V\nh : u ∈ support nil\n⊢ append (takeUntil nil u h) (dropUntil nil u h) = nil\n\ncase cons\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph ... | [
1071,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.lipschitz | [] | [
85,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Topology/Algebra/Algebra.lean | continuous_algebraMap_iff_smul | [
{
"state_after": "case refine'_1\nR : Type u_1\nA : Type u\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : TopologicalSpace R\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSemiring A\nh : Continuous ↑(algebraMap R A)\n⊢ Continuous fun p => p.fst • p.snd\n\ncase refine'_2\nR : Ty... | [
51,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.comp_iterate_pred_of_pos | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nf : α → α\nn : ℕ\nhn : 0 < n\n⊢ f ∘ f^[Nat.pred n] = f^[n]",
"tactic": "rw [← iterate_succ', Nat.succ_pred_eq_of_pos hn]"
}
] | [
189,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.bind_congr | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ns1 s2 : WSeq α\nf1 f2 : α → WSeq β\nh1 : s1 ~ʷ s2\nh2 : ∀ (a : α), f1 a ~ʷ f2 a\na b : α\nh : a = b\n⊢ LiftRel (fun x x_1 => x = x_1) (f1 b) (f2 b)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns1 s2 : WSeq α\nf1 f2 : α → WSeq β\nh1 : s1 ~ʷ s2\n... | [
1682,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Std/Data/Int/Lemmas.lean | Int.mul_lt_mul_of_pos_left | [
{
"state_after": "a b c : Int\nh₁ : a < b\nh₂ : 0 < c\nthis : 0 < c * (b - a)\n⊢ c * a < c * b",
"state_before": "a b c : Int\nh₁ : a < b\nh₂ : 0 < c\n⊢ c * a < c * b",
"tactic": "have : 0 < c * (b - a) := Int.mul_pos h₂ (Int.sub_pos_of_lt h₁)"
},
{
"state_after": "a b c : Int\nh₁ : a < b\nh₂ : ... | [
1154,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1150,
11
] |
Mathlib/Data/Complex/Exponential.lean | Complex.tan_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ tan 0 = 0",
"tactic": "simp [tan]"
}
] | [
973,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.ofConjAct_toConjAct | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ico_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ Ico a b = 0 ↔ ¬a < b",
"tactic": "rw [Ico, Finset.val_eq_zero, Finset.Ico_eq_empty_iff]"
}
] | [
54,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | IsLocalization.algEquiv_symm_mk' | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝⁷ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝⁶ : CommSemiring S\ninst✝⁵ : Algebra R S\nP : Type ?u.2555066\ninst✝⁴ : CommSemiring P\ninst✝³ : IsLocalization M S\ng : R →+* P\nhg : ∀ (y : { x // x ∈ M }), IsUnit (↑g ↑y)\nQ : Type u_3... | [
739,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Algebra/GroupPower/Ring.lean | RingHom.map_pow | [] | [
157,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
11
] |
Mathlib/RingTheory/AdjoinRoot.lean | AdjoinRoot.powerBasisAux'_repr_apply_to_fun | [] | [
518,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.comp_val | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
11
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr_iff_nhdsWithin | [
{
"state_after": "H : Type u_1\nM : Type ?u.2794\nH' : Type u_2\nM' : Type ?u.2800\nX : Type ?u.2803\ninst✝⁶ : TopologicalSpace H\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : TopologicalSpace H'\ninst✝² : TopologicalSpace M'\ninst✝¹ : ChartedSpace H' M'\ninst✝ : TopologicalSpace X\nG : Stru... | [
102,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.range_im | [] | [
81,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.IsIso.hom_inv_id | [] | [
281,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_emetric_closedBall | [
{
"state_after": "case inl\nι : Type ?u.132364\ninst✝ : Fintype ι\na : ℝ\n⊢ ↑↑volume (EMetric.closedBall a ⊤) = 2 * ⊤\n\ncase inr\nι : Type ?u.132364\ninst✝ : Fintype ι\na : ℝ\nr : ℝ≥0∞\nhr : r ≠ ⊤\n⊢ ↑↑volume (EMetric.closedBall a r) = 2 * r",
"state_before": "ι : Type ?u.132364\ninst✝ : Fintype ι\na : ℝ\n... | [
135,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Data/List/Basic.lean | List.get_length_sub_one | [
{
"state_after": "ι : Type ?u.88829\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nh : length [] - 1 < length []\n⊢ False",
"state_before": "ι : Type ?u.88829\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\nh : length l - 1 < length l\n⊢ l ≠ []",
"tactic": "rintro rf... | [
1358,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1356,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.congr_right | [] | [
345,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/List/ProdSigma.lean | List.length_sigma | [
{
"state_after": "case nil\nα : Type u_1\nβ : Type ?u.16166\nσ : α → Type u_2\nl₂ : (a : α) → List (σ a)\n⊢ length (List.sigma [] l₂) = sum (map (fun a => length (l₂ a)) [])\n\ncase cons\nα : Type u_1\nβ : Type ?u.16166\nσ : α → Type u_2\nl₂ : (a : α) → List (σ a)\nx : α\nl₁ : List α\nIH : length (List.sigma l₁... | [
94,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bitCasesOn_bit0 | [] | [
131,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.coe_snd | [] | [
367,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
1
] |
Mathlib/LinearAlgebra/Basic.lean | Submodule.map_comap_eq_of_surjective | [] | [
898,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
897,
1
] |
Mathlib/Algebra/Module/Basic.lean | Module.subsingleton | [] | [
332,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
11
] |
Mathlib/Algebra/Associated.lean | Irreducible.not_dvd_one | [] | [
176,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_diag | [] | [
182,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.neg_seq | [] | [
283,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Complex/ExponentialBounds.lean | Real.exp_one_near_20 | [
{
"state_after": "case h\n\n⊢ Abs.abs (exp 1 - expNear 0 1 (363916618873 / 133877442384)) ≤ Abs.abs 1 ^ 0 / ↑(Nat.factorial 0) * (1 / 10 ^ 20)",
"state_before": "⊢ Abs.abs (exp 1 - 363916618873 / 133877442384) ≤ 1 / 10 ^ 20",
"tactic": "apply exp_approx_start"
},
{
"state_after": "case h\n\n⊢ Ab... | [
36,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.mul_mem | [] | [
171,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
11
] |
Mathlib/Topology/PathConnected.lean | Path.refl_trans_refl | [
{
"state_after": "case a.h\nX✝ : Type ?u.252121\nY : Type ?u.252124\ninst✝² : TopologicalSpace X✝\ninst✝¹ : TopologicalSpace Y\nx y z : X✝\nι : Type ?u.252139\nγ : Path x y\nX : Type u_1\ninst✝ : TopologicalSpace X\na : X\nx✝ : ↑I\n⊢ ↑(trans (refl a) (refl a)) x✝ = ↑(refl a) x✝",
"state_before": "X✝ : Type ... | [
376,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.image_symm | [] | [
278,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/GroupTheory/PresentedGroup.lean | PresentedGroup.closure_rels_subset_ker | [] | [
69,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/Cover.lean | ofDual_covby_ofDual_iff | [] | [
257,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Infinite.image2_left | [] | [
1341,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
11
] |
Mathlib/RingTheory/Polynomial/Dickson.lean | Polynomial.two_mul_C_half_eq_one | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.128222\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nk : ℕ\na : R\ninst✝ : Invertible 2\n⊢ 2 * ↑C ⅟2 = 1",
"tactic": "rw [two_mul, ← C_add, invOf_two_add_invOf_two, C_1]"
}
] | [
151,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
9
] |
Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.reflectsEpimorphisms.of_iso | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nE : Type u₃\ninst✝¹ : Category E\nF G : C ⥤ D\ninst✝ : ReflectsEpimorphisms F\nα : F ≅ G\nX Y : C\nf : X ⟶ Y\nh : Epi (G.map f)\n⊢ Epi (F.map f)",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Ca... | [
170,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.lt_iff_val_lt_val | [] | [
286,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter | [
{
"state_after": "α : Type u_1\nE : Type ?u.162681\nF : Type u_2\nF' : Type u_3\nG : Type ?u.162690\n𝕜 : Type ?u.162693\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
317,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Data/Set/Basic.lean | Subtype.mem | [] | [
224,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | absorbs_inter | [] | [
330,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | IsUpperSet.div_left | [
{
"state_after": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nht : IsUpperSet t\n⊢ IsLowerSet (s * t⁻¹)",
"state_before": "α : Type u_1\ninst✝ : OrderedCommGroup α\ns t : Set α\na : α\nht : IsUpperSet t\n⊢ IsLowerSet (s / t)",
"tactic": "rw [div_eq_mul_inv]"
},
{
"state_after":... | [
106,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | mem_affineSpan_iff_eq_affineCombination | [
{
"state_after": "case mp\nk : Type u_2\nV : Type u_4\nP : Type u_3\ninst✝⁴ : Ring k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_1\ninst✝ : Nontrivial k\np1 : P\np : ι → P\n⊢ p1 ∈ affineSpan k (Set.range p) → ∃ s w x, p1 = ↑(Finset.affineCombination k s p) w\n\ncase mpr\n... | [
1150,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1144,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.mem_toList | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nx : α\nt : RBNode α\n⊢ x ∈ toList t ↔ x ∈ t",
"tactic": "induction t <;> simp [*, or_left_comm]"
}
] | [
341,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
340,
9
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.mapDomain_sum | [] | [
1219,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1216,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.add_le_to_le_sub | [
{
"state_after": "no goals",
"state_before": "x y k : Nat\nh : k ≤ y\n⊢ x + k ≤ y ↔ x ≤ y - k",
"tactic": "rw [← Nat.add_sub_cancel x k, Nat.sub_le_sub_right_iff h, Nat.add_sub_cancel]"
}
] | [
136,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
134,
11
] |
Mathlib/Data/Set/Function.lean | Set.range_extend | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort ?u.4909\nπ : α → Type ?u.4914\nf : α → β\nhf : Injective f\ng : α → γ\ng' : β → γ\n⊢ range g ∪ g' '' range fᶜ ⊆ range (extend f g g')",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Sort ?u.4909\nπ : α → Type ?u.4914\nf : ... | [
146,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.toAddSubmonoid_mono | [] | [
149,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.one_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝² : CommRing R\nS : Submonoid R\nP : Type u_2\ninst✝¹ : CommRing P\ninst✝ : Algebra R P\nloc : IsLocalization S P\nI : FractionalIdeal S P\n⊢ 1 ≤ I ↔ 1 ∈ I",
"tactic": "rw [← coe_le_coe, coe_one, Submodule.one_le, mem_coe]"
}
] | [
685,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ici_pred | [] | [
805,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftr_eq_div_pow | [
{
"state_after": "m n : ℕ\n⊢ ↑(m / 2 ^ n) = ↑m / ↑(2 ^ n)",
"state_before": "m n : ℕ\n⊢ shiftr ↑m ↑n = ↑m / ↑(2 ^ n)",
"tactic": "rw [shiftr_coe_nat, Nat.shiftr_eq_div_pow _ _]"
},
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ ↑(m / 2 ^ n) = ↑m / ↑(2 ^ n)",
"tactic": "simp"
... | [
442,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.Nonempty.of_smul_left | [] | [
141,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_singleton | [] | [
347,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
346,
1
] |
Mathlib/Order/CompleteLattice.lean | isGLB_iInf | [] | [
779,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Data/List/Basic.lean | List.intersperse_singleton | [] | [
2842,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2841,
1
] |
Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.hasLimits_of_reflective | [] | [
371,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | AnalyticOn.continuousOn | [] | [
887,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
886,
11
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.opow_principal_add_of_principal_add | [
{
"state_after": "case inl\nb : Ordinal\nha : Principal (fun x x_1 => x + x_1) 0\n⊢ Principal (fun x x_1 => x + x_1) (0 ^ b)\n\ncase inr.intro\nb c : Ordinal\nha : Principal (fun x x_1 => x + x_1) (ω ^ c)\n⊢ Principal (fun x x_1 => x + x_1) ((ω ^ c) ^ b)",
"state_before": "a : Ordinal\nha : Principal (fun x... | [
253,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Order/RelClasses.lean | ne_of_irrefl' | [] | [
140,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.gcd_eq_gcd_ab | [
{
"state_after": "x y : ℕ\nthis : Nat.P x y (xgcdAux x 1 0 y 0 1)\n⊢ ↑(gcd x y) = ↑x * gcdA x y + ↑y * gcdB x y",
"state_before": "x y : ℕ\n⊢ ↑(gcd x y) = ↑x * gcdA x y + ↑y * gcdB x y",
"tactic": "have := @xgcd_aux_P x y x y 1 0 0 1 (by simp [P]) (by simp [P])"
},
{
"state_after": "no goals",
... | [
153,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Order/Interval.lean | Interval.disjoint_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.41709\nγ : Type ?u.41712\nδ : Type ?u.41715\nι : Sort ?u.41718\nκ : ι → Sort ?u.41723\ninst✝ : Lattice α\ns t : Interval α\n⊢ Disjoint ↑s ↑t ↔ Disjoint s t",
"tactic": "classical\n rw [disjoint_iff_inf_le, disjoint_iff_inf_le, ← co... | [
625,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/CategoryTheory/Sites/CoverPreserving.lean | CategoryTheory.idCoverPreserving | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nA : Type u₃\ninst✝ : Category A\nJ : GrothendieckTopology C\nK : GrothendieckTopology D\nL : GrothendieckTopology A\nU✝ : C\nS✝ : Sieve U✝\nhS : S✝ ∈ GrothendieckTopology.sieves J U✝\n⊢ Sieve.fu... | [
73,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.Red.reduce_right | [] | [
1233,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1232,
1
] |
Mathlib/Topology/FiberBundle/IsHomeomorphicTrivialBundle.lean | IsHomeomorphicTrivialFiberBundle.continuous_proj | [
{
"state_after": "case intro\nB : Type u_1\nF : Type u_2\nZ : Type u_3\ninst✝² : TopologicalSpace B\ninst✝¹ : TopologicalSpace F\ninst✝ : TopologicalSpace Z\ne : Z ≃ₜ B × F\nh : IsHomeomorphicTrivialFiberBundle F (Prod.fst ∘ ↑e)\n⊢ Continuous (Prod.fst ∘ ↑e)",
"state_before": "B : Type u_1\nF : Type u_2\nZ ... | [
54,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
11
] |
Mathlib/Topology/Separation.lean | disjoint_lift'_closure_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : T25Space α\nx y : α\nh : Disjoint (Filter.lift' (𝓝 x) closure) (Filter.lift' (𝓝 y) closure)\nhxy : x = y\n⊢ False",
"tactic": "simp [hxy, nhds_neBot.ne] at h"
}
] | [
995,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
993,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.coprime_of_lt_prime | [] | [
688,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | isCobounded_le_nhds | [] | [
108,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.Lex.mono | [
{
"state_after": "case inl\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type ?u.31025\nδ : Type ?u.31028\nr r₁ r₂ : α → α → Prop\ns s₁ s₂ : β → β → Prop\na a₁ a₂ : α\nb b₁ b₂ : β\nhr : ∀ (a b : α), r₁ a b → r₂ a b\nhs : ∀ (a b : β), s₁ a b → s₂ a b\na₁✝ a₂✝ : α\nh✝ : r₁ a₁✝ a₂✝\n⊢ Lex r₂ s₂ (inl a₁✝) ... | [
516,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.le_prod_iff | [
{
"state_after": "case mp\nM : Type u_1\nN : Type u_2\nP : Type ?u.110903\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.110924\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\ns : Submonoid M\nt : Submonoid N\nu : Submonoid (M × N)\n⊢ u ≤ prod s t → ... | [
971,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/Data/Dfinsupp/Multiset.lean | Dfinsupp.toMultiset_toDfinsupp | [] | [
115,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.max_zero_right | [] | [
1009,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1008,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.not_specializes_infty_coe | [] | [
411,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.symm_mk | [] | [
123,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multifork.app_right_eq_ι_comp_snd | [
{
"state_after": "C : Type u\ninst✝ : Category C\nI : MulticospanIndex C\nK : Multifork I\nb : I.R\n⊢ K.π.app (WalkingMulticospan.left (MulticospanIndex.sndTo I b)) ≫\n (MulticospanIndex.multicospan I).map (WalkingMulticospan.Hom.snd b) =\n ι K (MulticospanIndex.sndTo I b) ≫ MulticospanIndex.snd I b",
... | [
360,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_union_left | [] | [
587,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
src/lean/Init/Core.lean | not_false | [] | [
519,
33
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
519,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | mem_emetric_ball_one_iff | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.330243\n𝕜 : Type ?u.330246\nα : Type ?u.330249\nι : Type ?u.330252\nκ : Type ?u.330255\nE : Type u_1\nF : Type ?u.330261\nG : Type ?u.330264\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁... | [
995,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
994,
1
] |
Mathlib/Data/Polynomial/Reverse.lean | Polynomial.reflect_sub | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Ring R\nf g : R[X]\nN : ℕ\n⊢ reflect N (f - g) = reflect N f - reflect N g",
"tactic": "rw [sub_eq_add_neg, sub_eq_add_neg, reflect_add, reflect_neg]"
}
] | [
378,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/Data/List/Count.lean | List.countp_cons_of_neg | [
{
"state_after": "α : Type u_1\nl✝ : List α\np q : α → Bool\na : α\nl : List α\npa : ¬p a = true\n⊢ (bif p a then countp.go p l (0 + 1) else countp.go p l 0) = countp.go p l 0",
"state_before": "α : Type u_1\nl✝ : List α\np q : α → Bool\na : α\nl : List α\npa : ¬p a = true\n⊢ countp p (a :: l) = countp p l"... | [
60,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.merge_node | [] | [
654,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.concat_take_nth | [] | [
599,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
9
] |
Mathlib/Data/Fintype/Basic.lean | Finset.univ_eq_attach | [] | [
955,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
954,
1
] |
Mathlib/Logic/IsEmpty.lean | not_isEmpty_of_nonempty | [] | [
211,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.isOpen_iff | [
{
"state_after": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nU : Set (ProjectiveSpectrum 𝒜)\n⊢ IsOpen U ↔ ∃ s, zeroLocus 𝒜 s = Uᶜ",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ni... | [
351,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
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