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/List/ProdSigma.lean | List.sigma_nil | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7878\nσ : α → Type u_2\nhead✝ : α\nl : List α\n⊢ (List.sigma (head✝ :: l) fun a => []) = []",
"tactic": "simp [sigma_cons, sigma_nil]"
}
] | [
80,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.HasBasis.lift' | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type ?u.28763\nι✝ : Sort ?u.28766\nf f₁ f₂ : Filter α\nh h₁ h₂ : Set α → Set β\nι : Sort u_1\np : ι → Prop\ns : ι → Set α\nhf : HasBasis f p s\nhh : Monotone h\nt : Set β\n⊢ (∃ i, p i ∧ ∃ x, True ∧ h (s i) ⊆ t) ↔ ∃ i, p i ∧ (h ∘ s... | [
261,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_pair | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nβ₂ : Type ?u.142048\nγ : Type ?u.142051\nι : Sort ?u.142054\nι' : Sort ?u.142057\nκ : ι → Sort ?u.142062\nκ' : ι' → Sort ?u.142067\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b✝ : α\nf : β → α\na b : β\n⊢ (⨅ (x : β) (_ : x ∈ {a, ... | [
1470,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1469,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformSpace.replaceTopology_eq | [] | [
387,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.toSubalgebra_subtype | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | AntivaryOn.sum_mul_eq_sum_comp_perm_mul_iff | [] | [
439,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | tendsto_one_plus_div_pow_exp | [
{
"state_after": "no goals",
"state_before": "t : ℝ\n⊢ ∀ (x : ℕ), ((fun x => (1 + t / x) ^ x) ∘ Nat.cast) x = (1 + t / ↑x) ^ ↑x",
"tactic": "simp"
}
] | [
627,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
] |
Mathlib/CategoryTheory/Abelian/Pseudoelements.lean | CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext' | [] | [
290,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.left_ne | [] | [
247,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Logic/Nonempty.lean | subsingleton_of_not_nonempty | [] | [
171,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Atoms.lean | OrderIso.isCoatom_iff | [] | [
812,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
810,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.biInf_le_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.69959\nβ : Type ?u.69962\nγ : Type ?u.69965\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\n⊢ 𝓟 (Icc (⊤ - 1) (⊤ + 1)) ≤ 𝓝 ⊤",
"tactic": "simpa only [← coe_one, top_sub_coe, top_add, Icc_self, principal_singleton] using pure_le... | [
267,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.card_image₂_singleton_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nα' : Type ?u.50799\nβ : Type u_1\nβ' : Type ?u.50805\nγ : Type u_2\nγ' : Type ?u.50811\nδ : Type ?u.50814\nδ' : Type ?u.50817\nε : Type ?u.50820\nε' : Type ?u.50823\nζ : Type ?u.50826\nζ' : Type ?u.50829\nν : Type ?u.50832\ninst✝⁷ : DecidableEq α'\... | [
258,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_append | [
{
"state_after": "no goals",
"state_before": "ctx : Context\np q : Poly\n⊢ denote ctx (p ++ q) = denote ctx p + denote ctx q",
"tactic": "match p with\n| [] => simp\n| (k, v) :: p => simp [denote_append]"
},
{
"state_after": "no goals",
"state_before": "ctx : Context\np q : Poly\n⊢ denote c... | [
300,
40
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
297,
1
] |
Mathlib/Data/LazyList/Basic.lean | LazyList.mem_nil | [] | [
252,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/VectorBundle/Basic.lean | VectorPrebundle.coordChange_apply | [] | [
895,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
891,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_zero_iff_subsingleton' | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\na✝ : Subsingleton R\n⊢ (∀ (f g : R[X]), f = g) ∧ ∀ (a b : R), a = b",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np q r : R[X]\n⊢ Subsingleton R → (∀ (f g ... | [
51,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Std/Data/Nat/Gcd.lean | Nat.exists_coprime' | [] | [
289,
57
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
287,
1
] |
Mathlib/Combinatorics/Composition.lean | List.map_length_splitWrtCompositionAux | [
{
"state_after": "case nil\nn : ℕ\nα : Type u_1\nl : List α\nh : True\n⊢ map length (splitWrtCompositionAux l []) = []\n\ncase cons\nn✝ : ℕ\nα : Type u_1\nn : ℕ\nns : List ℕ\nIH : ∀ {l : List α}, sum ns ≤ length l → map length (splitWrtCompositionAux l ns) = ns\nl : List α\nh : n + sum ns ≤ length l\n⊢ map leng... | [
701,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/RingTheory/Localization/Basic.lean | Localization.mk_algebraMap | [
{
"state_after": "R : Type u_2\ninst✝⁵ : CommSemiring R\nM : Submonoid R\nS : Type ?u.2882462\ninst✝⁴ : CommSemiring S\ninst✝³ : Algebra R S\nP : Type ?u.2882629\ninst✝² : CommSemiring P\nA : Type u_1\ninst✝¹ : CommSemiring A\ninst✝ : Algebra A R\nm : A\n⊢ ↑(algebraMap ((fun x => R) m) (Localization M)) (↑(alge... | [
1040,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
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Mathlib/Order/WellFoundedSet.lean | Set.IsWf.mono | [] | [
199,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_eq_blsub_or_succ_bsup_eq_blsub | [
{
"state_after": "α : Type ?u.353871\nβ : Type ?u.353874\nγ : Type ?u.353877\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\n⊢ sup (familyOfBFamily o f) = lsub (familyOfBFamily o f) ∨ succ (sup (familyOfBFamily o f)) = lsub (familyOfBFamily o f)",
"st... | [
1837,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1834,
1
] |
Mathlib/AlgebraicTopology/DoldKan/PInfty.lean | AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ HomologicalComplex.Hom.f PInfty n ≫ HomologicalComplex.Hom.f (𝟙 K[X] - PInfty) n = 0",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn : ℕ\n⊢ Hom... | [
135,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/CategoryTheory/Sites/DenseSubsite.lean | CategoryTheory.CoverDense.sheaf_eq_amalgamation | [] | [
150,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.comap_eq_top_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nF : Type u_1\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nrc : RingHomClass F R S\nf : F\nI✝ J : Ideal R\nK L : Ideal S\nG : Type ?u.781465\nrcg : RingHomClass G S R\nI : Ideal S\nh : I = ⊤\n⊢ comap f I = ⊤",
"tactic": "rw [h, comap_top]... | [
1446,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1444,
1
] |
Mathlib/GroupTheory/SpecificGroups/Quaternion.lean | QuaternionGroup.orderOf_xa | [
{
"state_after": "n : ℕ\ninst✝ : NeZero n\ni : ZMod (2 * n)\n⊢ orderOf (xa i) = 2 ^ 2",
"state_before": "n : ℕ\ninst✝ : NeZero n\ni : ZMod (2 * n)\n⊢ orderOf (xa i) = 4",
"tactic": "change _ = 2 ^ 2"
},
{
"state_after": "n : ℕ\ninst✝ : NeZero n\ni : ZMod (2 * n)\nthis : Fact (Nat.Prime 2)\n⊢ ord... | [
226,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_preimage_ofInjective_subset_range | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\ns✝ t : Set α\na b x y : α\nf : α → β\ns : Set β\nH : Function.Injective f\nhs : s ⊆ range f\n⊢ ncard (f ⁻¹' s) = ncard s",
"tactic": "rw [← ncard_image_ofInjective _ H, image_preimage_eq_iff.mpr hs]"
}
] | [
276,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.IsImage.image_eq | [] | [
405,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.union_smul_inter_subset_union | [] | [
226,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_linear_lt_degree_C_mul_X_sq | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\na b c d : R\nn m : ℕ\ninst✝ : Semiring R\np q : R[X]\nι : Type ?u.1018519\nha : a ≠ 0\n⊢ degree (↑C b * X + ↑C c) < degree (↑C a * X ^ 2)",
"tactic": "simpa only [degree_C_mul_X_pow 2 ha] using degree_linear_lt"
}
] | [
1185,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.mkPiAlgebraFin_apply_const | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁸ : CommSemiring R\ninst✝⁷ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁶ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁵ : AddCommMo... | [
1032,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1031,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.rotateL_lemma₄ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.313834\ninst✝ : Preorder α\na b : ℕ\nH3 : 2 * b ≤ 9 * a + 3\n⊢ 3 * b ≤ 16 * a + 9",
"tactic": "linarith"
}
] | [
1232,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1231,
1
] |
Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.mul_nonsing_inv_cancel_left | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.206113\nm : Type u\nn : Type u'\nα : Type v\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing α\nA B✝ : Matrix n n α\nB : Matrix n m α\nh : IsUnit (det A)\n⊢ A ⬝ (A⁻¹ ⬝ B) = B",
"tactic": "simp [← Matrix.mul_assoc, mul_nonsing_inv A h... | [
331,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/Data/Set/Function.lean | Set.injOn_iff_injective | [] | [
684,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
682,
1
] |
Mathlib/AlgebraicTopology/SplitSimplicialObject.lean | SimplicialObject.Split.comp_f | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | Cardinal.Categorical.isComplete | [
{
"state_after": "case intro\nL : Language\nκ : Cardinal\nT : Theory L\nh : Categorical κ T\nh1 : ℵ₀ ≤ κ\nh2 : lift (card L) ≤ lift κ\nhS : Theory.IsSatisfiable T\nhT : ∀ (M : Theory.ModelType T), Infinite ↑M\nφ : Sentence L\nw✝ : Theory.ModelType T\nh✝ : (#↑w✝) = κ\n⊢ T ⊨ᵇ φ ∨ T ⊨ᵇ Formula.not φ",
"state_b... | [
674,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
656,
1
] |
Mathlib/RingTheory/Algebraic.lean | polynomial_smul_apply' | [] | [
434,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Chain.mem_map | [] | [
124,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.eqOn_quadrant_II | [] | [
528,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
519,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.int_cast_eq_zero_iff | [
{
"state_after": "case inl\nR : Type u_1\ninst✝¹ : AddGroupWithOne R\np : ℕ\ninst✝ : CharP R p\na : ℤ\nh : a < 0\n⊢ ↑a = 0 ↔ ↑p ∣ a\n\ncase inr.inl\nR : Type u_1\ninst✝¹ : AddGroupWithOne R\np : ℕ\ninst✝ : CharP R p\n⊢ ↑0 = 0 ↔ ↑p ∣ 0\n\ncase inr.inr\nR : Type u_1\ninst✝¹ : AddGroupWithOne R\np : ℕ\ninst✝ : Cha... | [
141,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_subset | [] | [
1942,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1941,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.pure_sets | [] | [
1972,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1971,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.centroid_map | [
{
"state_after": "no goals",
"state_before": "k : Type u_4\nV : Type u_5\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type u_1\ns₂ : Finset ι₂\ne : ι₂ ↪ ι\np : ι → P\n⊢ centroid k (map e s₂) p = centroid k s₂ ... | [
889,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
888,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.ne_and_ne_of_swap_mul_apply_ne_self | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\nf : Perm α\nx y : α\nhy : (if ↑f y = x then ↑f x else if y = x then x else ↑f y) ≠ y\n⊢ ↑f y ≠ y ∧ y ≠ x",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\nf : Perm α\nx y : α\nhy : ↑(swap x (↑f x) * f) y ≠ y\n⊢ ↑f y ≠ y ∧ y ≠ x",
"tactic": "si... | [
249,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.indicator_nonpos_le_indicator | [] | [
895,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
893,
1
] |
Mathlib/AlgebraicTopology/DoldKan/GammaCompN.lean | AlgebraicTopology.DoldKan.N₁Γ₀_hom_app | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\ninst✝ : HasFiniteCoproducts C\nK : ChainComplex C ℕ\n⊢ (N₁Γ₀.app K).hom =\n (Splitting.toKaroubiNondegComplexIsoN₁ (Γ₀.splitting K)).inv ≫\n (toKaroubi (ChainComplex C ℕ)).map (Γ₀NondegComplexIso K).hom",
"state_before": "C... | [
91,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.cons_right_injective | [] | [
117,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/LinearAlgebra/Isomorphisms.lean | LinearMap.quotKerEquivRange_symm_apply_image | [] | [
63,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Std/Data/Nat/Gcd.lean | Nat.lcm_one_left | [
{
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"state_before": "m : Nat\n⊢ lcm 1 m = m",
"tactic": "simp [lcm]"
}
] | [
189,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
189,
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Mathlib/Algebra/Ring/Defs.lean | mul_one_sub | [
{
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}
] | [
419,
84
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419,
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_image_le_iff | [
{
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"tactic": "simp only [diam_... | [
884,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
882,
1
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Mathlib/Order/Filter/Pointwise.lean | Filter.isUnit_iff_singleton | [
{
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887,
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886,
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Mathlib/Data/Rat/Cast.lean | Rat.cast_add | [] | [
220,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_eq_zero_of_column_eq_zero | [
{
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373,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
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Mathlib/Algebra/Lie/Semisimple.lean | LieAlgebra.center_eq_bot_of_semisimple | [
{
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83,
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Mathlib/NumberTheory/Padics/PadicNorm.lean | padicNorm.sum_le' | [
{
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356,
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352,
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Mathlib/Topology/Homeomorph.lean | Homeomorph.symm_trans_self | [
{
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"state... | [
168,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
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Mathlib/Data/List/Dedup.lean | List.Nodup.dedup | [] | [
84,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
11
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineSubspace.subtypeₐᵢ_toAffineMap | [] | [
304,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
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Mathlib/Data/Nat/Interval.lean | Nat.card_Icc | [] | [
98,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
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Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.exp_inj_of_neg_pi_lt_of_le_pi | [
{
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"tactic": "rw [← log_exp hx₁ hx₂, ← log_exp hy₁ hy₂, hxy]"
}
] | [
70,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.card_erase_of_mem | [] | [
1106,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1105,
1
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Mathlib/Topology/Category/Profinite/CofilteredLimit.lean | Profinite.exists_locallyConstant_finite_nonempty | [
{
"state_after": "J : Type u\ninst✝³ : SmallCategory J\ninst✝² : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝¹ : Finite α\ninst✝ : Nonempty α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toCompHaus.toTop) α\ninhabited_h : Inhabited α\n⊢ ∃ j g, f = LocallyConstant.comap ((forget Profinite).m... | [
212,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
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Mathlib/FieldTheory/IsAlgClosed/Basic.lean | IsAlgClosed.exists_root | [] | [
82,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.exists_mul_lt_of_lt_op_norm | [
{
"state_after": "case intro\n𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type ?u.744106\nE : Type u_3\nEₗ : Type ?u.744112\nF : Type u_4\nFₗ : Type ?u.744118\nG : Type ?u.744121\nGₗ : Type ?u.744124\n𝓕 : Type ?u.744127\ninst✝¹⁶ : SeminormedAddCommGroup E\ninst✝¹⁵ : SeminormedAddCommGroup Eₗ\ninst✝¹⁴ : SeminormedAddC... | [
516,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
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Mathlib/Analysis/InnerProductSpace/Basic.lean | isBoundedBilinearMap_inner | [
{
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1870,
40
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1859,
1
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Mathlib/Topology/Algebra/ContinuousAffineMap.lean | ContinuousLinearMap.coe_toContinuousAffineMap | [] | [
283,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
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Mathlib/Order/Filter/Basic.lean | Filter.mem_inf_of_left | [] | [
426,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.Monic.leadingCoeff | [] | [
93,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/FieldTheory/Subfield.lean | Subfield.comap_comap | [] | [
501,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
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Mathlib/Data/Set/Basic.lean | Set.MemUnion.elim | [] | [
751,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_nat_val | [] | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithBot.coe_iInf | [] | [
160,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Order/Filter/AtTopBot.lean | OrderIso.tendsto_atTop_iff | [
{
"state_after": "ι : Type ?u.53584\nι' : Type ?u.53587\nα : Type u_2\nβ : Type u_3\nγ : Type u_1\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nl : Filter γ\nf : γ → α\ne : α ≃o β\n⊢ Tendsto (fun x => ↑e (f x)) l atTop ↔ Tendsto (↑e ∘ f) l atTop",
"state_before": "ι : Type ?u.53584\nι' : Type ?u.53587\nα : Type... | [
432,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
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Mathlib/Analysis/Calculus/FDerivSymmetric.lean | Convex.isLittleO_alternate_sum_square | [
{
"state_after": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ (x : E), x ∈ interior s → HasFDerivAt f (f' x) x\nx : E\nx... | [
229,
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182,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_not | [] | [
617,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
616,
1
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Mathlib/Data/Set/Finite.lean | Set.finite_of_finite_preimage | [
{
"state_after": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → β\ns : Set β\nh : Set.Finite (f ⁻¹' s)\nhs : s ⊆ range f\n⊢ Set.Finite (f '' (f ⁻¹' s))",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nf : α → β\ns : Set β\nh : Set.Finite (f ⁻¹' s)\nhs : s ⊆ range f\n⊢ Set.Finite ... | [
882,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
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Mathlib/Dynamics/PeriodicPts.lean | MulAction.zpow_smul_mod_minimalPeriod | [] | [
632,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
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Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_compl_mul_prod | [] | [
491,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.bsup_eq | [
{
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"tactic": "rw [← IsNormal.bsup.{u... | [
1964,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1962,
1
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Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_zmod | [
{
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"state_before": "α : Type ?u.13639\nβ : Type ?u.13642\nn : ℕ\n⊢ Nat.card (ZMod n) = n",
"tactic": "cases n"... | [
129,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.snd_colimit_cocone | [] | [
1156,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1155,
1
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoLocallyUniformlyOn_sUnion | [
{
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672,
47
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669,
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Mathlib/GroupTheory/Perm/List.lean | List.formPerm_apply_mem_of_mem | [
{
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"state_be... | [
102,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/MeasureTheory/Measure/Regular.lean | MeasurableSet.exists_isClosed_diff_lt | [
{
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596,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
589,
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Mathlib/Data/List/Basic.lean | List.append_left_injective | [] | [
413,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_subset_Iic_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.52044\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\ninst✝ : LocallyFiniteOrderBot α\n⊢ Icc a b ⊆ Iic b",
"tactic": "simpa [← coe_subset] using Set.Icc_subset_Iic_self"
}
] | [
427,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_subset_mul | [] | [
257,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Set/Function.lean | Set.bijective_iff_bijOn_univ | [] | [
1007,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | modelWithCornersSelf_coe | [] | [
383,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.zpow_eq_one | [
{
"state_after": "M : Type ?u.2599937\nN : Type ?u.2599940\nG : Type u_1\nR : Type ?u.2599946\nS : Type ?u.2599949\nF : Type ?u.2599952\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk l : ℕ\nζ : G\nh : IsPrimitiveRoot ζ k\n⊢ ζ ^ k = 1",
"state_before": "M : Type ?u.2599937\nN ... | [
558,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
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Mathlib/MeasureTheory/Covering/Besicovitch.lean | Besicovitch.ae_tendsto_measure_inter_div | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1407422\ninst✝¹⁰ : MetricSpace α\nβ : Type u\ninst✝⁹ : SecondCountableTopology α\ninst✝⁸ : MeasurableSpace α\ninst✝⁷ : OpensMeasurableSpace α\ninst✝⁶ : HasBesicovitchCovering α\ninst✝⁵ : MetricSpace β\ninst✝⁴ : MeasurableSpace β\ninst✝³ : BorelSpace ... | [
1194,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1190,
1
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Mathlib/Data/Set/Lattice.lean | Set.image_seq | [
{
"state_after": "no goals",
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1989,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1987,
1
] |
Mathlib/Data/Set/Finite.lean | Set.infinite_of_finite_compl | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\ninst✝ : Infinite α\ns : Set α\nhs : Set.Finite (sᶜ)\nh : Set.Finite s\n⊢ Set.Finite univ",
"tactic": "simpa using hs.union h"
}
] | [
1300,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1299,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_at_one | [
{
"state_after": "case h.e'_2.h.e'_6\nR : 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]\nx : R\nS : Type u_1\ninst✝ : Semiring S\nf : R →+* S\n⊢ 1 = ↑f 1",
"state_before": "R : Type u\nS✝ : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring... | [
341,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearMap.coe_toContinuousLinearMap_symm | [] | [
312,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.infs_sups_subset_left | [] | [
410,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_restrict | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nI J J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\n⊢ Prepartition.iUnion (restrict π J) = ↑J ∩ Prepartition.iUnion π",
"tactic": "simp [restrict, ← inter_iUnion, ← iUnion_def]"
}
] | [
527,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivAt.comp_hasFDerivAt | [] | [
145,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | Submodule.finrank_add_inf_finrank_orthogonal' | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.998953\ninst✝⁵ : IsROrC 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : InnerProductSpace ℝ F\nK K₁ K₂ : Submodule 𝕜 E\ninst✝ : FiniteDimensional 𝕜 { x // x ∈ K₂ }\nh : K₁ ≤ K₂\nn : ℕ\nh_dim ... | [
1103,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
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