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/Computability/TMToPartrec.lean | Turing.PartrecToTM2.tr_ret_cons₁ | [] | [
1137,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1134,
1
] |
Mathlib/Data/PFun.lean | PFun.coe_comp | [
{
"state_after": "no goals",
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"tactic": "simp only [coe_val, comp_apply, Function.comp, P... | [
629,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.exp_bound_div_one_sub_of_interval' | [
{
"state_after": "case H\nx : ℝ\nh1 : 0 < x\nh2 : x < 1\n⊢ 0 < 1 - (1 + x + x ^ 2) * (1 - x)\n\nx : ℝ\nh1 : 0 < x\nh2 : x < 1\nH : 0 < 1 - (1 + x + x ^ 2) * (1 - x)\n⊢ exp x < 1 / (1 - x)",
"state_before": "x : ℝ\nh1 : 0 < x\nh2 : x < 1\n⊢ exp x < 1 / (1 - x)",
"tactic": "have H : 0 < 1 - (1 + x + x ^ 2... | [
1952,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1930,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_mul | [] | [
172,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.coe_injective | [] | [
77,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
11
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.108782\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : AddZeroClass α\nh : Periodic f c\n⊢ f c = f 0",
"tactic": "simpa only [zero_add] using h 0"
}
] | [
262,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
11
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_congr | [
{
"state_after": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na' b' : R\n⊢ a' * b' = a' * b'",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na a' b b' c : R\nx✝² : a = a'\nx✝¹ : b = b'\nx✝ ... | [
965,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.le_log_iff_exp_le | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhy : 0 < y\n⊢ x ≤ log y ↔ exp x ≤ y",
"tactic": "rw [← exp_le_exp, exp_log hy]"
}
] | [
164,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Std/Data/String/Lemmas.lean | String.append_assoc | [] | [
492,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
491,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_0 | [
{
"state_after": "case pos\nR : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ν ≤ n\n⊢ eval 0 ((↑derivative^[ν]) (bernsteinPolynomial R n ν)) = eval (↑(n - (ν - 1))) (pochhammer R ν)\n\ncase neg\nR : Type u_1\ninst✝ : CommRing R\nn ν : ℕ\nh : ¬ν ≤ n\n⊢ eval 0 ((↑derivative^[ν]) (bernsteinPolynomial R n ν)) = eval ... | [
199,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/CategoryTheory/EqToHom.lean | CategoryTheory.comp_eqToHom_iff | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category C\nX Y Y' : C\np : Y = Y'\nf : X ⟶ Y\ng : X ⟶ Y'\nh : f ≫ eqToHom p = g\n⊢ f = (f ≫ eqToHom p) ≫ eqToHom (_ : Y' = Y)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝ : Category ... | [
66,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/List/Basic.lean | List.removeNth_insertNth | [
{
"state_after": "ι : Type ?u.113196\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nn : ℕ\nl : List α\n⊢ modifyNthTail (tail ∘ cons a) n l = l",
"state_before": "ι : Type ?u.113196\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nn : ℕ\nl : List α\n⊢ removeNth... | [
1618,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
] |
Mathlib/Data/Finset/NAry.lean | Finset.Nonempty.of_image₂_left | [] | [
131,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_coe_pi | [
{
"state_after": "⊢ ∃ k, -π - π = 2 * π * ↑k",
"state_before": "⊢ -↑π = ↑π",
"tactic": "rw [← coe_neg, angle_eq_iff_two_pi_dvd_sub]"
},
{
"state_after": "⊢ -π - π = 2 * π * ↑(-1)",
"state_before": "⊢ ∃ k, -π - π = 2 * π * ↑k",
"tactic": "use -1"
},
{
"state_after": "no goals",
... | [
137,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.forall_mem_cons | [] | [
251,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Topology/Order/Basic.lean | IsGLB.mem_lowerBounds_of_tendsto | [] | [
2050,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2047,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.disjoint_singleton_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.69965\nγ : Type ?u.69968\nf : α → β\ns t u : Finset α\na b : α\n⊢ _root_.Disjoint {a} s ↔ ¬a ∈ s",
"tactic": "simp only [disjoint_left, mem_singleton, forall_eq]"
}
] | [
959,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
958,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.lift_umax | [] | [
204,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.add_moveRight_inr | [
{
"state_after": "case mk\ny : PGame\ni : RightMoves y\nα✝ β✝ : Type u_1\na✝¹ : α✝ → PGame\na✝ : β✝ → PGame\n⊢ moveRight (mk α✝ β✝ a✝¹ a✝ + y) (↑toRightMovesAdd (Sum.inr i)) = mk α✝ β✝ a✝¹ a✝ + moveRight y i",
"state_before": "x y : PGame\ni : RightMoves y\n⊢ moveRight (x + y) (↑toRightMovesAdd (Sum.inr i))... | [
1556,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/CategoryTheory/Monoidal/OfHasFiniteProducts.lean | CategoryTheory.monoidalOfHasFiniteCoproducts.tensorObj | [] | [
181,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.coe_smul | [] | [
1287,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1286,
1
] |
Mathlib/Order/SymmDiff.lean | Pi.bihimp_apply | [] | [
871,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
869,
1
] |
Mathlib/Analysis/NormedSpace/Ray.lean | norm_injOn_ray_right | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.122924\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nx y : F\nhy : y ≠ 0\n⊢ Set.InjOn Norm.norm {x | SameRay ℝ x y}",
"tactic": "simpa only [SameRay.sameRay_com... | [
73,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.not_isUnit_X_pow_sub_one | [
{
"state_after": "R✝ : Type u\nS : Type v\na b : R✝\nm n✝ : ℕ\nι : Type y\ninst✝² : Ring R✝\np : R✝[X]\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\nn : ℕ\nh : IsUnit (X ^ n - 1)\n⊢ False",
"state_before": "R✝ : Type u\nS : Type v\na b : R✝\nm n✝ : ℕ\nι : Type y\ninst✝² : Ring R✝\np : R✝[X]\nR :... | [
399,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.le_succ_of_pred_le | [] | [
342,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
339,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | separated_def | [
{
"state_after": "α✝ : Type u\nβ : Type v\nγ : Type w\ninst✝³ : UniformSpace α✝\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\nα : Type u\ninst✝ : UniformSpace α\n⊢ (∀ (a b : α), (∀ (t : Set (α × α)), t ∈ (𝓤 α).sets → (a, b) ∈ t) ↔ a = b) ↔\n ∀ (x y : α), (∀ (r : Set (α × α)), r ∈ 𝓤 α → (x, y) ∈ r) → x... | [
139,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/FieldTheory/Subfield.lean | RingHom.fieldRange_eq_map | [
{
"state_after": "case h\nK : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\ng : L →+* M\nf : K →+* L\nx✝ : L\n⊢ x✝ ∈ fieldRange f ↔ x✝ ∈ Subfield.map f ⊤",
"state_before": "K : Type u\nL : Type v\nM : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field M\ng : L →... | [
565,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
563,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mul_single_one_apply | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.504877\ninst✝¹ : Semiring k\ninst✝ : MulOneClass G\nf : MonoidAlgebra k G\nr : k\nx a : G\n⊢ a * 1 = x ↔ a = x",
"tactic": "rw [mul_one]"
}
] | [
558,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mono_fst_of_is_pullback_of_mono | [
{
"state_after": "C : Type u\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nW✝ X Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\nt : PullbackCone f g\nht : IsLimit t\ninst✝ : Mono g\nW : C\nh k : W ⟶ t.pt\ni : h ≫ fst t = k ≫ fst t\n⊢ h ≫ snd t = k ≫ snd t",
"state_before": "C : Type u\ninst✝² : Category C\nD : Typ... | [
641,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.left_le_or | [
{
"state_after": "no goals",
"state_before": "⊢ ∀ (x y : Bool), x ≤ (x || y)",
"tactic": "decide"
}
] | [
364,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/GroupTheory/GroupAction/Defs.lean | smul_zero | [] | [
702,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
701,
1
] |
Mathlib/Order/RelClasses.lean | eq_or_ssubset_of_subset | [] | [
769,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
768,
1
] |
Mathlib/Analysis/Convex/Between.lean | sbtw_iff_right_ne_and_left_mem_image_Ioi | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.511588\nP : Type u_3\nP' : Type ?u.511594\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y z : P\n⊢ Sbtw R x y z ↔ z ≠ y ∧ x ∈ ↑(lineMap z y) '' Set.Ioi 1",
"tac... | [
754,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/CategoryTheory/Adjunction/Basic.lean | CategoryTheory.Adjunction.CoreHomEquiv.homEquiv_naturality_left | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nF : C ⥤ D\nG : D ⥤ C\nadj : CoreHomEquiv F G\nX' X : C\nY Y' : D\nf : X' ⟶ X\ng : F.obj X ⟶ Y\n⊢ F.map f ≫ g = ↑(homEquiv adj X' Y).symm (f ≫ ↑(homEquiv adj X Y) g)",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : T... | [
287,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Computability/Partrec.lean | Computable.option_getD | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.191844\nσ : Type ?u.191847\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α → Option β\ng : α → β\nhf : Computable f\nhg : Computable g\na : α\n⊢ (Option.casesOn (f a) (... | [
706,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_sub_one | [] | [
143,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
143,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.one_sub | [
{
"state_after": "no goals",
"state_before": "M : Type ?u.2741\nN : Type ?u.2744\nS : Type ?u.2747\nM₀ : Type ?u.2750\nM₁ : Type ?u.2753\nR : Type u_1\nG : Type ?u.2759\nG₀ : Type ?u.2762\ninst✝⁷ : Mul M\ninst✝⁶ : Monoid N\ninst✝⁵ : Semigroup S\ninst✝⁴ : MulZeroClass M₀\ninst✝³ : MulOneClass M₁\ninst✝² : No... | [
69,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Topology/Homotopy/HSpaces.lean | unitInterval.qRight_zero_right | [
{
"state_after": "t : ↑I\n⊢ ↑(Set.projIcc 0 1 qRight.proof_1 (2 * ↑t)) = if ↑t ≤ 1 / 2 then 2 * ↑t else 1",
"state_before": "t : ↑I\n⊢ ↑(qRight (t, 0)) = if ↑t ≤ 1 / 2 then 2 * ↑t else 1",
"tactic": "simp only [qRight, coe_zero, add_zero, div_one]"
},
{
"state_after": "case inl\nt : ↑I\nh✝ : ↑t ... | [
214,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Int.addLeft_one_isCycle | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.3065754\nα : Type ?u.3065757\nβ : Type ?u.3065760\ninst✝ : DecidableEq α\nn : ℤ\nx✝ : ↑(Equiv.addLeft 1) n ≠ n\n⊢ ↑(Equiv.addLeft 1 ^ n) 0 = n",
"tactic": "simp"
}
] | [
1860,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1859,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.isSymm_zero | [] | [
935,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_finset_sum' | [
{
"state_after": "case empty\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.929424\nδ : Type ?u.929427\nm : MeasurableSpace α\nμ ν : Measure α\ns : Finset β\nf : β → α → ℝ≥0∞\nhf✝ : ∀ (b : β), b ∈ s → AEMeasurable (f b)\nhf : ∀ (b : β), b ∈ ∅ → AEMeasurable (f b)\n⊢ (∫⁻ (a : α), ∑ b in ∅, f b a ∂μ) = ∑ b in ∅, ∫⁻ (a ... | [
670,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
663,
1
] |
Std/Data/Option/Lemmas.lean | Option.forall | [] | [
18,
70
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
17,
11
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_two_add_inv_two | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.312605\nβ : Type ?u.312608\na b c d : ℝ≥0∞\nr p q : ℝ≥0\n⊢ 2⁻¹ + 2⁻¹ = 1",
"tactic": "rw [← two_mul, ← div_eq_mul_inv, ENNReal.div_self two_ne_zero two_ne_top]"
}
] | [
1720,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1719,
1
] |
Mathlib/Order/Filter/Pointwise.lean | IsUnit.filter | [] | [
724,
45
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.d_eq_three_roots | [
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Mathlib/LinearAlgebra/FreeModule/Rank.lean | rank_directSum | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.mono_set_ae | [] | [
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Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.ext | [
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Mathlib/Analysis/LocallyConvex/ContinuousOfBounded.lean | LinearMap.clmOfExistsBoundedImage_coe | [] | [
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Mathlib/Analysis/SpecialFunctions/Pow/Continuity.lean | ContinuousWithinAt.rpow_const | [] | [
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Mathlib/Order/Atoms.lean | isAtomic_of_isCoatomic_of_complementedLattice_of_isModular | [] | [
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Mathlib/Data/PNat/Xgcd.lean | PNat.XgcdType.finish_isReduced | [
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Mathlib/Analysis/Normed/Group/Basic.lean | squeeze_one_norm' | [] | [
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Mathlib/Topology/Instances/Matrix.lean | HasSum.matrix_transpose | [] | [
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Mathlib/Algebra/Lie/Basic.lean | LieHom.coe_mk | [] | [
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Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.toMonoidWithZeroHom_injective | [
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Mathlib/GroupTheory/EckmannHilton.lean | EckmannHilton.mul_assoc | [
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Mathlib/Order/Filter/Prod.lean | Filter.map_const_principal_coprod_map_id_principal | [
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_atBot | [] | [
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Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformRight.fst_mul_snd_subset | [
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | lineMap_le_map_iff_slope_le_slope | [] | [
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Mathlib/Algebra/Module/Basic.lean | inv_int_cast_smul_comm | [] | [
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Std/Data/Nat/Lemmas.lean | Nat.mul_dvd_mul_left | [] | [
687,
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Mathlib/Analysis/NormedSpace/Basic.lean | interior_sphere' | [
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Mathlib/Order/Hom/CompleteLattice.lean | CompleteLatticeHom.setPreimage_comp | [] | [
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Mathlib/Data/Nat/Prime.lean | Nat.minFac_eq_one_iff | [
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Mathlib/Analysis/Convex/StrictConvexSpace.lean | StrictConvexSpace.ofPairwiseSphereNormNeTwo | [] | [
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Mathlib/Data/Nat/Dist.lean | Nat.dist_tri_left' | [
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bsup_le_iff | [
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Mathlib/Data/Vector/Zip.lean | Vector.prod_mul_prod_eq_prod_zipWith | [] | [
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_zpow | [] | [
63,
99
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Mathlib/Algebra/Ring/BooleanRing.lean | RingHom.asBoolAlg_id | [] | [
371,
6
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Mathlib/Algebra/Hom/Aut.lean | MulAut.one_apply | [] | [
98,
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Mathlib/Analysis/Convex/Gauge.lean | interior_subset_gauge_lt_one | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.sub | [
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Mathlib/Order/CompleteLattice.lean | le_iInf | [] | [
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820,
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Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior | [] | [
677,
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676,
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Mathlib/Algebra/Hom/Equiv/Basic.lean | MulHom.toMulEquiv_apply | [] | [
745,
6
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Mathlib/Algebra/Ring/Commute.lean | Commute.bit1_left | [] | [
68,
44
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Std/Data/List/Lemmas.lean | List.erase_sublist | [] | [
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41
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Std/Data/List/Lemmas.lean | List.set_comm | [
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Mathlib/Algebra/Lie/Solvable.lean | LieIdeal.derivedSeries_eq_derivedSeriesOfIdeal_map | [
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Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.stdBasis_eq_single | [] | [
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57
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Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.hasStrictFDerivAt | [
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Mathlib/Data/Int/GCD.lean | Int.coe_nat_gcd | [] | [
185,
6
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Mathlib/Data/Rat/Cast.lean | MonoidWithZeroHom.ext_rat' | [
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Mathlib/Topology/MetricSpace/Antilipschitz.lean | AntilipschitzWith.closedEmbedding | [] | [
200,
85
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197,
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Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.semiconjBy_iff_semiconj | [] | [
274,
10
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272,
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Mathlib/LinearAlgebra/Basic.lean | Submodule.map_sup_comap_of_surjective | [] | [
911,
30
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909,
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Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_one | [] | [
830,
6
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Mathlib/RingTheory/DedekindDomain/Dvr.lean | IsLocalization.AtPrime.isDedekindDomain | [] | [
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71
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114,
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Mathlib/Order/Filter/Extr.lean | IsMaxFilter.sub | [
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95
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Mathlib/Algebra/Order/Monoid/Lemmas.lean | MulLECancellable.Injective | [] | [
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47
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Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.eventually_hasSum | [
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapRange_finset_sum | [] | [
244,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | invOf_exp_of_mem_ball | [
{
"state_after": "𝕂 : Type u_1\n𝔸 : Type u_2\n𝔹 : Type ?u.124210\ninst✝⁷ : NontriviallyNormedField 𝕂\ninst✝⁶ : NormedRing 𝔸\ninst✝⁵ : NormedRing 𝔹\ninst✝⁴ : NormedAlgebra 𝕂 𝔸\ninst✝³ : NormedAlgebra 𝕂 𝔹\ninst✝² : CompleteSpace 𝔸\ninst✝¹ : CharZero 𝕂\nx : 𝔸\nhx : x ∈ EMetric.ball 0 (FormalMultilinea... | [
309,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.fst_apply | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/FieldTheory/Minpoly/Basic.lean | minpoly.monic | [
{
"state_after": "A : Type u_1\nB : Type u_2\nB' : Type ?u.2178\ninst✝⁴ : CommRing A\ninst✝³ : Ring B\ninst✝² : Ring B'\ninst✝¹ : Algebra A B\ninst✝ : Algebra A B'\nx : B\nhx : IsIntegral A x\n⊢ Monic\n (if hx : IsIntegral A x then\n WellFounded.min (_ : WellFounded fun p q => degree p < degree q)\n ... | [
58,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Data/Option/Basic.lean | Option.pmap_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\nδ : Type ?u.7286\np : α → Prop\nf : (a : α) → p a → β\nx✝ : Option α\ng : γ → α\nx : Option γ\nH : ∀ (a : α), a ∈ Option.map g x → p a\n⊢ pmap f (Option.map g x) H = pmap (fun a h => f (g a) h) x (_ : ∀ (a : γ), a ∈ x → ... | [
185,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/FieldTheory/Separable.lean | isSeparable_tower_top_of_isSeparable | [] | [
544,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
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