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/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.const_mul_right | [] | [
1558,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.fderiv | [] | [
83,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
11
] |
Mathlib/Algebra/Algebra/Subalgebra/Tower.lean | Subalgebra.restrictScalars_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nA : Type w\nB : Type u₁\nM : Type v₁\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra S A\ninst✝⁴ : Algebra R A\ninst✝³ : Algebra S B\ninst✝² : Algebra R ... | [
122,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_mul_left_add_right | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ gcd m (m * k + n) = gcd m n",
"tactic": "simp [add_comm _ n]"
}
] | [
51,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Polynomial/Expand.lean | Polynomial.map_expand | [
{
"state_after": "case pos\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q✝ p : ℕ\nf : R →+* S\nq : R[X]\nhp : p = 0\n⊢ map f (↑(expand R p) q) = ↑(expand S p) (map f q)\n\ncase neg\nR : Type u\ninst✝¹ : CommSemiring R\nS : Type v\ninst✝ : CommSemiring S\np✝ q✝ p : ℕ\nf : R →+* S\... | [
187,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.Disjoint.card_support_mul | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : Disjoint f g\n⊢ card (support (f * g)) = card (support f ∪ support g)\n\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : Disjoint f g\n⊢ _root_.Disjoint (support f) (support g)",
"state_be... | [
646,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.span_induction | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.21086\nK : Type ?u.21089\nM : Type u_1\nM₂ : Type ?u.21095\nV : Type ?u.21098\nS : Type ?u.21101\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx✝ : M\np✝ p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ninst✝... | [
154,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Data/Fintype/BigOperators.lean | Fintype.prod_option | [] | [
117,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Data/Set/Function.lean | Set.restrict_piecewise | [] | [
111,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.map_id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : WSeq α\n⊢ map id s = s",
"tactic": "simp [map]"
}
] | [
1414,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1414,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Filter.lean | BoxIntegral.IntegrationParams.toFilteriUnion_mono | [] | [
462,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
460,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.not_nonempty_empty | [
{
"state_after": "no goals",
"state_before": "⊢ ¬ZFSet.Nonempty ∅",
"tactic": "simp [ZFSet.Nonempty]"
}
] | [
841,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Int/GCD.lean | Nat.exists_mul_emod_eq_gcd | [
{
"state_after": "k n : ℕ\nhk : gcd n k < k\nhk' : ↑k ≠ 0\n⊢ ∃ m, n * m % k = gcd n k",
"state_before": "k n : ℕ\nhk : gcd n k < k\n⊢ ∃ m, n * m % k = gcd n k",
"tactic": "have hk' := Int.ofNat_ne_zero.2 (ne_of_gt (lt_of_le_of_lt (zero_le (gcd n k)) hk))"
},
{
"state_after": "k n : ℕ\nhk : gcd n... | [
166,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Std/Logic.lean | neq_of_not_iff | [] | [
49,
58
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
49,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aeval_bit0 | [] | [
237,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.op_norm_lsmul_le | [
{
"state_after": "𝕜 : Type u_3\n𝕜₂ : Type ?u.2145036\n𝕜₃ : Type ?u.2145039\nE : Type u_1\nEₗ : Type ?u.2145045\nF : Type ?u.2145048\nFₗ : Type ?u.2145051\nG : Type ?u.2145054\nGₗ : Type ?u.2145057\n𝓕 : Type ?u.2145060\ninst✝²² : SeminormedAddCommGroup E\ninst✝²¹ : SeminormedAddCommGroup Eₗ\ninst✝²⁰ : Semino... | [
1227,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1224,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableWithinAt.sub | [] | [
498,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.splits_comp_of_splits | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nj : L →+* F\nf : K[X]\nh : Splits i f\n⊢ Splits j (map i f)",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nj : L →... | [
435,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/LinearAlgebra/PiTensorProduct.lean | PiTensorProduct.tprodCoeff_eq_smul_tprod | [
{
"state_after": "ι : Type u_1\nι₂ : Type ?u.228081\nι₃ : Type ?u.228084\nR : Type u_2\ninst✝⁷ : CommSemiring R\nR₁ : Type ?u.228093\nR₂ : Type ?u.228096\ns : ι → Type u_3\ninst✝⁶ : (i : ι) → AddCommMonoid (s i)\ninst✝⁵ : (i : ι) → Module R (s i)\nM : Type ?u.228286\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R ... | [
328,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.findGreatest_zero | [] | [
886,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.Ioo_zero_top_eq_iUnion_Ico_zpow | [
{
"state_after": "case h\nα : Type ?u.661501\nβ : Type ?u.661504\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ny : ℝ≥0∞\nhy : 1 < y\nh'y : y ≠ ⊤\nx : ℝ≥0∞\n⊢ x ∈ Ioo 0 ⊤ ↔ x ∈ ⋃ (n : ℤ), Ico (y ^ n) (y ^ (n + 1))",
"state_before": "α : Type ?u.661501\nβ : Type ?u.661504\na b c d : ℝ≥0∞\nr p q : ℝ≥0\ny : ℝ≥0∞\nhy : 1 < y\nh... | [
1912,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1900,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.not_gt_eq | [] | [
731,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
730,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.lift_map | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : NonPreadditiveAbelian C\nX Y : C\nf : X ⟶ Y\n⊢ prod.lift (𝟙 X) 0 ≫ prod.map f f = f ≫ prod.lift (𝟙 Y) 0",
"tactic": "simp"
}
] | [
297,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
296,
1
] |
Mathlib/Tactic/IntervalCases.lean | Mathlib.Tactic.IntervalCases.of_not_le_right | [] | [
135,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearMap.prodMap_id | [] | [
336,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/RingTheory/MvPolynomial/Tower.lean | MvPolynomial.aeval_algebraMap_eq_zero_iff_of_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_3\nB : Type u_4\nσ : Type u_1\ninst✝⁶ : CommSemiring R\ninst✝⁵ : CommSemiring A\ninst✝⁴ : CommSemiring B\ninst✝³ : Algebra R A\ninst✝² : Algebra A B\ninst✝¹ : Algebra R B\ninst✝ : IsScalarTower R A B\nx : σ → A\np : MvPolynomial σ R\nh :... | [
72,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | NNReal.coe_real_pi | [] | [
195,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.type_cardinal | [
{
"state_after": "⊢ (type fun x x_1 => x < x_1) = type fun x x_1 => x < x_1",
"state_before": "⊢ (type fun x x_1 => x < x_1) = Ordinal.univ",
"tactic": "rw [Ordinal.univ_id]"
},
{
"state_after": "no goals",
"state_before": "⊢ (type fun x x_1 => x < x_1) = type fun x x_1 => x < x_1",
"tac... | [
146,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.range_extend | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1132782\nι' : Type ?u.1132785\nR : Type ?u.1132788\nR₂ : Type ?u.1132791\nK : Type u_1\nM : Type ?u.1132797\nM' : Type ?u.1132800\nM'' : Type ?u.1132803\nV : Type u\nV' : Type ?u.1132808\ninst✝⁴ : DivisionRing K\ninst✝³ : AddCommGroup V\ninst✝² : Add... | [
1431,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
] |
Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.single_le_iff | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → CanonicallyOrderedAddMonoid (α i)\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → (x : α i) → Decidable (x ≠ 0)\nf g : Π₀ (i : ι), α i\ns : Finset ι\ni : ι\na : α i\n⊢ (∀ (i_1 : ι), i_1 ∈ {i} → ↑(single i a) i_1 ≤ ↑f... | [
184,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/MeasureTheory/Group/Measure.lean | MeasureTheory.measure_preimage_mul_right | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type ?u.426884\nG : Type u_1\nH : Type ?u.426890\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableSpace H\ninst✝² : Group G\ninst✝¹ : MeasurableMul G\nμ : Measure G\ninst✝ : IsMulRightInvariant μ\ng : G\nA : Set G\n⊢ ↑↑(Measure.map (fun h => h * g) μ) A = ↑↑... | [
294,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.extend_comp | [] | [
781,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Algebra.Initial.str_isIso | [] | [
255,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | IsBoundedLinearMap.differentiableWithinAt | [] | [
131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_distrib_subset_left | [
{
"state_after": "case intro.intro.intro.intro.intro.intro.intro.intro\nα : Type u_2\nα' : Type ?u.46266\nβ : Type u_4\nβ' : Type u_6\nγ : Type u_5\nγ' : Type u_7\nδ : Type u_3\nδ' : Type ?u.46284\nε : Type u_1\nε' : Type ?u.46290\nζ : Type ?u.46293\nζ' : Type ?u.46296\nν : Type ?u.46299\nf✝ f' : α → β → γ\ng✝ ... | [
385,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_neg | [] | [
592,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.map_map | [] | [
565,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Order/MinMax.lean | max_lt_max | [] | [
219,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/MeasureTheory/Integral/IntegrableOn.lean | MeasureTheory.IntegrableOn.restrict | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1499967\nE : Type u_2\nF : Type ?u.1499973\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nf g : α → E\ns t : Set α\nμ ν : Measure α\nh : IntegrableOn f s\nhs : MeasurableSet s\n⊢ Integrable f",
"state_before": "α : Type u_1\nβ : Type ?u.1499967\nE : Ty... | [
172,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Log.lean | Complex.exp_eq_exp_iff_exists_int | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ exp x = exp y ↔ ∃ n, x = y + ↑n * (2 * ↑π * I)",
"tactic": "simp only [exp_eq_exp_iff_exp_sub_eq_one, exp_eq_one_iff, sub_eq_iff_eq_add']"
}
] | [
160,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Std/Data/Int/Lemmas.lean | Int.nonneg_def | [] | [
545,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
544,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.Nonempty.sigma_fst | [] | [
211,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDerivWithin_eq_iterate | [
{
"state_after": "case zero\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type ?u.85634\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nn : ℕ\nf : 𝕜 → F\ns : Set 𝕜\nx✝¹ x✝ : 𝕜\nhs : UniqueDiffOn 𝕜 s\nhx✝ : x✝ ∈ s\nx... | [
206,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/PathConnected.lean | IsOpen.isConnected_iff_isPathConnected | [
{
"state_after": "X : Type u_1\nY : Type ?u.708006\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\nx y z : X\nι : Type ?u.708021\nF : Set X\ninst✝ : LocPathConnectedSpace X\nU : Set X\nU_op : IsOpen U\n⊢ PathConnectedSpace ↑U ↔ ConnectedSpace ↑U",
"state_before": "X : Type u_1\nY : Type ?u.708006... | [
1266,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/Probability/Integration.lean | ProbabilityTheory.IndepFun.integral_mul | [
{
"state_after": "case pos\nΩ : Type u_1\nmΩ : MeasurableSpace Ω\nμ : MeasureTheory.Measure Ω\nf g : Ω → ℝ≥0∞\nX Y : Ω → ℝ\nhXY : IndepFun X Y\nhX : AEStronglyMeasurable X μ\nhY : AEStronglyMeasurable Y μ\nh'X : X =ᵐ[μ] 0\n⊢ integral μ (X * Y) = integral μ X * integral μ Y\n\ncase neg\nΩ : Type u_1\nmΩ : Measur... | [
295,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.prod_properDivisors_prime_pow | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nα : Type u_1\ninst✝ : CommMonoid α\nk p : ℕ\nf : ℕ → α\nh : Prime p\n⊢ ∏ x in properDivisors (p ^ k), f x = ∏ x in range k, f (p ^ x)",
"tactic": "simp [h, properDivisors_prime_pow]"
}
] | [
457,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_congr | [] | [
2719,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2718,
1
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.memℓp | [] | [
355,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
11
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | edist_inv_inv | [
{
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132,
16
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129,
1
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Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.leftUnitor_comp_inv | [
{
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] | [
470,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
469,
1
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Over.mono_of_mono_left | [] | [
232,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.thickening_eq_preimage_infEdist | [] | [
914,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
912,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.star_eq_two_re_sub | [] | [
1125,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
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Mathlib/Data/Real/Hyperreal.lean | Hyperreal.st_neg | [
{
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}
] | [
650,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
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Mathlib/Data/Sym/Sym2.lean | Sym2.inductionOn | [] | [
119,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
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Mathlib/CategoryTheory/Sites/Limits.lean | CategoryTheory.Sheaf.isSheaf_of_isLimit | [
{
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146,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
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Mathlib/Algebra/MonoidAlgebra/Degree.lean | AddMonoidAlgebra.le_inf_support_mul | [
{
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82,
46
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77,
1
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Mathlib/Computability/TMToPartrec.lean | Turing.PartrecToTM2.codeSupp_succ | [] | [
1824,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1823,
1
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Mathlib/Algebra/GroupWithZero/Units/Basic.lean | Ring.mul_inverse_cancel_right | [
{
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"tactic": "rw [mul_assoc, mul_inverse_cancel x h, mu... | [
117,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
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Mathlib/Data/Int/Bitwise.lean | Int.bitwise_xor | [
{
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},
{
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293,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_pos_iff_support_of_nonneg_ae | [
{
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566,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
562,
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Mathlib/RingTheory/DiscreteValuationRing/Basic.lean | DiscreteValuationRing.addVal_def | [
{
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412,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
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Mathlib/Algebra/GroupPower/Basic.lean | pow_inv_comm | [] | [
431,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
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Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.intersecting_iff_eq_empty_of_subsingleton | [
{
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110,
51
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102,
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Mathlib/Data/Nat/Basic.lean | Nat.decreasingInduction_succ | [
{
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512,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
508,
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Mathlib/Combinatorics/Composition.lean | CompositionAsSet.lt_length' | [] | [
904,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
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Mathlib/Topology/MetricSpace/MetricSeparated.lean | IsMetricSeparated.finite_iUnion_right_iff | [
{
"state_after": "no goals",
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"tactic": "simpa only [@co... | [
120,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
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Mathlib/MeasureTheory/Function/Jacobian.lean | exists_partition_approximatesLinearOn_of_hasFDerivWithinAt | [
{
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272,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Complex.abs_cpow_of_ne_zero | [
{
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}
] | [
264,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
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Mathlib/Order/Basic.lean | update_le_update_iff' | [
{
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877,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
876,
1
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.div_mul_cancel | [
{
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"tactic": "rw [mul_div_cancel _ a0]"
}
] | [
999,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
998,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.Ici_eq_Icc | [] | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
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Mathlib/Data/UnionFind.lean | UnionFind.rank_eq | [
{
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"tactic": "simp [rank, h, H.rank_eq]"
}
] | [
199,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.tan_arccos | [
{
"state_after": "no goals",
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"tactic": "rw [arccos, tan_pi_div_two_sub, tan_arcsin, inv_div]"
}
] | [
455,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.sOppSide_smul_vsub_vadd_right | [] | [
755,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.mul_right | [
{
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191,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.span_tmul_eq_top | [
{
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418,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfTopHom.inf_apply | [] | [
1010,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.lt_sup'_iff | [
{
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1092,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.coe_ennreal_lt_coe_ennreal_iff | [] | [
507,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | monotone_Iic | [] | [
31,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
31,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | Real.contDiff_arctan | [
{
"state_after": "no goals",
"state_before": "n : ℕ∞\nx : ℝ\nthis : cos (arctan x) ≠ 0\n⊢ ↑1 / cos (↑(LocalHomeomorph.symm tanLocalHomeomorph) x) ^ 2 ≠ 0",
"tactic": "simpa"
}
] | [
114,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.coeff_X_of_ne_one | [
{
"state_after": "no goals",
"state_before": "R : Type u\na b : R\nm n✝ : ℕ\ninst✝ : Semiring R\np q : R[X]\nn : ℕ\nhn : n ≠ 1\n⊢ coeff X n = 0",
"tactic": "rw [coeff_X, if_neg hn.symm]"
}
] | [
708,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.ext | [
{
"state_after": "case mk\nR : Type u_1\nA : Type u_2\nB : Type ?u.4479\ninst✝⁴ : CommRing R\ninst✝³ : Ring A\ninst✝² : Ring B\ninst✝¹ : Algebra R A\ninst✝ : Algebra R B\nc₁ c₂ : R\nq₂ : Basis A c₁ c₂\ni✝ j✝ k✝ : A\ni_mul_i✝ : i✝ * i✝ = c₁ • 1\nj_mul_j✝ : j✝ * j✝ = c₂ • 1\ni_mul_j✝ : i✝ * j✝ = k✝\nj_mul_i✝ : j✝... | [
61,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.count_ne_zero' | [
{
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2301,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2299,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_biUnion_le | [
{
"state_after": "α✝ β ι α : Type u\nA : ι → Set α\ns : Set ι\n⊢ (#↑(⋃ (x : ↑s), A ↑x)) ≤ (#↑s) * ⨆ (x : ↑s), #↑(A ↑x)",
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"tactic": "rw [biUnion_eq_iUnion]"
},
{
"stat... | [
2059,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2056,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidHom.coe_comp_orderHom | [] | [
437,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | Submodule.norm_subtypeL | [] | [
1927,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1926,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.right_mem_Icc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.4512\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\n⊢ b ∈ Icc a b ↔ a ≤ b",
"tactic": "simp only [mem_Icc, and_true_iff, le_rfl]"
}
] | [
134,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/GroupTheory/GroupAction/Units.lean | IsUnit.smul | [] | [
162,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.le_map_apply | [] | [
1269,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1263,
1
] |
Mathlib/GroupTheory/Subgroup/Finite.lean | Subgroup.multiset_noncommProd_mem | [] | [
70,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_symm_apply | [
{
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172,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.denom_eq_conts_b | [] | [
101,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Topology/Homotopy/HSpaces.lean | TopologicalGroup.one_eq_hSpace_e | [] | [
166,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.add_coeff | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
376,
1
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Mathlib/Algebra/Quaternion.lean | Quaternion.sub_imK | [] | [
936,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
936,
9
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Mathlib/Topology/Algebra/Monoid.lean | exists_nhds_one_split4 | [
{
"state_after": "case intro.intro\nι : Type ?u.161653\nα : Type ?u.161656\nX : Type ?u.161659\nM : Type u_1\nN : Type ?u.161665\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace M\ninst✝¹ : Monoid M\ninst✝ : ContinuousMul M\nu : Set M\nhu : u ∈ 𝓝 1\nW : Set M\nW1 : W ∈ 𝓝 1\nh : ∀ (v : M), v ∈ W → ∀ (w ... | [
500,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_pow_strictAnti | [] | [
652,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
651,
1
] |
Mathlib/Algebra/Group/Units.lean | isUnit_iff_exists_inv | [] | [
650,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
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