file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_of_re_neg_of_im_nonneg | [
{
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"tactic": "simp only [arg, hx_re.not_le, hx_im, if_true, if_false]"
}
] | [
282,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_iff | [
{
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.const_smul_left | [
{
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93
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Mathlib/Tactic/NormNum/GCD.lean | Tactic.NormNum.nat_gcd_helper_2 | [
{
"state_after": "d x y a b : ℕ\nhu : x % d = 0\nhv : y % d = 0\nh : x * a = y * b + d\n⊢ Int.gcd ↑x ↑y = d",
"state_before": "d x y a b : ℕ\nhu : x % d = 0\nhv : y % d = 0\nh : x * a = y * b + d\n⊢ Nat.gcd x y = d",
"tactic": "rw [← Int.coe_nat_gcd]"
},
{
"state_after": "d x y a b : ℕ\nhu : x %... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/AtTopBot.lean | Filter.atBot_basis | [] | [
144,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
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Mathlib/Data/Finset/LocallyFinite.lean | Finset.left_not_mem_Ioo | [] | [
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79
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Mathlib/Data/Set/Opposite.lean | Set.singleton_op | [
{
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"tactic": "ext"
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{
"state_after": "case h.mp\nα : Type u_1\nx : α\nx✝ : αᵒᵖ\n⊢ x✝ ∈ Set.op {x} → x✝ ∈ {op x}\n\ncase h.mpr\nα : Type u_1\nx :... | [
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Mathlib/Data/Nat/Basic.lean | Nat.mul_def | [] | [
282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Algebra/Order/AbsoluteValue.lean | IsAbsoluteValue.abv_sub_le | [
{
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"tactic": "simpa [sub_eq_add_neg, add_assoc] using abv_add abv (a - b) (b - c)"
}
] | [
400,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.coe_nsmul | [] | [
910,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
909,
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Mathlib/Data/Finset/Lattice.lean | List.foldr_sup_eq_sup_toFinset | [
{
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Mathlib/Order/Bounds/Basic.lean | isGLB_Ioc | [] | [
754,
99
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Mathlib/Data/ZMod/Basic.lean | ZMod.mul_inv_eq_gcd | [
{
"state_after": "case zero\na : ZMod Nat.zero\n⊢ a * a⁻¹ = ↑(Nat.gcd (val a) Nat.zero)\n\ncase succ\nn : ℕ\na : ZMod (Nat.succ n)\n⊢ a * a⁻¹ = ↑(Nat.gcd (val a) (Nat.succ n))",
"state_before": "n : ℕ\na : ZMod n\n⊢ a * a⁻¹ = ↑(Nat.gcd (val a) n)",
"tactic": "cases' n with n"
},
{
"state_after":... | [
659,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.mkPiAlgebra_apply | [] | [
547,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
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Mathlib/Algebra/Star/SelfAdjoint.lean | skewAdjoint.star_val_eq | [] | [
472,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
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] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Coloring.colorClasses_finite | [] | [
111,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
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Mathlib/Algebra/Order/Rearrangement.lean | Antivary.sum_smul_lt_sum_smul_comp_perm_iff | [
{
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84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
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Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.refl | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Ico_ae_eq_Icc | [] | [
3356,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3355,
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Mathlib/Data/Set/Intervals/ProjIcc.lean | StrictMono.strictMonoOn_IccExtend | [] | [
167,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
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Mathlib/Data/Finset/Card.lean | Finset.inj_on_of_surj_on_of_card_le | [
{
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393,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
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] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.zero_div | [
{
"state_after": "no goals",
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"tactic": "simpa only [zero_mul] using mul_div_cancel 0 a0"
}
] | [
86,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Basic.lean | LinearMap.injOn_of_disjoint_ker | [] | [
1500,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1498,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_along_fiber_finite_of_finite | [] | [
252,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
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Mathlib/Data/List/Sigma.lean | List.NodupKeys.kunion | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl : List (Sigma β)\ninst✝ : DecidableEq α\nl₂ : List (Sigma β)\nnd₁ : NodupKeys []\nnd₂ : NodupKeys l₂\n⊢ NodupKeys (List.kunion [] l₂)\n\ncase cons\nα : Type u\nβ : α → Type v\nl : List (Sigma β)\ninst✝ : DecidableEq α\nhead✝ : Sigma β\ntail✝ : List (Sigm... | [
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.fderiv | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1057,
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Mathlib/CategoryTheory/Limits/Final.lean | CategoryTheory.Functor.Initial.hasLimit_of_comp | [] | [
624,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Set/List.lean | Set.range_list_map | [
{
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"tactic": "refine'\n antisy... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.t'_inv | [
{
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114,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Ring/Defs.lean | zero_le_bit0 | [
{
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"state_before": "α : Type u\nβ : Type ?u.144727\ninst✝ : LinearOrderedSemiring α\na b c d : α\n⊢ 0 ≤ bit0 a ↔ 0 ≤ a",
"tactic": "rw [bit0, ← two_mul, zero_le_mul_left (zero_lt_two : 0 < (2 : α))]"
}
] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Connected.lean | nonempty_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Type ?u.69212\nπ : ι → Type ?u.69217\ninst✝¹ : TopologicalSpace α\ns✝ t✝ u v : Set α\ninst✝ : PreconnectedSpace α\ns t : Set α\n⊢ IsOpen s → IsOpen t → s ∪ t = univ → Set.Nonempty s → Set.Nonempty t → Set.Nonempty (s ∩ t)",
"tacti... | [
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Mathlib/Topology/ContinuousOn.lean | IsOpen.continuousOn_iff | [] | [
859,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/Filtration.lean | Ideal.stableFiltration_stable | [
{
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"state_before": "... | [
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44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Lie/Basic.lean | lie_zsmul | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/Haar/OfBasis.lean | convex_parallelepiped | [
{
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"state_before": "ι : Type u_2\nι' : Ty... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.sub_contLinear | [] | [
143,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.comp_tendsto | [] | [
427,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
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Mathlib/GroupTheory/MonoidLocalization.lean | Localization.smul_mk | [
{
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466,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffOn.prod | [] | [
533,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Category/Ring/Basic.lean | CommSemiRing.coe_of | [] | [
303,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
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Mathlib/Data/Nat/Factorization/Basic.lean | Nat.ord_compl_mul | [
{
"state_after": "case inl\nb p : ℕ\n⊢ 0 * b / p ^ ↑(factorization (0 * b)) p = 0 / p ^ ↑(factorization 0) p * (b / p ^ ↑(factorization b) p)\n\ncase inr\na b p : ℕ\nha : a ≠ 0\n⊢ a * b / p ^ ↑(factorization (a * b)) p = a / p ^ ↑(factorization a) p * (b / p ^ ↑(factorization b) p)",
"state_before": "a b p ... | [
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73
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411,
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Mathlib/Order/Disjoint.lean | IsCompl.dual | [] | [
476,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
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Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.coe_ofTop_symm_apply | [] | [
2108,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Analytic/Basic.lean | FormalMultilinearSeries.le_radius_of_eventually_le | [
{
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"state_before": "𝕜 : Type u_3\nE : Type u_1\nF : Type u_2\nG : Type ?u.72515\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSp... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsSymm.ortho_comm | [] | [
236,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_fin_three | [
{
"state_after": "m : Type ?u.2654416\nn : Type ?u.2654419\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nA : Matrix (Fin 3) (Fin 3) R\n⊢ A 0 0 * (A 1 1 * A 2 2 + -(A 1 2 * A 2 1)) +\n (-(A 0 1 * (A 1 0 * A 2 2 + -(A 1 2 * A 2 0))) +... | [
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811,
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Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.findMin_val | [
{
"state_after": "α : Type u_1\ns✝ : Heap α\nle : α → α → Bool\nk : Heap α → Heap α\nres : FindMin α\nr : Nat\na : α\nc : HeapNode α\ns : Heap α\n⊢ (findMin le (k ∘ cons r a c) s\n (if le res.val a = true then res else { before := k, val := a, node := c, next := s })).val =\n headD le (if le res.val a... | [
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Mathlib/Topology/Algebra/GroupWithZero.lean | nhds_translation_mul_inv₀ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.57877\nβ : Type ?u.57880\nG₀ : Type u_1\ninst✝² : TopologicalSpace G₀\ninst✝¹ : GroupWithZero G₀\ninst✝ : ContinuousMul G₀\na : G₀\nha : a ≠ 0\n⊢ 𝓝 (↑(Homeomorph.symm (Homeomorph.symm (Homeomorph.mulRight₀ a ha))) 1) = 𝓝 a",
"tactic": "simp"
... | [
298,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
297,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw | [
{
"state_after": "case mp\nV : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\n⊢ ∠ p₁ p₂ p₃ = 0 → p₁ ≠ p₂ ∧ Wbtw ℝ p₂ p₁ p₃ ∨ p₃ ≠ p₂ ∧ Wbtw ℝ p₂ p₃ p₁\n\ncase mpr\nV : Type u_1\nP : Type u_2\ninst✝³ : Norm... | [
402,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.coe_toMonoidHom | [] | [
184,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Geometry/Euclidean/Sphere/SecondInter.lean | EuclideanGeometry.Sphere.secondInter_secondInter | [
{
"state_after": "case pos\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\ns : Sphere P\np : P\nv : V\nhv : v = 0\n⊢ secondInter s (secondInter s p v) v = p\n\ncase neg\nV : Type u_2\nP : Type u_1\ninst✝³ : NormedAd... | [
132,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.mapDomain_one | [
{
"state_after": "no goals",
"state_before": "k : Type u₁\nG : Type u₂\nR : Type ?u.399139\ninst✝⁴ : Semiring k\nα : Type u_1\nβ : Type u_2\nα₂ : Type u_3\ninst✝³ : Semiring β\ninst✝² : One α\ninst✝¹ : One α₂\nF : Type u_4\ninst✝ : OneHomClass F α α₂\nf : F\n⊢ mapDomain (↑f) 1 = 1",
"tactic": "simp_rw [... | [
479,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
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Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.flip | [] | [
59,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.le_multiplicity_of_δ_of_fin | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn : ℕ\nf : Fin n → E\nh : ∀ (i : Fin n), ‖f i‖ ≤ 2\nh' : ∀ (i j : Fin n), i ≠ j → 1 - goodδ E ≤ ‖f i - f j‖\n⊢ n ≤ multiplicity E",
"tactic": "classical\nha... | [
334,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.one_sub_self_mul_hsum_powers | [
{
"state_after": "Γ : Type u_1\nR : Type u_2\ninst✝² : LinearOrderedCancelAddCommMonoid Γ\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nx : HahnSeries Γ R\nhx : 0 < ↑(addVal Γ R) x\n⊢ hsum (powers x hx) - hsum (powers x hx - ofFinsupp (Finsupp.single 0 1)) = 1",
"state_before": "Γ : Type u_1\nR : Type u_2\ninst... | [
1810,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1807,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.coe_add | [] | [
422,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.conjAut_mul | [] | [
150,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.predAbove_succAbove | [
{
"state_after": "n m : ℕ\np i : Fin n\n⊢ (if h : ↑castSucc p < if ↑castSucc i < ↑castSucc p then ↑castSucc i else succ i then\n pred (if ↑castSucc i < ↑castSucc p then ↑castSucc i else succ i)\n (_ : (if ↑castSucc i < ↑castSucc p then ↑castSucc i else succ i) ≠ 0)\n else\n castLT (if ↑castS... | [
2402,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2390,
1
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Mathlib/Algebra/Order/Sub/Canonical.lean | tsub_lt_self | [] | [
478,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Topology/Basic.lean | isOpen_biInter_finset | [] | [
180,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.mk_coe | [
{
"state_after": "case h\nR : Type u_1\nA : Type u_2\nB : Type u_3\nC : Type ?u.207014\nD : Type ?u.207017\ninst✝¹² : Monoid R\ninst✝¹¹ : NonUnitalNonAssocSemiring A\ninst✝¹⁰ : DistribMulAction R A\ninst✝⁹ : Star A\ninst✝⁸ : NonUnitalNonAssocSemiring B\ninst✝⁷ : DistribMulAction R B\ninst✝⁶ : Star B\ninst✝⁵ : N... | [
182,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.liftPropAt_chart | [] | [
514,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.mul | [] | [
1404,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1402,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.mem_cons_of_mem | [] | [
241,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Order/Bounds/Basic.lean | isLeast_Icc | [] | [
700,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
699,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.closure_univ | [] | [
524,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.integral_sub | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.470478\n𝕜 : Type ?u.470481\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : SMulCommClass ℝ 𝕜 E\ninst... | [
717,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
715,
1
] |
Mathlib/Order/Lattice.lean | AntitoneOn.max | [] | [
1229,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1227,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_sub_pi | [] | [
1153,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1152,
1
] |
Mathlib/Algebra/Ring/Idempotents.lean | IsIdempotentElem.one_sub_iff | [] | [
74,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.shiftl_coe_nat | [] | [
382,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.piecewise_apply | [] | [
222,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.singleton_inj | [] | [
1119,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1118,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_lt_iff_one_lt_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group 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 : α\n⊢ a * a⁻¹ < a * b ↔ 1 < a * b",
"tactic": "rw [mul_inv_self]"
}
] | [
188,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/Data/Real/Pi/Bounds.lean | Real.pi_gt_sqrtTwoAddSeries | [
{
"state_after": "n : ℕ\nthis : sqrt (2 - sqrtTwoAddSeries 0 n) / 2 * 2 ^ (n + 2) < π\n⊢ 2 ^ (n + 1) * sqrt (2 - sqrtTwoAddSeries 0 n) < π",
"state_before": "n : ℕ\n⊢ 2 ^ (n + 1) * sqrt (2 - sqrtTwoAddSeries 0 n) < π",
"tactic": "have : sqrt (2 - sqrtTwoAddSeries 0 n) / (2 : ℝ) * (2 : ℝ) ^ (n + 2) < π :... | [
38,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/ModelTheory/Satisfiability.lean | FirstOrder.Language.BoundedFormula.imp_semanticallyEquivalent_not_sup | [
{
"state_after": "no goals",
"state_before": "L : Language\nT : Theory L\nα : Type w\nn : ℕ\nφ ψ : BoundedFormula L α n\nM : Theory.ModelType T\nv : α → ↑M\nxs : Fin n → ↑M\n⊢ Realize (φ ⟹ ψ ⇔ ∼φ ⊔ ψ) v xs",
"tactic": "simp [imp_iff_not_or]"
}
] | [
527,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | UniformSpace.Completion.coe_add | [] | [
99,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.withTopEquiv_le | [] | [
706,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_eq_coe | [] | [
690,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_of_lt_of_le | [] | [
289,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
11
] |
Mathlib/Data/Vector/Basic.lean | Vector.get_map | [
{
"state_after": "case mk\nn : ℕ\nα : Type u_2\nβ : Type u_1\nf : α → β\ni : Fin n\nval✝ : List α\nproperty✝ : List.length val✝ = n\n⊢ get (map f { val := val✝, property := property✝ }) i = f (get { val := val✝, property := property✝ } i)",
"state_before": "n : ℕ\nα : Type u_2\nβ : Type u_1\nv : Vector α n\... | [
136,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurableSet.exists_measurable_superset_ae_eq | [
{
"state_after": "case intro.intro\nι : Type ?u.5762\nα : Type u_1\nβ : Type ?u.5768\nγ : Type ?u.5771\nm0 : MeasurableSpace α\nμ : Measure α\ns t✝ t : Set α\nhtm : MeasurableSet t\nhst : s =ᵐ[μ] t\n⊢ ∃ t x, MeasurableSet t ∧ t =ᵐ[μ] s",
"state_before": "ι : Type ?u.5762\nα : Type u_1\nβ : Type ?u.5768\nγ :... | [
236,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Analysis/Convex/Star.lean | StarConvex.inter | [] | [
111,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.finiteDimensional | [
{
"state_after": "F : Type u\nK : Type v\nL : Type w\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Field F\ninst✝¹ : Algebra K L\nf : K[X]\ninst✝ : IsSplittingField K L f\ny : L\nhy : y ∈ ↑(Multiset.toFinset 0)\nhf : f = 0\n⊢ IsIntegral K y",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝⁴ : Fie... | [
138,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Bool/Basic.lean | Bool.or_and_distrib_right | [
{
"state_after": "no goals",
"state_before": "a b c : Bool\n⊢ (a && b || c) = ((a || c) && (b || c))",
"tactic": "cases a <;> cases b <;> cases c <;> simp"
}
] | [
195,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
] |
Mathlib/Data/List/MinMax.lean | List.le_of_mem_argmax | [] | [
177,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/FieldTheory/SeparableDegree.lean | Polynomial.Irreducible.hasSeparableContraction | [
{
"state_after": "case zero\nF : Type u_1\ninst✝¹ : Field F\nq : ℕ\nf✝ : F[X]\nhf : HasSeparableContraction q f✝\nf : F[X]\nirred : Irreducible f\ninst✝ : CharZero F\n⊢ HasSeparableContraction 1 f\n\ncase prime\nF : Type u_1\ninst✝ : Field F\nq✝ : ℕ\nf✝ : F[X]\nhf : HasSeparableContraction q✝ f✝\nq : ℕ\nf : F[X... | [
115,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/PFunctor/Univariate/M.lean | PFunctor.M.head_succ | [] | [
273,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.fract_zero | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.157606\nα : Type u_1\nβ : Type ?u.157612\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ fract 0 = 0",
"tactic": "rw [fract, floor_zero, cast_zero, sub_self]"
}
] | [
887,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.cons_le | [] | [
260,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Topology/Algebra/Valuation.lean | Valued.mem_nhds_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\n_i : Valued R Γ₀\ns : Set R\n⊢ s ∈ 𝓝 0 ↔ ∃ γ, {x | ↑v x < ↑γ} ⊆ s",
"tactic": "simp only [mem_nhds, sub_zero]"
}
] | [
146,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.diam_union | [
{
"state_after": "α : Type u\nβ : Type v\nX : Type ?u.298049\ninst✝ : PseudoEMetricSpace α\nx y z : α\nε ε₁ ε₂ : ℝ≥0∞\ns t✝ t : Set α\nxs : x ∈ s\nyt : y ∈ t\nA : ∀ (a : α), a ∈ s → ∀ (b : α), b ∈ t → edist a b ≤ diam s + edist x y + diam t\n⊢ diam (s ∪ t) ≤ diam s + edist x y + diam t",
"state_before": "α ... | [
963,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_inter | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.261503\nγ : Type ?u.261506\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b a : α\ns t : Finset α\n⊢ erase s a ∩ t = erase (s ∩ t) a",
"tactic": "simpa only [inter_comm t] using inter_erase a t s"
}
] | [
2250,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2249,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.append_take_drop | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nn : ℕ\n⊢ ∀ (s : Stream' α), take n s ++ₛ drop n s = s",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\n⊢ ∀ (n : ℕ) (s : Stream' α), take n s ++ₛ drop n s = s",
"tactic": "intro n"
},
{
"state_after": "case zero\nα : Type u\nβ : Type v\n... | [
622,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.semiconj_of_bijective_of_translationNumber_eq | [] | [
1031,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1028,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_a_ne_zero | [] | [
386,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.addNat_mk | [] | [
1363,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/Data/List/AList.lean | AList.perm_lookup | [] | [
180,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/LocalExtr.lean | Filter.EventuallyEq.isLocalMin_iff | [] | [
620,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Order/CompleteLattice.lean | Antitone.iInf_nat_add | [] | [
1642,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1641,
1
] |
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