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/Combinatorics/Additive/SalemSpencer.lean | MulSalemSpencer.mul_right₀ | [
{
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248,
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Mathlib/Order/Antichain.lean | isAntichain_iff_forall_not_lt | [] | [
268,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
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Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.interpolate_eq_sum_interpolate_insert_sdiff | [
{
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"state_before": "F : T... | [
454,
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Mathlib/Data/Set/Intervals/Disjoint.lean | iUnion_Iic_eq_Iic_iSup | [] | [
249,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Field/Basic.lean | Units.nnnorm_pos | [] | [
447,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.one_def | [] | [
463,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
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Mathlib/Analysis/Convex/SpecificFunctions/Deriv.lean | strictConcaveOn_sin_Icc | [
{
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"state_before": "⊢ StrictConcaveOn ℝ (Icc 0 π) sin",
"tactic": "apply strictConcaveOn_of_deriv2_neg (convex_Icc _ _) continuousOn_sin fun x hx => ?_"
},
{
"state_after": "x : ℝ\nhx : x ∈ Ioo 0 π\n⊢ (deriv^[2]) sin x ... | [
173,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
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Mathlib/Combinatorics/Colex.lean | Nat.sum_two_pow_lt | [
{
"state_after": "α : Type ?u.638\nk : ℕ\nA : Finset ℕ\nh₁ : ∀ {x : ℕ}, x ∈ A → x < k\n⊢ ∑ x in range k, Nat.pow 2 x < 2 ^ k",
"state_before": "α : Type ?u.638\nk : ℕ\nA : Finset ℕ\nh₁ : ∀ {x : ℕ}, x ∈ A → x < k\n⊢ Finset.sum A (Nat.pow 2) < 2 ^ k",
"tactic": "apply lt_of_le_of_lt (sum_le_sum_of_subset ... | [
111,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
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Mathlib/Algebra/Group/Basic.lean | mul_rotate' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.8273\nβ : Type ?u.8276\nG : Type u_1\ninst✝ : CommSemigroup G\na b c : G\n⊢ a * (b * c) = b * (c * a)",
"tactic": "simp only [mul_left_comm, mul_comm]"
}
] | [
122,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.symm_toLocalEquiv | [] | [
337,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
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Mathlib/Topology/ContinuousFunction/Basic.lean | Homeomorph.symm_comp_toContinuousMap | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.69498\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α ≃ₜ β\ng : β ≃ₜ γ\n⊢ ContinuousMap.comp (toContinuousMap (Homeomorph.symm f)) (toContinuousMap f) = ContinuousMap.id α",
... | [
492,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
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Mathlib/Topology/MetricSpace/Basic.lean | dist_pi_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.396731\nι : Type ?u.396734\ninst✝³ : PseudoMetricSpace α\nπ : β → Type ?u.396742\ninst✝² : Fintype β\ninst✝¹ : (b : β) → PseudoMetricSpace (π b)\ninst✝ : Nonempty β\na b : α\n⊢ (dist (fun x => a) fun x => b) = dist a b",
"... | [
2029,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2028,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.map_eq_sum | [
{
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91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2133,
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.map_rel_iff | [] | [
276,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_filter_not | [
{
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... | [
629,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Constructions.lean | isClosed_set_pi | [
{
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1335,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Logic/Equiv/Basic.lean | Equiv.optionEquivSumPUnit_symm_inl | [] | [
440,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
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Mathlib/RepresentationTheory/Basic.lean | Representation.ofModule_asAlgebraHom_apply_apply | [
{
"state_after": "case hM\nk : Type u_1\nG : Type u_2\nV : Type ?u.309923\ninst✝⁵ : CommSemiring k\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : Module k V\nρ : Representation k G V\nM : Type u_3\ninst✝¹ : AddCommMonoid M\ninst✝ : Module (MonoidAlgebra k G) M\nr : MonoidAlgebra k G\nm : RestrictScalars... | [
221,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.opNorm_le_bound | [] | [
283,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.coe_strictlyPositive | [] | [
618,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
617,
1
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Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.derivFamily_succ | [] | [
173,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.SimplicialObject.δ_comp_σ_of_gt' | [
{
"state_after": "no goals",
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"tactic": "simp only [Fin.not_lt_zero, hi] at H"
},
{
"state_after": "C : Type u\ninst✝ : Category C\nX : Simpl... | [
197,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
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Mathlib/LinearAlgebra/Matrix/AbsoluteValue.lean | Matrix.det_sum_smul_le | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nS : Type u_4\ninst✝⁴ : CommRing R\ninst✝³ : Nontrivial R\ninst✝² : LinearOrderedCommRing S\nn : Type u_2\ninst✝¹ : Fintype n\ninst✝ : DecidableEq n\nι : Type u_1\ns : Finset ι\nc : ι → R\nA : ι → Matrix n n R\nabv : AbsoluteValue R S\nx : S\nhx : ∀... | [
79,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
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Mathlib/Order/CompleteLattice.lean | sup_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.102338\nβ₂ : Type ?u.102341\nγ : Type ?u.102344\nι : Sort u_1\nι' : Sort ?u.102350\nκ : ι → Sort ?u.102355\nκ' : ι' → Sort ?u.102360\ninst✝¹ : CompleteLattice α\nf✝ g s t : ι → α\na✝ b : α\ninst✝ : Nonempty ι\nf : ι → α\na : α\n⊢ (a ⊔ ⨆... | [
1258,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/BigOperators/Order.lean | Finset.le_prod_of_submultiplicative_on_pred | [
{
"state_after": "case inl\nι : Type u_3\nα : Type ?u.6427\nβ : Type ?u.6430\nM : Type u_2\nN : Type u_1\nG : Type ?u.6439\nk : Type ?u.6442\nR : Type ?u.6445\ninst✝¹ : CommMonoid M\ninst✝ : OrderedCommMonoid N\nf : M → N\np : M → Prop\nh_one : f 1 = 1\nh_mul : ∀ (x y : M), p x → p y → f (x * y) ≤ f x * f y\nhp... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.blsub_lt_ord_lift | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.39723\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal\nc : Ordinal\nho : Cardinal.lift (card o) < cof c\nhf : ∀ (i : Ordinal) (hi : i < o), f i hi < c\nh : blsub o f = c\n⊢ cof c ≤ Cardinal.lift (card o)",
"tactic": "simpa [← ... | [
446,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
443,
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Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_transpose | [
{
"state_after": "case a.h\nl : Type u_2\nm : Type u_4\nn : Type u_1\no : Type u_5\np : Type ?u.12383\nq : Type ?u.12386\nm' : o → Type ?u.12391\nn' : o → Type ?u.12396\np' : o → Type ?u.12401\nR : Type ?u.12404\nS : Type ?u.12407\nα : Type u_3\nβ : Type ?u.12413\nA : Matrix n l α\nB : Matrix n m α\nC : Matrix ... | [
155,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | Submodule.norm_subtypeL_le | [] | [
1299,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1298,
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Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | BoundedContinuousFunction.NNReal.coe_ennreal_comp_measurable | [] | [
320,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_pow | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.41650\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np✝ q p : MvPolynomial σ R\n⊢ 0 ≤ 0 • degrees p",
"state_before": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.41650\nr : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemi... | [
186,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.monomorphisms.infer_property | [] | [
420,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
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Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.not_iff | [] | [
477,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
11
] |
Std/Data/List/Lemmas.lean | List.cons_diff_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl₂ : List α\nh : a ∈ l₂\nl₁ : List α\n⊢ List.diff (a :: l₁) l₂ = List.diff l₁ (List.erase l₂ a)",
"tactic": "rw [cons_diff, if_pos h]"
}
] | [
1513,
76
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1512,
1
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Mathlib/Order/Basic.lean | Prod.mk_lt_mk | [] | [
1248,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1247,
1
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Mathlib/Algebra/Lie/Nilpotent.lean | LieSubmodule.ucs_zero | [] | [
364,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.neg_apply | [] | [
693,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.imageSubobject_zero | [
{
"state_after": "no goals",
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"tactic": "simp"
... | [
379,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
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Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.image_source_inter_eq | [] | [
282,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
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Mathlib/Data/Fin/Basic.lean | Fin.coe_neg_one | [
{
"state_after": "case zero\nm : ℕ\n⊢ ↑(-1) = zero\n\ncase succ\nm n✝ : ℕ\n⊢ ↑(-1) = Nat.succ n✝",
"state_before": "n m : ℕ\n⊢ ↑(-1) = n",
"tactic": "cases n"
},
{
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"state_before": "case succ\nm n✝ : ℕ\n⊢ ↑(-1) = Nat.succ n✝",
... | [
1946,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1942,
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Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | DifferentiableWithinAt.cpow | [] | [
129,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Perm.lean | List.Perm.foldl_eq | [] | [
522,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
520,
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_apply_eq_zero | [
{
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Mathlib/Logic/Equiv/Fin.lean | finSumFinEquiv_symm_apply_castAdd | [] | [
344,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Filter/FilterProduct.lean | Filter.Germ.const_inf | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_preimage_mul_right | [
{
"state_after": "ι : Type ?u.2210287\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\ns : Set ℝ\n⊢ ↑↑(ofReal (abs a⁻¹) • volume) s = ofReal (abs a⁻¹) * ↑↑volume s",
"state_before": "ι : Type ?u.2210287\ninst✝ : Fintype ι\na : ℝ\nh : a ≠ 0\ns : Set ℝ\n⊢ ↑↑(Measure.map (fun x => x * a) volume) s = ofReal (abs a⁻¹) * ↑↑... | [
343,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.liftPropWithinAt_self_target | [] | [
236,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/Topology/Algebra/UniformGroup.lean | CauchySeq.mul | [] | [
442,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Data/Part.lean | Part.inv_some | [] | [
752,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
751,
1
] |
Mathlib/Analysis/Calculus/TangentCone.lean | uniqueDiffWithinAt_congr | [] | [
295,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
293,
1
] |
Mathlib/GroupTheory/NielsenSchreier.lean | IsFreeGroupoid.path_nonempty_of_hom | [
{
"state_after": "case intro\nG : Type u\ninst✝¹ : Groupoid G\ninst✝ : IsFreeGroupoid G\na b : G\np : a ⟶ b\n⊢ Nonempty (Path (IsFreeGroupoid.symgen a) (IsFreeGroupoid.symgen b))",
"state_before": "G : Type u\ninst✝¹ : Groupoid G\ninst✝ : IsFreeGroupoid G\na b : G\n⊢ Nonempty (a ⟶ b) → Nonempty (Path (IsFre... | [
291,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Data/Fintype/Basic.lean | Finset.ssubset_univ_iff | [] | [
142,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.minFac_le | [] | [
348,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Max.lean | isMin_toDual_iff | [] | [
243,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_eq_left_iff_subset | [] | [
1794,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1793,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.normUnit_eq | [] | [
102,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_union_Ioc_eq_Icc | [] | [
1587,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1584,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.succ_succAbove_zero | [
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\ni : Fin n\n⊢ ↑castSucc 0 < succ i",
"tactic": "simp only [castSucc_zero, succ_pos]"
}
] | [
2212,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2211,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithBot.image_coe_Ioo | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ioo a b = Ioo ↑a ↑b",
"tactic": "rw [← preimage_coe_Ioo, image_preimage_eq_inter_range, range_coe,\n inter_eq_self_of_subset_left (Subset.trans Ioo_subset_Ioi_self <| Ioi_subset_Ioi bot_le)]"
}
] | [
235,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Analysis/Convex/Function.lean | concaveOn_id | [
{
"state_after": "𝕜 : Type u_2\nE : Type ?u.14565\nF : Type ?u.14568\nα : Type ?u.14571\nβ : Type u_1\nι : Type ?u.14577\ninst✝⁷ : OrderedSemiring 𝕜\ninst✝⁶ : AddCommMonoid E\ninst✝⁵ : AddCommMonoid F\ninst✝⁴ : OrderedAddCommMonoid α\ninst✝³ : OrderedAddCommMonoid β\ninst✝² : SMul 𝕜 E\ninst✝¹ : SMul 𝕜 α\nin... | [
103,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.StableUnderBaseChange.snd | [] | [
211,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.pi_apply | [] | [
1223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1222,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | nnnorm_pow_le_mul_norm | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.791224\n𝕜 : Type ?u.791227\nα : Type ?u.791230\nι : Type ?u.791233\nκ : Type ?u.791236\nE : Type u_1\nF : Type ?u.791242\nG : Type ?u.791245\ninst✝¹ : SeminormedCommGroup E\ninst✝ : SeminormedCommGroup F\na✝ a₁ a₂ b b₁ b₂ : E\nr r₁ r₂ : ℝ\nn : ℕ\na... | [
1558,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1556,
1
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.coe_im | [] | [
293,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
292,
1
] |
Mathlib/CategoryTheory/LiftingProperties/Basic.lean | CategoryTheory.HasLiftingProperty.op | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nA B B' X Y Y' : C\ni : A ⟶ B\ni' : B ⟶ B'\np : X ⟶ Y\np' : Y ⟶ Y'\nh : HasLiftingProperty i p\nf : Y.op ⟶ B.op\ng : X.op ⟶ A.op\nsq : CommSq f p.op i.op g\n⊢ CommSq.HasLift (_ : CommSq g.unop i p f.unop)",
"state_before": "C : Type u_1\ninst✝ : Category C\... | [
61,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | Continuous.tendstoUniformly | [] | [
262,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Computability/Encoding.lean | Computability.FinEncoding.card_le_aleph0 | [] | [
261,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieHom.mem_idealRange | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\ninst✝⁹ : LieRing L'\ninst✝⁸ : LieAlgebra R L'\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCo... | [
963,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
961,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Diagonal.lean | CategoryTheory.Limits.pullbackDiagonalMapIdIso_inv_snd_snd | [
{
"state_after": "C : Type u_2\ninst✝⁵ : Category C\nX Y Z : C\ninst✝⁴ : HasPullbacks C\nS T : C\nf : X ⟶ T\ng : Y ⟶ T\ni : T ⟶ S\ninst✝³ : HasPullback i i\ninst✝² : HasPullback f g\ninst✝¹ : HasPullback (f ≫ i) (g ≫ i)\ninst✝ :\n HasPullback (diagonal i) (map (f ≫ i) (g ≫ i) i i f g (𝟙 S) (_ : (f ≫ i) ≫ 𝟙 S... | [
274,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Functor.map_hom_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ Z : C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\nX Y : C\nf : X ⟶ Y\ninst✝ : IsIso f\n⊢ F.map f ≫ F.map (inv f) = 𝟙 (F.obj X)",
"tactic": "simp"
}
] | [
628,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
627,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_filter_lt_of_lt_right | [] | [
356,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Data/List/Duplicate.lean | List.duplicate_cons_iff_of_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\nx y : α\nhne : x ≠ y\n⊢ x ∈+ y :: l ↔ x ∈+ l",
"tactic": "simp [duplicate_cons_iff, hne.symm]"
}
] | [
107,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.mem_localTrivAt_target | [] | [
728,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndinter_eq_zero_iff_disjoint | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ s t : Multiset α\n⊢ ndinter s t ⊆ 0 ↔ Disjoint s t",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns✝ s t : Multiset α\n⊢ ndinter s t = 0 ↔ Disjoint s t",
"tactic": "rw [← subset_zero]"
},
{
"state_after": "no goals",
"state_b... | [
282,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
] |
Mathlib/Analysis/NormedSpace/FiniteDimension.lean | LinearIsometry.toLinearIsometryEquiv_apply | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.insert.valid | [
{
"state_after": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : IsTotal α fun x x_1 => x ≤ x_1\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nx : α\nt : Ordnode α\nh : Valid t\n⊢ Valid (insertWith (fun x_1 => x) x t)",
"state_before": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : IsTotal α fun x x_1 => x ≤ x_1\ni... | [
1549,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1547,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.translationNumber_lt_of_forall_lt_add | [
{
"state_after": "case intro.intro\nf g : CircleDeg1Lift\nhf : Continuous ↑f\nz : ℝ\nhz : ∀ (x : ℝ), ↑f x < x + z\nx : ℝ\nhx : ∀ (y : ℝ), y ∈ Icc 0 1 → ↑f y - y ≤ ↑f x - x\n⊢ τ f < z",
"state_before": "f g : CircleDeg1Lift\nhf : Continuous ↑f\nz : ℝ\nhz : ∀ (x : ℝ), ↑f x < x + z\n⊢ τ f < z",
"tactic": "... | [
915,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_mono | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.817681\nδ : Type ?u.817684\ninst✝² : MeasurableSpace α\nK : Type ?u.817690\ninst✝¹ : Zero β\ninst✝ : Preorder β\ns : Set α\nf g : α →ₛ β\nH : f ≤ g\nhs : MeasurableSet s\nx : α\n⊢ ↑(restrict f s) x ≤ ↑(restrict g s) x",
... | [
815,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Independent.lean | affineIndependent_of_ne_of_mem_of_mem_of_not_mem | [
{
"state_after": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type ?u.444767\ns : AffineSubspace k P\np₁ p₂ p₃ : P\nhp₁p₂ : p₁ ≠ p₂\nhp₁ : p₁ ∈ s\nhp₂ : p₂ ∈ s\nhp₃ : ¬p₃ ∈ s\nha : AffineIndependent k fun x => Matr... | [
693,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
] |
Mathlib/GroupTheory/Subgroup/Pointwise.lean | AddSubgroup.le_pointwise_smul_iff₀ | [] | [
557,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
555,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_le_of_le | [] | [
475,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Algebra/Module/Submodule/Pointwise.lean | Submodule.neg_sup | [] | [
123,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.rightLim | [] | [
144,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
11
] |
Mathlib/NumberTheory/LSeries.lean | Nat.ArithmeticFunction.LSeriesSummable_zero | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ LSeriesSummable 0 z",
"tactic": "simp [LSeriesSummable, summable_zero]"
}
] | [
61,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.floor_logb_nat_cast | [
{
"state_after": "case inl\nb✝ x y : ℝ\nb : ℕ\nhb : 1 < b\nhr : 0 ≤ 0\n⊢ ⌊logb (↑b) 0⌋ = Int.log b 0\n\ncase inr\nb✝ x y : ℝ\nb : ℕ\nr : ℝ\nhb : 1 < b\nhr✝ : 0 ≤ r\nhr : 0 < r\n⊢ ⌊logb (↑b) r⌋ = Int.log b r",
"state_before": "b✝ x y : ℝ\nb : ℕ\nr : ℝ\nhb : 1 < b\nhr : 0 ≤ r\n⊢ ⌊logb (↑b) r⌋ = Int.log b r",
... | [
366,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Measurable.real_toNNReal | [] | [
1753,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1751,
1
] |
Std/Data/Int/DivMod.lean | Int.natAbs_div_le_natAbs | [
{
"state_after": "a b : Int\nn : Nat\n⊢ natAbs (a / ↑n) ≤ natAbs a",
"state_before": "a b : Int\nn : Nat\n⊢ natAbs (a / -↑n) ≤ natAbs a",
"tactic": "rw [Int.ediv_neg, natAbs_neg]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nn : Nat\n⊢ natAbs (a / ↑n) ≤ natAbs a",
"tactic"... | [
573,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
565,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_smul | [] | [
178,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
11
] |
Mathlib/Data/Nat/Interval.lean | Nat.card_fintypeIoo | [
{
"state_after": "no goals",
"state_before": "a b c : ℕ\n⊢ Fintype.card ↑(Set.Ioo a b) = b - a - 1",
"tactic": "rw [Fintype.card_ofFinset, card_Ioo]"
}
] | [
145,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Topology/UnitInterval.lean | unitInterval.coe_ne_zero | [] | [
80,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | stronglyMeasurable_of_stronglyMeasurable_union_cover | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.197809\nι : Type ?u.197812\ninst✝¹ : Countable ι\nf✝¹ g : α → β\nm : MeasurableSpace α\ninst✝ : TopologicalSpace β\nf✝ : α → β\ns t : Set α\nhs : MeasurableSet s\nht : MeasurableSet t\nh : univ ⊆ s ∪ t\nhc : StronglyMeasurable fun a => f✝ ↑a\nhd : Strong... | [
799,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/Topology/ContinuousOn.lean | tendsto_nhds_of_tendsto_nhdsWithin | [] | [
390,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Order/Filter/Ultrafilter.lean | Filter.tendsto_iff_ultrafilter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.52285\nf✝ : Filter α\ns : Set α\na : α\nf : α → β\nl₁ : Filter α\nl₂ : Filter β\n⊢ Tendsto f l₁ l₂ ↔ ∀ (g : Ultrafilter α), ↑g ≤ l₁ → Tendsto f (↑g) l₂",
"tactic": "simpa only [tendsto_iff_comap] using le_iff_ultrafilter"
... | [
454,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.toPrefunctor_symm_comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : SingleObj α ⥤q SingleObj β\ng : SingleObj β ⥤q SingleObj γ\n⊢ ↑toPrefunctor.symm (f ⋙q g) = ↑toPrefunctor.symm g ∘ ↑toPrefunctor.symm f",
"tactic": "simp only [Equiv.symm_apply_eq, toPrefunctor_comp, Equiv.apply_... | [
118,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Combinatorics/Composition.lean | Composition.mem_range_embedding_iff' | [
{
"state_after": "case mp\nn : ℕ\nc : Composition n\nj : Fin n\ni : Fin (length c)\n⊢ j ∈ Set.range ↑(embedding c i) → i = index c j\n\ncase mpr\nn : ℕ\nc : Composition n\nj : Fin n\ni : Fin (length c)\n⊢ i = index c j → j ∈ Set.range ↑(embedding c i)",
"state_before": "n : ℕ\nc : Composition n\nj : Fin n\n... | [
431,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
1
] |
Mathlib/Algebra/GroupPower/Basic.lean | Commute.zpow_zpow_self | [] | [
514,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
513,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.mem_add | [] | [
73,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.map_toPoly | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nS : Type u_1\nF : Type ?u.679043\nK : Type ?u.679046\nP Q : Cubic R\na b c d a' b' c' d' : R\ninst✝¹ : Semiring R\ninst✝ : Semiring S\nφ : R →+* S\n⊢ toPoly (map φ P) = Polynomial.map φ (toPoly P)",
"tactic": "simp only [map, toPoly, map_C, map... | [
462,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/Data/Sym/Sym2.lean | Sym2.eq_of_ne_mem | [] | [
385,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_pos_iff | [
{
"state_after": "x y : ℝ\nhx : 0 < x\n⊢ log 1 < log x ↔ 1 < x",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ 0 < log x ↔ 1 < x",
"tactic": "rw [← log_one]"
},
{
"state_after": "no goals",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ log 1 < log x ↔ 1 < x",
"tactic": "exact log_lt_log_iff zero_lt_... | [
172,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/MeasureTheory/Function/L2Space.lean | MeasureTheory.L2.snorm_inner_lt_top | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.44217\n𝕜 : Type u_3\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedAddCommGroup F\nf g : { x // x ∈ Lp E 2 }\nh : ∀ (x : α), ‖inner (↑↑f x) (↑↑g x)‖ ≤ ‖‖↑↑f x... | [
146,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
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