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/Calculus/FDeriv/Prod.lean | DifferentiableOn.fst | [] | [
211,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
11
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_im | [] | [
846,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
846,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.map_swap | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ A B X Y : C\nf : A ⟶ B\ng : X ⟶ Y\ninst✝ : HasLimitsOfShape (Discrete WalkingPair) C\n⊢ map (𝟙 X) f ≫ map g (𝟙 B) = map g (𝟙 A) ≫ map (𝟙 Y) f",
"tactic": "simp"
}
] | [
763,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
761,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.dvd_iff_mod_eq_zero | [] | [
1077,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.op_smul_finset_subset_mul | [] | [
1838,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1837,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Equiv.hasSum_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nδ : Type ?u.56247\ninst✝¹ : AddCommMonoid α\ninst✝ : TopologicalSpace α\nf g : β → α\na b : α\ns : Finset β\ne : γ ≃ β\n⊢ ∀ (x : β), ¬x ∈ Set.range ↑e → f x = 0",
"tactic": "simp"
}
] | [
220,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_self | [
{
"state_after": "no goals",
"state_before": "i : ℤ\n⊢ gcd i i = natAbs i",
"tactic": "simp [gcd]"
}
] | [
272,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | Uniform.continuousWithinAt_iff'_right | [
{
"state_after": "no goals",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.198607\ninst✝¹ : UniformSpace α\ninst✝ : TopologicalSpace β\nf : β → α\nb : β\ns : Set β\n⊢ ContinuousWithinAt f s b ↔ Tendsto (fun x => (f b, f x)) (𝓝[s] b) (𝓤 α)",
"tactic": "rw [ContinuousW... | [
1941,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1939,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.center_eq_top | [] | [
810,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
809,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.irreducible_iff_prime | [] | [
584,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.properDivisors_zero | [
{
"state_after": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ properDivisors 0 ↔ a✝ ∈ ∅",
"state_before": "n : ℕ\n⊢ properDivisors 0 = ∅",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_before": "case a\nn a✝ : ℕ\n⊢ a✝ ∈ properDivisors 0 ↔ a✝ ∈ ∅",
"tactic": "simp"
}
] | [
169,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.bit0_re | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_mul_const_atTop_of_pos | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.216245\nι' : Type ?u.216248\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.216257\ninst✝ : LinearOrderedSemifield α\nl : Filter β\nf : β → α\nr c : α\nn : ℕ\nhr : 0 < r\n⊢ Tendsto (fun x => f x * r) l atTop ↔ Tendsto f l atTop",
"tactic": "simpa only [... | [
1013,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1011,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.closedBall_div | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\ninst✝ : SeminormedCommGroup E\nε δ : ℝ\ns t : Set E\nx✝ y : E\nhs : IsCompact s\nhδ : 0 ≤ δ\nx : E\n⊢ closedBall x δ * s = x • cthickening δ s",
"tactic": "simp [div_eq_mul_inv, hs.closedBall_mul hδ]"
}
] | [
306,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.add_toOuterMeasure | [] | [
785,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | Matrix.toLinearMap₂_toMatrix₂ | [] | [
423,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_mk | [] | [
215,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
] |
Mathlib/Combinatorics/SimpleGraph/Metric.lean | SimpleGraph.Connected.exists_walk_of_dist | [] | [
65,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
11
] |
Mathlib/Probability/Independence/ZeroOne.lean | ProbabilityTheory.measure_zero_or_one_of_measurableSet_limsup | [] | [
124,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Topology/Order/Basic.lean | IsCompact.bddBelow | [
{
"state_after": "case inl\nα : Type u\nβ : Type v\nγ : Type w\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderClosedTopology α\nf g : β → α\ninst✝¹ : Nonempty α\ninst✝ : TopologicalSpace β\ns : Set α\nhs : IsCompact s\nh : OrderBot α\n⊢ BddBelow s\n\ncase inr\nα : Type u\nβ : Type v\nγ : Ty... | [
813,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Deprecated/Submonoid.lean | Univ.isSubmonoid | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : Monoid M\ns : Set M\nA : Type ?u.23073\ninst✝ : AddMonoid A\nt : Set A\n⊢ IsSubmonoid Set.univ",
"tactic": "constructor <;> simp"
}
] | [
171,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean | GeneralizedContinuedFraction.of_correctness_of_nth_stream_eq_none | [
{
"state_after": "no goals",
"state_before": "case zero\nK : Type u_1\ninst✝¹ : LinearOrderedField K\nv : K\nn : ℕ\ninst✝ : FloorRing K\nnth_stream_eq_none : IntFractPair.stream v Nat.zero = none\n⊢ v = convergents (of v) (Nat.zero - 1)",
"tactic": "contradiction"
},
{
"state_after": "case succ\... | [
243,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.num_denom_neg | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝ : Field K\nx : RatFunc K\n⊢ num (-x) * denom x = -num x * denom (-x)",
"tactic": "rw [num_mul_eq_mul_denom_iff (denom_ne_zero x), _root_.map_neg, neg_div, num_div_denom]"
}
] | [
1279,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/LinearAlgebra/DirectSum/TensorProduct.lean | TensorProduct.directSumLeft_tmul_lof | [
{
"state_after": "R : Type u\ninst✝¹⁰ : CommRing R\nι₁ : Type v₁\nι₂ : Type v₂\ninst✝⁹ : DecidableEq ι₁\ninst✝⁸ : DecidableEq ι₂\nM₁ : ι₁ → Type w₁\nM₁' : Type w₁'\nM₂ : ι₂ → Type w₂\nM₂' : Type w₂'\ninst✝⁷ : (i₁ : ι₁) → AddCommGroup (M₁ i₁)\ninst✝⁶ : AddCommGroup M₁'\ninst✝⁵ : (i₂ : ι₂) → AddCommGroup (M₂ i₂)\... | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/CategoryTheory/Functor/Basic.lean | CategoryTheory.Functor.comp_id | [
{
"state_after": "case mk\nC : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nE : Type u₃\ninst✝ : Category E\ntoPrefunctor✝ : C ⥤q D\nmap_id✝ : ∀ (X : C), toPrefunctor✝.map (𝟙 X) = 𝟙 (toPrefunctor✝.obj X)\nmap_comp✝ : ∀ {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z), toPrefunctor✝.map (f ≫ g) = toPrefu... | [
133,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
11
] |
Mathlib/Data/Finset/Basic.lean | List.coe_toFinset | [] | [
3257,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3256,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.coprime_of_root_cyclotomic | [
{
"state_after": "case a\nn : ℕ\nhpos : 0 < n\np : ℕ\nhprime : Fact (Nat.Prime p)\na : ℕ\nhroot : IsRoot (cyclotomic n (ZMod p)) (↑(Nat.castRingHom (ZMod p)) a)\n⊢ Nat.coprime p a",
"state_before": "n : ℕ\nhpos : 0 < n\np : ℕ\nhprime : Fact (Nat.Prime p)\na : ℕ\nhroot : IsRoot (cyclotomic n (ZMod p)) (↑(Nat... | [
632,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | roots_mem_integralClosure | [] | [
1189,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1187,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.map_id' | [
{
"state_after": "case h\nα✝ : Type ?u.35215\nβ : Type ?u.35218\nn✝ n' m : ℕ\ns✝ : Sym α✝ n✝\na b : α✝\nα : Type u_1\nn : ℕ\ns : Sym α n\n⊢ ↑(map (fun x => x) s) = ↑s",
"state_before": "α✝ : Type ?u.35215\nβ : Type ?u.35218\nn✝ n' m : ℕ\ns✝ : Sym α✝ n✝\na b : α✝\nα : Type u_1\nn : ℕ\ns : Sym α n\n⊢ map (fun... | [
366,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.bypass_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝ : DecidableEq V\nu' v' : V\np : Walk G u' v'\n⊢ bypass (Walk.copy p (_ : u' = u') (_ : v' = v')) = Walk.copy (bypass p) (_ : u' = u') (_ : v' = v')",
"state_before": "V : Type u\nV' ... | [
1365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1362,
1
] |
Mathlib/Algebra/Order/Group/Abs.lean | abs_choice | [] | [
49,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.copy_eq | [] | [
198,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicatorAux_one_of_mem_closure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\nδ : ℝ\nE : Set α\nx : α\nx_mem : x ∈ closure E\n⊢ thickenedIndicatorAux δ E x = 1",
"tactic": "rw [← thickenedIndicatorAux_closure_eq, thickenedIndicatorAux_one δ (closure E) x_mem]"
}
] | [
94,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_self | [] | [
289,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.zero_smul_finset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.929758\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.929767\ninst✝³ : Zero α\ninst✝² : Zero β\ninst✝¹ : SMulWithZero α β\ninst✝ : DecidableEq β\ns✝ : Finset α\nt s : Finset β\nh : Finset.Nonempty s\n⊢ ↑(0 • s) = ↑0",
"tactic": "simpa using @Set.zero_s... | [
2113,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2112,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Equiv.injective | [] | [
849,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Data/Nat/Dist.lean | Nat.dist_zero_left | [] | [
75,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.sumArrowEquivProdArrow_symm_apply_inr | [] | [
898,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/GroupTheory/DoubleCoset.lean | Doset.mk_eq_of_doset_eq | [
{
"state_after": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.39521\ninst✝ : Mul α\nJ : Subgroup G\ng : G\nH K : Subgroup G\na b : G\nh : doset a ↑H ↑K = doset b ↑H ↑K\n⊢ ∃ h, h ∈ H ∧ ∃ k, k ∈ K ∧ b = h * a * k",
"state_before": "G : Type u_1\ninst✝¹ : Group G\nα : Type ?u.39521\ninst✝ : Mul α\nJ : Subgroup... | [
153,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.mono | [] | [
253,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
11
] |
Mathlib/Order/LocallyFinite.lean | Finset.subtype_Ico_eq | [] | [
1272,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/Data/Vector3.lean | Vector3.append_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm✝ n✝ m : ℕ\nv : Vector3 α (succ m)\nn : ℕ\nw : Vector3 α n\na : α\n_t : Vector3 α m\n⊢ ((a :: _t) +-+ w) (left n fz) = (a :: _t) fz",
"tactic": "simp [*, left]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\nm✝ n✝ m... | [
176,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.Ioi_le_Ici | [] | [
1211,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1210,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.supported_mono | [] | [
268,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Logic/Basic.lean | exists_of_bex | [] | [
1073,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.atomise_empty | [
{
"state_after": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nF : Finset (Finset α)\nhs : Finset.Nonempty s\n⊢ (ofErase {s} (_ : SupIndep {s} id) (_ : sup {s} id = s)).parts = {s}",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nF : Fin... | [
572,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/LinearAlgebra/Matrix/Orthogonal.lean | Matrix.transpose_hasOrthogonalRows_iff_hasOrthogonalCols | [] | [
57,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_lt_sub_one_of_pos | [
{
"state_after": "case h\nx y : ℝ\nhx1 : 0 < x\nhx2 : x ≠ 1\n⊢ log x ≠ 0\n\nx y : ℝ\nhx1 : 0 < x\nhx2 : x ≠ 1\nh : log x ≠ 0\n⊢ log x < x - 1",
"state_before": "x y : ℝ\nhx1 : 0 < x\nhx2 : x ≠ 1\n⊢ log x < x - 1",
"tactic": "have h : log x ≠ 0"
},
{
"state_after": "no goals",
"state_before":... | [
226,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.partiallyWellOrderedOn_sublistForall₂ | [
{
"state_after": "case inl\nι : Type ?u.147263\nα : Type u_1\nβ : Type ?u.147269\nr✝ r : α → α → Prop\ninst✝¹ : IsRefl α r\ninst✝ : IsTrans α r\ns : Set α\nh : PartiallyWellOrderedOn s r\nh✝ : IsEmpty α\n⊢ PartiallyWellOrderedOn {l | ∀ (x : α), x ∈ l → x ∈ s} (List.SublistForall₂ r)\n\ncase inr\nι : Type ?u.147... | [
781,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
744,
1
] |
Mathlib/Init/CcLemmas.lean | iff_eq_of_eq_true_right | [] | [
16,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
15,
1
] |
Mathlib/Data/List/Zip.lean | List.zipWith3_same_mid | [] | [
328,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_id | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
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Mathlib/MeasureTheory/Lattice.lean | Finset.measurable_sup' | [] | [
247,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.adj_injective | [] | [
223,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
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Mathlib/Data/Nat/Digits.lean | Nat.digits_ofDigits | [
{
"state_after": "case nil\nn b : ℕ\nh : 1 < b\nL : List ℕ\nw₁✝ : ∀ (l : ℕ), l ∈ L → l < b\nw₂✝ : ∀ (h : L ≠ []), List.getLast L h ≠ 0\nw₁ : ∀ (l : ℕ), l ∈ [] → l < b\nw₂ : ∀ (h : [] ≠ []), List.getLast [] h ≠ 0\n⊢ digits b (ofDigits b []) = []\n\ncase cons\nn b : ℕ\nh : 1 < b\nL✝ : List ℕ\nw₁✝ : ∀ (l : ℕ), l ∈... | [
253,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
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Mathlib/RingTheory/FiniteType.lean | AddMonoidAlgebra.fg_of_finiteType | [] | [
476,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
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Mathlib/Analysis/NormedSpace/BoundedLinearMaps.lean | ContinuousLinearMap.map_neg₂ | [
{
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319,
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318,
1
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Mathlib/Data/Finsupp/Basic.lean | Finsupp.mapDomain_injOn | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.292155\nι : Type ?u.292158\nM : Type u_3\nM' : Type ?u.292164\nN : Type ?u.292167\nP : Type ?u.292170\nG : Type ?u.292173\nH : Type ?u.292176\nR : Type ?u.292179\nS✝ : Type ?u.292182\ninst✝ : AddCommMonoid M\nv v₁✝ v₂✝ : α →₀ M\nS : Set α\nf : α → β\nhf ... | [
676,
15
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665,
1
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Mathlib/Topology/Sober.lean | IsIrreducible.genericPoint_spec | [] | [
135,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
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Mathlib/Data/List/Lemmas.lean | List.foldr_range_subset_of_range_subset | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : β → α → α\ng : γ → α → α\nhfg : Set.range f ⊆ Set.range g\na : α\nl : List β\n⊢ foldr f a l ∈ Set.range (foldr g a)",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : β → α → α\ng : γ → α → α\nhfg : Set.range f ⊆ Set.r... | [
55,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.csinh | [] | [
535,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
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Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.Measure.quasiMeasurePreserving_snd | [
{
"state_after": "α : Type u_2\nα' : Type ?u.4452406\nβ : Type u_1\nβ' : Type ?u.4452412\nγ : Type ?u.4452415\nE : Type ?u.4452418\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : MeasurableSpace α'\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace β'\ninst✝² : MeasurableSpace γ\nμ μ' : Measure α\nν ν' : Measure β\nτ ... | [
475,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
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Mathlib/SetTheory/ZFC/Ordinal.lean | ZFSet.IsTransitive.sUnion | [
{
"state_after": "case intro.intro\nx y✝ z✝ : ZFSet\nh : IsTransitive x\ny : ZFSet\nhy : y ∈ ⋃₀ x\nz : ZFSet\nhz : z ∈ y\nw : ZFSet\nhw : w ∈ x\nhw' : y ∈ w\n⊢ z ∈ ⋃₀ x",
"state_before": "x y✝ z✝ : ZFSet\nh : IsTransitive x\ny : ZFSet\nhy : y ∈ ⋃₀ x\nz : ZFSet\nhz : z ∈ y\n⊢ z ∈ ⋃₀ x",
"tactic": "rcases... | [
71,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
11
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Mathlib/CategoryTheory/Limits/Shapes/Images.lean | CategoryTheory.Limits.HasImage.of_arrow_iso | [] | [
288,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.constVAdd_symm | [] | [
502,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
501,
1
] |
Mathlib/Order/Filter/Pi.lean | Filter.mem_pi' | [] | [
89,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
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Mathlib/Topology/Algebra/Polynomial.lean | Polynomial.continuous | [] | [
60,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
11
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.ker_prod | [
{
"state_after": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.226252\nM₆ : Type ?u.226255\ninst✝⁸ : Semiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : AddCommMonoid M₂\ninst✝⁵ : AddCommMonoid M₃\ninst✝⁴ : AddCommMonoid... | [
500,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.comp_eq_zero | [] | [
308,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Data/Sign.lean | SignType.zero_eq_zero | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.monic_of_d_eq_one' | [] | [
277,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_eq_ball | [] | [
457,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
455,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.isMin_of_apply | [] | [
591,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | dualTensorHom_apply | [] | [
85,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.lintegral_lintegral_symm | [] | [
792,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Splitting.epi | [] | [
256,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.AdjoinSimple.algebraMap_gen | [] | [
496,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Algebra/BigOperators/Pi.lean | Prod.snd_prod | [] | [
140,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | orthogonalProjection_map_apply | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nE✝ : Type ?u.545265\nF : Type ?u.545268\ninst✝¹⁰ : IsROrC 𝕜\ninst✝⁹ : NormedAddCommGroup E✝\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : InnerProductSpace 𝕜 E✝\ninst✝⁶ : InnerProductSpace ℝ F\nK : Submodule 𝕜 E✝\ninst✝⁵ : CompleteSpace { x // x ∈ K... | [
557,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
551,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.disjoint_principal_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.56071\nγ : Type ?u.56074\nι : Sort ?u.56077\nι' : Sort ?u.56080\nl l' : Filter α\np : ι → Prop\ns✝ : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nf : Filter α\ns : Set α\n⊢ Disjoint f (𝓟 s) ↔ sᶜ ∈ f",
"tac... | [
699,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
698,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | IsometryEquiv.image_ball | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1147478\nα : Type u\nβ : Type v\nγ : Type w\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\nh✝ h : α ≃ᵢ β\nx : α\nr : ℝ\n⊢ ↑h '' Metric.ball x r = Metric.ball (↑h x) r",
"tactic": "rw [← h.preimage_symm, h.symm.preimage_ball, symm_sym... | [
629,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | ContinuousLinearMap.toSpanSingleton_homothety | [
{
"state_after": "𝕜 : Type u_2\n𝕜₂ : Type ?u.369942\nE : Type u_1\nF : Type ?u.369948\nG : Type ?u.369951\ninst✝³ : NormedField 𝕜\ninst✝² : NormedField 𝕜₂\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nc : 𝕜\n⊢ ‖↑(LinearMap.toSpanSingleton 𝕜 E x) c‖ = ‖c‖ * ‖x‖",
"state_before": ... | [
236,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/RingTheory/Prime.lean | Prime.neg | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝ : CommRing α\np : α\nh1 : p ≠ 0\nh2 : ¬IsUnit p\nh3 : ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b\n⊢ Prime (-p)",
"state_before": "α : Type u_1\ninst✝ : CommRing α\np : α\nhp : Prime p\n⊢ Prime (-p)",
"tactic": "obtain ⟨h1, h2, h3⟩ := hp"
},
{
"... | [
71,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_inf_le | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K L : Subgroup G\n⊢ index (H ⊓ K) ≤ index H * index K",
"tactic": "simp_rw [← relindex_top_right, relindex_inf_le]"
}
] | [
448,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
447,
1
] |
Mathlib/Algebra/Divisibility/Basic.lean | Dvd.elim | [] | [
63,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | bit1_mono | [] | [
240,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Topology/Basic.lean | interior_setOf_eq | [] | [
1219,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1218,
1
] |
Mathlib/Order/Lattice.lean | inf_le_of_right_le | [] | [
416,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.copy_eq | [] | [
1260,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1259,
1
] |
Mathlib/FieldTheory/ChevalleyWarning.lean | char_dvd_card_solutions_of_add_lt | [
{
"state_after": "K : Type u_2\nσ : Type u_1\nι : Type ?u.683318\ninst✝⁵ : Fintype K\ninst✝⁴ : Field K\ninst✝³ : Fintype σ\ninst✝² : DecidableEq σ\ninst✝¹ : DecidableEq K\np : ℕ\ninst✝ : CharP K p\nf₁ f₂ : MvPolynomial σ K\nh : totalDegree f₁ + totalDegree f₂ < Fintype.card σ\nF : Bool → MvPolynomial σ K := fun... | [
206,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.EqOnSource.symm_eqOn_target | [] | [
968,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
966,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.counitInv_functor_comp | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\ne : C ≌ D\nX : C\n⊢ (e.functor.mapIso (e.unitIso.app X) ≪≫ e.counitIso.app (e.functor.obj X)).hom =\n (Iso.refl (e.functor.obj ((𝟭 C).obj X))).hom",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ ... | [
164,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_of_norm_sub_le | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.985379\nδ : Type ?u.985382\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝² : MeasurableSpace δ\ninst✝¹ : NormedAddCommGroup β\ninst✝ : NormedAddCommGroup γ\nf₀ f₁ : α → β\ng : α → ℝ\nhf₁_m : AEStronglyMeasurable f₁ μ\nhf₀_i : Integrable f₀\nhg_i : Integr... | [
780,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Data/Part.lean | Part.Dom.of_bind | [] | [
511,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
510,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.diagonal_apply_ne | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.45650\nm : Type ?u.45653\nn : Type u_1\no : Type ?u.45659\nm' : o → Type ?u.45664\nn' : o → Type ?u.45669\nR : Type ?u.45672\nS : Type ?u.45675\nα : Type v\nβ : Type w\nγ : Type ?u.45682\ninst✝¹ : DecidableEq n\ninst✝ : Zero α\nd : n → α\ni j : n\nh ... | [
440,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.nil_append | [
{
"state_after": "case H\nα : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ ∀ (s : Seq α), BisimO (fun s1 s2 => ∃ s, s1 = append nil s ∧ s2 = s) (destruct (append nil s)) (destruct s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns : Seq α\n⊢ append nil s = s",
"tactic": "apply coinduction2"
}... | [
653,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_div_iff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LE α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na✝ b c a : α\n⊢ a / b ≤ a / c ↔ c ≤ b",
"tactic": "rw [div_eq_m... | [
781,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
779,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.isHermitian_conjTranspose_mul_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type ?u.33164\nm : Type u_1\nn : Type u_3\nA✝ : Matrix n n α\ninst✝⁴ : NonUnitalSemiring α\ninst✝³ : StarRing α\ninst✝² : NonUnitalSemiring β\ninst✝¹ : StarRing β\ninst✝ : Fintype m\nA : Matrix m m α\nB : Matrix m n α\nhA : IsHermitian A\n⊢ IsH... | [
212,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | zero_apply | [] | [
64,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Sequence₂.lift_mk | [
{
"state_after": "no goals",
"state_before": "a₀ a₁ a₂ : Type u\ni : ℕ\n⊢ lift (#Sequence₂ a₀ a₁ a₂ i) = (#Sequence₂ (ULift a₀) (ULift a₁) (ULift a₂) i)",
"tactic": "rcases i with (_ | _ | _ | i) <;>\n simp only [Sequence₂, mk_uLift, mk_fintype, Fintype.card_of_isEmpty, Nat.cast_zero, lift_zero]"
}
] | [
100,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
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