file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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Mathlib/Data/Set/Intervals/Infinite.lean | Set.Icc.infinite | [] | [
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39
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Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.mul_pp_pf_overlap | [
{
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Mathlib/Analysis/MeanInequalities.lean | NNReal.summable_Lp_add | [] | [
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Mathlib/Topology/LocalExtr.lean | isLocalMax_const | [] | [
207,
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Mathlib/ModelTheory/FinitelyGenerated.lean | FirstOrder.Language.Substructure.fg_iff_structure_fg | [
{
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{
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277,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.setToL1_eq_setToL1' | [] | [
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Mathlib/LinearAlgebra/Matrix/NonsingularInverse.lean | Matrix.det_nonsing_inv_mul_det | [
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}
] | [
393,
47
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Mathlib/Order/Concept.lean | Concept.sup_fst | [] | [
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Mathlib/FieldTheory/Subfield.lean | RingHom.coe_fieldRange | [] | [
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Mathlib/Data/TypeVec.lean | TypeVec.dropFun_from_append1_drop_last | [] | [
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6
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Mathlib/Algebra/Lie/Basic.lean | LieModuleHom.ext | [] | [
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28
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803,
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Mathlib/LinearAlgebra/Span.lean | Submodule.span_singleton_eq_top_iff | [
{
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422,
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegrable_const | [] | [
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62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Group/Basic.lean | Real.norm_coe_nat | [] | [
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1727,
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Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.const_mul_atTop | [] | [
1037,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/RelClasses.lean | IsWellFounded.fix_eq | [] | [
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14
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Mathlib/Analysis/Calculus/Inverse.lean | ContDiffAt.to_localInverse | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_zero_eq_constantCoeff | [] | [
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Mathlib/Algebra/GradedMonoid.lean | GradedMonoid.GMonoid.gnpowRec_succ | [] | [
168,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_multiset_of_countable | [
{
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}
] | [
1085,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.rpow_lt_one_of_one_lt_of_neg | [] | [
209,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_mk | [] | [
349,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Semiquot.lean | Semiquot.mem_map | [] | [
134,
22
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133,
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Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.adjoint_comp | [
{
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420,
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Mathlib/MeasureTheory/Measure/MeasureSpaceDef.lean | MeasureTheory.measure_union_eq_top_iff | [
{
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"tactic": "simp only [← lt_top_iff_ne_top, ← Ne.def, ... | [
326,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.sSup_closed_unit_ball_eq_norm | [
{
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Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.Integrable.smul_of_top_left | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1043,
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Mathlib/Topology/MetricSpace/Isometry.lean | UniformEmbedding.to_isometry | [] | [
281,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/MetricSpace/IsometricSMul.lean | edist_mul_right | [] | [
117,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
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Mathlib/Algebra/Tropical/BigOperators.lean | trop_sum | [
{
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Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.res_eq_res | [
{
"state_after": "case mp.zero\nE : ℕ → Type ?u.20736\nα : Type u_1\nx y : ℕ → α\nn : ℕ\nh✝ : res x n = res y n\nh : res x Nat.zero = res y Nat.zero\n⊢ ∀ ⦃m : ℕ⦄, m < Nat.zero → x m = y m\n\ncase mp.succ\nE : ℕ → Type ?u.20736\nα : Type u_1\nx y : ℕ → α\nn✝ : ℕ\nh✝ : res x n✝ = res y n✝\nn : ℕ\nih : res x n = r... | [
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Mathlib/Order/RelIso/Basic.lean | wellFounded_liftOn₂'_iff | [] | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_one | [
{
"state_after": "case h\nl : Type ?u.897846\nm : Type u_2\nn : Type u_1\no : Type ?u.897855\nm' : o → Type ?u.897860\nn' : o → Type ?u.897865\nR : Type ?u.897868\nS : Type ?u.897871\nα : Type v\nβ : Type w\nγ : Type ?u.897878\ninst✝¹ : NonAssocSemiring α\ninst✝ : Fintype n\nA : Matrix m n α\nx✝ : m\n⊢ mulVec A... | [
1869,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1868,
1
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Mathlib/Topology/PathConnected.lean | Path.extend_of_le_zero | [] | [
291,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
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Mathlib/Combinatorics/SimpleGraph/Density.lean | SimpleGraph.mem_interedges_iff | [] | [
331,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
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Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.uniformEquicontinuous_iff_right | [] | [
79,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
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] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_add_mul_left_right | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ gcd m (n + m * k) = gcd m n",
"tactic": "simp [gcd_rec m (n + m * k), gcd_rec m n]"
}
] | [
43,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.pow_mono | [
{
"state_after": "no goals",
"state_before": "f✝ g✝ f g : CircleDeg1Lift\nh : f ≤ g\nn : ℕ\nx : ℝ\n⊢ ↑(f ^ n) x ≤ ↑(g ^ n) x",
"tactic": "simp only [coe_pow, iterate_mono h n x]"
}
] | [
445,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
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Mathlib/Data/Finset/Sups.lean | Finset.singleton_infs | [] | [
325,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | div_mul_div_cancel | [
{
"state_after": "no goals",
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"tactic": "rw [← mul... | [
136,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
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Mathlib/Data/Polynomial/Monic.lean | Polynomial.Monic.sub_of_left | [
{
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407,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.coe_lsum | [] | [
372,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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src/lean/Init/Control/Lawful.lean | StateT.run_map | [
{
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"tactic": "simp [Functor.map, StateT.map, run, map_eq_pure_bind]"
}
] | [
255,
56
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
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Mathlib/RingTheory/Ideal/Operations.lean | Submodule.span_smul_span | [] | [
240,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
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Mathlib/NumberTheory/RamificationInertia.lean | Ideal.FinrankQuotientMap.linearIndependent_of_nontrivial | [
{
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287,
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257,
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Mathlib/Order/Filter/Prod.lean | Filter.tendsto_swap4_prod | [] | [
335,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
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Mathlib/Data/Polynomial/FieldDivision.lean | Polynomial.C_mul_dvd | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nk : Type y\nA : Type z\na b : R\nn : ℕ\ninst✝ : Field R\np q : R[X]\nha : a ≠ 0\nx✝ : p ∣ q\nr : R[X]\nhr : q = p * r\n⊢ q = ↑C a * p * (↑C a⁻¹ * r)",
"tactic": "rw [mul_assoc, mul_left_comm p, ← mul_assoc, ← C.map_mul, _root_.mul_inv... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
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Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.order_eq | [
{
"state_after": "case a\nR : Type u_1\ninst✝ : Semiring R\nφ✝ φ : PowerSeries R\n⊢ order φ = ⊤ ↔ (∀ (i : ℕ), ↑i = ⊤ → ↑(coeff R i) φ ≠ 0) ∧ ∀ (i : ℕ), ↑i < ⊤ → ↑(coeff R i) φ = 0\n\ncase a\nR : Type u_1\ninst✝ : Semiring R\nφ✝ φ : PowerSeries R\nn✝ : ℕ\n⊢ order φ = ↑n✝ ↔ (∀ (i : ℕ), ↑i = ↑n✝ → ↑(coeff R i) φ ≠... | [
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2323,
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Mathlib/Topology/Basic.lean | continuous_id | [] | [
1629,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1628,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.coe_valMinAbs | [
{
"state_after": "k n : ℕ\nh✝ : k = n + 1\nx : ZMod (namedPattern k (n + 1) h✝)\n⊢ ↑(if val x ≤ namedPattern k (n + 1) h✝ / 2 then ↑(val x) else ↑(val x) - ↑(namedPattern k (n + 1) h✝)) = x",
"state_before": "k n : ℕ\nh✝ : k = n + 1\nx : ZMod (namedPattern k (n + 1) h✝)\n⊢ ↑(valMinAbs x) = x",
"tactic":... | [
924,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
] |
Mathlib/Data/List/Zip.lean | List.lt_length_left_of_zip | [] | [
105,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
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Mathlib/Data/Finmap.lean | Finmap.keys_ext | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ns₁ s₂ : AList β\n⊢ keys ⟦s₁⟧ = keys ⟦s₂⟧ ↔ AList.keys s₁ ~ AList.keys s₂",
"tactic": "simp [keys, AList.keys]"
}
] | [
202,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_subset_Ici_self | [] | [
542,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.PartiallyWellOrderedOn.wellFoundedOn | [
{
"state_after": "ι : Type ?u.95097\nα : Type u_1\nβ : Type ?u.95103\nr : α → α → Prop\nr' : β → β → Prop\nf : α → β\ns t : Set α\na : α\ninst✝ : IsPreorder α r\nh : PartiallyWellOrderedOn s r\nthis : Preorder α := Preorder.mk (_ : ∀ (a : α), r a a) (_ : ∀ (x x_1 x_2 : α), r x x_1 → r x_1 x_2 → r x x_2)\n⊢ Well... | [
390,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/MeasureTheory/Function/EssSup.lean | OrderIso.essInf_apply | [] | [
194,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.iSupLift_inclusion | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\ninst✝⁵ : CommSemiring R\ninst✝⁴ : Semiring A\ninst✝³ : Algebra R A\ninst✝² : Semiring B\ninst✝¹ : Algebra R B\nS : Subalgebra R A\nι : Type u_1\ninst✝ : Nonempty ι\nK : ι → Subalgebra R A\ndir : Directed (fun x x_1 => x ≤ x_1) K\nf : (i : ι) → { x // x ∈ K i... | [
1214,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1211,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | iInf_sup_eq | [] | [
203,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Set/Function.lean | Set.LeftInvOn.image_inter' | [
{
"state_after": "case h₁\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.59103\nι : Sort ?u.59106\nπ : α → Type ?u.59111\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\np : Set γ\nf f₁ f₂ f₃ : α → β\ng g₁ g₂ : β → γ\nf' f₁' f₂' : β → α\ng' : γ → β\na : α\nb : β\nhf : LeftInvOn f' f s\n⊢ f '' (s₁ ∩ s) ⊆ f' ⁻¹' s₁ ∩ f '' s\n\ncase ... | [
1077,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.zeroLocus_singleton_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf g : R\nx : PrimeSpectrum R\n⊢ x ∈ zeroLocus {f * g} ↔ x ∈ zeroLocus {f} ∪ zeroLocus {g}",
"tactic": "simpa using x.2.mul_mem_iff_mem_or_mem"
}
] | [
375,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sub_isLimit | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.133611\nβ : Type ?u.133614\nγ : Type ?u.133617\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na b : Ordinal\nl : IsLimit a\nh : b < a\n⊢ b + 0 < a",
"tactic": "rwa [add_zero]"
},
{
"state_after": "α : Type ?u.133611\nβ : Type ?u.1... | [
614,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
612,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.isBridge_iff_adj_and_forall_walk_mem_edges | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nv w : V\n⊢ ¬Reachable (G \\ fromEdgeSet {Quotient.mk (Sym2.Rel.setoid V) (v, w)}) v w ↔\n ∀ (p : Walk G v w), Quotient.mk (Sym2.Rel.setoid V) (v, w) ∈ Walk.edges p",
"state_before": "V ... | [
2468,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2465,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.Continuous'.to_bundled | [] | [
274,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Metrizable.lean | measurable_of_tendsto_ennreal' | [
{
"state_after": "case intro\nα : Type u_2\nβ : Type ?u.48\ninst✝⁶ : MeasurableSpace α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : PseudoMetrizableSpace β\ninst✝³ : MeasurableSpace β\ninst✝² : BorelSpace β\nι : Type u_1\nf : ι → α → ℝ≥0∞\ng : α → ℝ≥0∞\nu : Filter ι\ninst✝¹ : NeBot u\ninst✝ : IsCountablyGenerated u\n... | [
42,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
32,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_eq_zero | [] | [
200,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/RingTheory/Noetherian.lean | isNoetherian_submodule_right | [] | [
112,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.base_pow_length_digits_le | [
{
"state_after": "case succ.succ\nn m b : ℕ\n⊢ ¬m = 0 → succ (succ b) ^ List.length (digits (succ (succ b)) m) ≤ succ (succ b) * m",
"state_before": "n b m : ℕ\nhb : 1 < b\n⊢ m ≠ 0 → b ^ List.length (digits b m) ≤ b * m",
"tactic": "rcases b with (_ | _ | b) <;> try simp_all"
},
{
"state_after":... | [
474,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/Topology/Instances/TrivSqZeroExt.lean | TrivSqZeroExt.continuous_inl | [] | [
70,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieSubmodule.map_bracket_eq | [
{
"state_after": "R : Type u\nL : Type v\nM : Type w\nM₂ : Type w₁\ninst✝¹⁰ : CommRing R\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 : AddCommGroup M₂\ninst✝² : Module R M₂\ninst✝¹ : LieRingModule L M₂\n... | [
221,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Quot.lean | Quot.map₂_mk | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | tendsto_self_mul_const_pow_of_lt_one | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.130031\nβ : Type ?u.130034\nι : Type ?u.130037\nr : ℝ\nhr : 0 ≤ r\nh'r : r < 1\n⊢ Tendsto (fun n => ↑n * r ^ n) atTop (𝓝 0)",
"tactic": "simpa only [pow_one] using tendsto_pow_const_mul_const_pow_of_lt_one 1 hr h'r"
}
] | [
264,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.ModEq.add_nsmul | [] | [
144,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
11
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.bot_snoc | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\ns : CompositionSeries X\nx : X\nhsat : IsMaximal (top s) x\n⊢ bot (snoc s x hsat) = bot s",
"tactic": "rw [bot, bot, ← snoc_castSucc s _ _ 0, Fin.castSucc_zero]"
}
] | [
577,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | edist_ne_top_of_mem_ball | [
{
"state_after": "α : Type ?u.350406\nβ : Type u_1\nγ : Type ?u.350412\ninst✝ : EMetricSpace β\na : β\nr : ℝ≥0∞\nx y : ↑(EMetric.ball a r)\n⊢ edist (↑x) a + edist (↑y) a < r + r",
"state_before": "α : Type ?u.350406\nβ : Type u_1\nγ : Type ?u.350412\ninst✝ : EMetricSpace β\na : β\nr : ℝ≥0∞\nx y : ↑(EMetric.... | [
1381,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.mem_completeTheory | [] | [
793,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
1
] |
Mathlib/Data/Fintype/Card.lean | is_empty_fintype | [] | [
939,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
938,
1
] |
Mathlib/Data/List/Basic.lean | List.dropLast_append_of_ne_nil | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.198199\nα✝ : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α✝\nα : Type u_1\nl : List α\nx✝ : l ≠ []\n⊢ dropLast ([] ++ l) = [] ++ dropLast l",
"tactic": "simp only [nil_append]"
},
{
"state_after": "case x_2\nι : Type ?u.19819... | [
2093,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2088,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.conjTranspose_rat_smul | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.1036039\nm : Type u_1\nn : Type u_2\no : Type ?u.1036048\nm' : o → Type ?u.1036053\nn' : o → Type ?u.1036058\nR : Type ?u.1036061\nS : Type ?u.1036064\nα : Type v\nβ : Type w\nγ : Type ?u.1036071\ninst✝² : AddCommGroup α\ninst✝¹ : StarAddMonoid α\nin... | [
2236,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2234,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂Hom_zero_apply | [] | [
1491,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1489,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.tendsto_inf | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.313910\nι : Sort x\nf : α → β\nx : Filter α\ny₁ y₂ : Filter β\n⊢ Tendsto f x (y₁ ⊓ y₂) ↔ Tendsto f x y₁ ∧ Tendsto f x y₂",
"tactic": "simp only [Tendsto, le_inf_iff, iff_self_iff]"
}
] | [
2986,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2984,
1
] |
Mathlib/Data/List/Sigma.lean | List.mem_dlookup_kunion_middle | [] | [
793,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Mathlib/GroupTheory/Subsemigroup/Operations.lean | MulHom.map_srange | [
{
"state_after": "no goals",
"state_before": "M : Type u_3\nN : Type u_1\nP : Type u_2\nσ : Type ?u.60762\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Mul P\nS : Subsemigroup M\ng : N →ₙ* P\nf : M →ₙ* N\n⊢ map g (srange f) = srange (comp g f)",
"tactic": "simpa only [srange_eq_map] using (⊤ : Subsemigroup M... | [
778,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.one_mem_one | [] | [
108,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Analysis/SpecialFunctions/Exp.lean | Complex.tendsto_exp_comap_re_atTop | [] | [
455,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Order/UpperLower/Basic.lean | IsLowerSet.preimage | [] | [
250,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
249,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.smul_nat | [
{
"state_after": "u : Lean.Level\nR : Type ?u.195256\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b : ℕ\n⊢ a • b = a * b",
"state_before": "u : Lean.Level\nR : Type ?u.195256\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na b c : ℕ\nx✝ : a * b = c\n⊢ a • b = c",
... | [
505,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Order/Circular.lean | btw_iff_not_sbtw | [] | [
324,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/ZeroObjects.lean | CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom | [
{
"state_after": "C : Type u_2\ninst✝³ : Category C\ninst✝² : HasZeroObject C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\ninst✝ : HasBinaryCoproduct X Y\n⊢ pushout.inr ≫\n (colimit.isoColimitCocone\n { cocone := PushoutCocone.mk coprod.inl coprod.inr (_ : 0 ≫ coprod.inl = 0 ≫ coprod.inr),\n ... | [
220,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Algebra/Order/Pi.lean | Function.one_le_const | [] | [
139,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | Submodule.eq_top_iff' | [] | [
179,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.uIcc_comm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.174713\nα : Type u_1\ninst✝¹ : Lattice α\ninst✝ : LocallyFiniteOrder α\na✝ a₁ a₂ b✝ b₁ b₂ c x a b : α\n⊢ [[a, b]] = [[b, a]]",
"tactic": "rw [uIcc, uIcc, inf_comm, sup_comm]"
}
] | [
891,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/Algebra/Order/Monoid/Canonical/Defs.lean | exists_one_lt_mul_of_lt | [
{
"state_after": "case intro\nα : Type u\ninst✝ : CanonicallyOrderedMonoid α\na b c✝ d : α\nh : a < b\nc : α\nhc : b = a * c\n⊢ ∃ c x, a * c = b",
"state_before": "α : Type u\ninst✝ : CanonicallyOrderedMonoid α\na b c d : α\nh : a < b\n⊢ ∃ c x, a * c = b",
"tactic": "obtain ⟨c, hc⟩ := le_iff_exists_mul.... | [
267,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.comp | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf g✝ : α → β\nc c₁ c₂ x : α\ninst✝ : Add α\nh : Periodic f c\ng : β → γ\n⊢ Periodic (g ∘ f) c",
"tactic": "simp_all"
}
] | [
61,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/Order/SemiconjSup.lean | isOrderRightAdjoint_csSup | [] | [
57,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | mem_comp_comp | [
{
"state_after": "case mk\nα : Type ua\nβ : Type ub\nγ : Type uc\nδ : Type ud\nι : Sort ?u.56107\ninst✝ : UniformSpace α\nV W M : Set (β × β)\nhW' : SymmetricRel W\nx y : β\n⊢ (x, y) ∈ V ○ M ○ W ↔ Set.Nonempty (ball (x, y).fst V ×ˢ ball (x, y).snd W ∩ M)",
"state_before": "α : Type ua\nβ : Type ub\nγ : Type... | [
682,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.bliminf_congr' | [] | [
724,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.isSt_ofSeq_iff_tendsto | [] | [
257,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.CommSq.HasLift.mk' | [] | [
199,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.bit_le | [] | [
697,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
695,
1
] |
Mathlib/Data/Polynomial/EraseLead.lean | Polynomial.eraseLead_X | [] | [
145,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.inf_submodule | [
{
"state_after": "case h\nR M : Type u\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nI : Ideal R\nF F' : Filtration I M\nh : Stable F\nx✝ : PolynomialModule R M\n⊢ x✝ ∈ Filtration.submodule (F ⊓ F') ↔ x✝ ∈ Filtration.submodule F ⊓ Filtration.submodule F'",
"state_before": "R M : Type u\... | [
287,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
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