file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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|---|---|---|---|---|---|---|
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | map_lt_lineMap_iff_slope_lt_slope | [] | [
296,
50
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293,
1
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Mathlib/Data/Finset/Powerset.lean | Finset.powersetLen_zero | [
{
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{
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227,
35
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222,
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_eq_monomial_iff | [] | [
387,
39
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385,
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Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.ne_zero_of_out_nonempty | [] | [
289,
31
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288,
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.coeff_monomial | [
{
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Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.coe_top | [] | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.scalar_apply_eq | [
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Std/Logic.lean | and_iff_left | [] | [
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_iff_exists_le | [
{
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452,
7
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449,
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Mathlib/Data/Polynomial/Coeff.lean | Polynomial.support_smul | [
{
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12
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Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.cauchy_tendsto_of_tendsto | [
{
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1510,
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Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.sup_div_inf_eq_abs_div | [
{
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"tactic": "rw [sup_eq_mul_pos_div, inf_comm, inf_eq_div_pos_div, div_eq_mul_inv, div_eq... | [
392,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
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Mathlib/Algebra/Group/Basic.lean | mul_div_mul_left_eq_div | [
{
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910,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
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Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coprime_of_dvd_coprime | [
{
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40
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397,
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Mathlib/Analysis/Asymptotics/Theta.lean | Asymptotics.isTheta_of_norm_eventuallyEq | [
{
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167,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
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Mathlib/Analysis/NormedSpace/FiniteDimension.lean | AffineIsometry.toAffineIsometryEquiv_apply | [] | [
118,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.symm | [] | [
1102,
9
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1101,
8
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Mathlib/CategoryTheory/Simple.lean | CategoryTheory.cokernel_zero_of_nonzero_to_simple | [
{
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{
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179,
41
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174,
1
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Mathlib/Data/Sym/Basic.lean | SymOptionSuccEquiv.encode_decode | [
{
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665,
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654,
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Mathlib/Topology/Instances/Matrix.lean | Continuous.matrix_trace | [] | [
193,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
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Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.map_cyclotomic | [
{
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297,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_pos_iff''' | [
{
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1287,
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Mathlib/Data/Fin/Tuple/Basic.lean | Fin.mem_find_iff | [
{
"state_after": "case intro\nm n : ℕ\np : Fin n → Prop\ninst✝ : DecidablePred p\ni : Fin n\nhpi : p i\nhj : ∀ (j : Fin n), p j → i ≤ j\n⊢ i ∈ find p",
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"tactic": "rintro ⟨h... | [
937,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
930,
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Mathlib/Analysis/LocallyConvex/Bounded.lean | TotallyBounded.isVonNBounded | [
{
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266,
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246,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.single_coeff_same | [] | [
161,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/Algebra/Group/Basic.lean | eq_mul_inv_of_mul_eq | [
{
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"tactic": "simp [h.symm]"
}
] | [
628,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
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Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.infLELeft_apply | [] | [
96,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.liftPropWithinAt_self_source | [] | [
230,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Atoms.lean | IsAtom.disjoint_of_ne | [] | [
216,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
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Mathlib/RingTheory/Valuation/Basic.lean | Valuation.IsEquiv.comap | [] | [
401,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
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Mathlib/RingTheory/Adjoin/Tower.lean | Algebra.adjoin_restrictScalars | [
{
"state_after": "R : Type u\nS✝ : Type v\nA : Type w\nB : Type u₁\nC : Type u_1\nD : Type u_2\nE : Type u_3\ninst✝⁶ : CommSemiring C\ninst✝⁵ : CommSemiring D\ninst✝⁴ : CommSemiring E\ninst✝³ : Algebra C D\ninst✝² : Algebra C E\ninst✝¹ : Algebra D E\ninst✝ : IsScalarTower C D E\nS : Set E\n⊢ Set.range ↑(algebra... | [
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Mathlib/Data/Finset/Basic.lean | Finset.erase_cons | [
{
"state_after": "no goals",
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"tactic": "rw [cons_eq_insert, erase_insert_eq_erase, erase_eq_of_not_mem h]"
}
] | [
1977,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1976,
1
] |
Mathlib/Tactic/Linarith/Lemmas.lean | Linarith.eq_of_eq_of_eq | [
{
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"tactic": "simp [*]"
}
] | [
28,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
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Mathlib/Analysis/BoxIntegral/Partition/Split.lean | BoxIntegral.Prepartition.mem_split_iff' | [
{
"state_after": "no goals",
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"tactic": "simp [mem_split_iff, ← Box.withBotCoe_inj]"
}
] | [
184,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | UniformInducing.uniformEmbedding | [] | [
197,
30
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195,
11
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Mathlib/MeasureTheory/Measure/WithDensityVectorMeasure.lean | MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous | [
{
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142,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
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Mathlib/Data/Nat/Pow.lean | Nat.pow_dvd_pow_iff_pow_le_pow | [
{
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... | [
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61
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Mathlib/CategoryTheory/Monad/Limits.lean | CategoryTheory.hasLimit_of_reflective | [] | [
359,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
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Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.arrowCongr_trans | [
{
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477,
6
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472,
1
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Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.P_idem | [
{
"state_after": "case h\nC : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq n : ℕ\n⊢ HomologicalComplex.Hom.f (P q ≫ P q) n = HomologicalComplex.Hom.f (P q) n",
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173,
21
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171,
1
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Mathlib/CategoryTheory/Functor/EpiMono.lean | CategoryTheory.Functor.preservesEpimorphisms.iso_iff | [] | [
147,
90
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145,
1
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Mathlib/LinearAlgebra/Basis.lean | Basis.sum_equivFun | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.659117\nR : Type u_3\nR₂ : Type ?u.659123\nK : Type ?u.659126\nM : Type u_1\nM' : Type ?u.659132\nM'' : Type ?u.659135\nV : Type u\nV' : Type ?u.659140\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCommMonoid M'\ninst✝¹ : Module R M... | [
929,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
927,
1
] |
Mathlib/Algebra/ModEq.lean | AddCommGroup.neg_modEq_neg | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : AddCommGroup α\np a a₁ a₂ b b₁ b₂ c : α\nn : ℕ\nz : ℤ\n⊢ -b ≡ -a [PMOD p] ↔ a ≡ b [PMOD p]",
"tactic": "simp [ModEq, neg_add_eq_sub]"
}
] | [
83,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Tactic/Sat/FromLRAT.lean | Sat.Clause.reify_zero | [] | [
203,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
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Mathlib/Algebra/Order/Floor.lean | Int.floor_one | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.128362\nα : Type u_1\nβ : Type ?u.128368\ninst✝¹ : LinearOrderedRing α\ninst✝ : FloorRing α\nz : ℤ\na : α\n⊢ ⌊1⌋ = 1",
"tactic": "rw [← cast_one, floor_intCast]"
}
] | [
710,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.eventually_smallSets | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1327\nι : Sort ?u.1330\nl l' la : Filter α\nlb : Filter β\np : Set α → Prop\n⊢ (∃ t, t ∈ l ∧ ∀ (y : Set α), y ∈ 𝒫 t → p y) ↔ ∃ s, s ∈ l ∧ ∀ (t : Set α), t ⊆ s → p t\n\ncase hh\nα : Type u_1\nβ : Type ?u.1327\nι : Sort ?u.1330\nl l' la : Filter α\nlb : Filter β\np : S... | [
69,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
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Mathlib/MeasureTheory/Constructions/Polish.lean | MeasureTheory.measurableEquiv_range_coe_nat_of_infinite_of_countable | [
{
"state_after": "α : Type u_1\ninst✝⁵ : TopologicalSpace α\nι : Type ?u.398049\ninst✝⁴ : MeasurableSpace α\ninst✝³ : PolishSpace α\ninst✝² : BorelSpace α\ninst✝¹ : Infinite α\ninst✝ : Countable α\nthis : PolishSpace ↑(range Nat.cast)\n⊢ Nonempty (α ≃ᵐ ↑(range Nat.cast))",
"state_before": "α : Type u_1\nins... | [
797,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
791,
1
] |
Mathlib/Order/WithBot.lean | WithTop.coe_lt_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.88258\nγ : Type ?u.88261\nδ : Type ?u.88264\ninst✝ : LT α\na✝ b a : α\n⊢ ↑a < ⊤",
"tactic": "simp [← toDual_lt_toDual_iff, WithBot.bot_lt_coe]"
}
] | [
1065,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
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Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.W.dest_mk | [
{
"state_after": "case mk\nP : PFunctor\nα β : Type u\nfst✝ : P.A\nsnd✝ : B P fst✝ → W P\n⊢ dest (mk { fst := fst✝, snd := snd✝ }) = { fst := fst✝, snd := snd✝ }",
"state_before": "P : PFunctor\nα β : Type u\np : Obj P (W P)\n⊢ dest (mk p) = p",
"tactic": "cases p"
},
{
"state_after": "no goals"... | [
114,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Order/Disjoint.lean | disjoint_iff_inf_le | [] | [
125,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
1
] |
Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.restrict_lintegral | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.885602\nγ : Type ?u.885605\nδ : Type ?u.885608\nm : MeasurableSpace α\nμ ν : Measure α\nf : α →ₛ ℝ≥0∞\ns : Set α\nhs : MeasurableSet s\nx : α\nhx : ↑(restrict f s) x ≠ 0\nhxs : x ∈ s\nx✝ : ↑↑μ (↑(restrict f s) ⁻¹' {↑(restrict f s) x}) ≠... | [
1077,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1065,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_eq | [] | [
1284,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1282,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.empty' | [] | [
97,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/CategoryTheory/Functor/FullyFaithful.lean | CategoryTheory.Functor.map_surjective | [] | [
100,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
src/lean/Init/Prelude.lean | Nat.le_succ_of_le | [] | [
1603,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1602,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_pi_div_four | [
{
"state_after": "x : ℝ\n⊢ cos (π / 4) = cos (π / 2 ^ 2)\n\nx : ℝ\n⊢ cos (π / 2 ^ 2) = sqrt 2 / 2",
"state_before": "x : ℝ\n⊢ cos (π / 4) = sqrt 2 / 2",
"tactic": "trans cos (π / 2 ^ 2)"
},
{
"state_after": "case e_x.e_a\nx : ℝ\n⊢ 4 = 2 ^ 2\n\nx : ℝ\n⊢ cos (π / 2 ^ 2) = sqrt 2 / 2",
"state_b... | [
785,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Analysis/NormedSpace/Pointwise.lean | diam_smul₀ | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_2\nE : Type u_1\ninst✝³ : NormedDivisionRing 𝕜\ninst✝² : SeminormedAddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : BoundedSMul 𝕜 E\nc : 𝕜\nx : Set E\n⊢ diam (c • x) = ‖c‖ * diam x",
"tactic": "simp_rw [diam, ediam_smul₀, ENNReal.toReal_smul, NNR... | [
60,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.isBigO_of_degree_le | [
{
"state_after": "case pos\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nh : degree P ≤ degree Q\nhp : P = 0\n⊢ (fun x => eval x P) =O[atTop] fun x => eval x Q\n\ncase neg\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\n... | [
240,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_lsub_def_nonempty | [] | [
227,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Star/SelfAdjoint.lean | selfAdjoint.val_zpow | [] | [
399,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | uniformity_lift_le_comp | [] | [
564,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Data/Set/Image.lean | Set.rangeFactorization_coe | [] | [
1054,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1053,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.coeff_prod_of_natDegree_le | [
{
"state_after": "case mk\nR : Type u\nι : Type w\ninst✝ : CommSemiring R\nf✝ : ι → R[X]\nt : Multiset R[X]\nf : ι → R[X]\nn : ℕ\nl : Multiset ι\nhl : Nodup l\nh : ∀ (p : ι), p ∈ { val := l, nodup := hl } → natDegree (f p) ≤ n\n⊢ coeff (∏ i in { val := l, nodup := hl }, f i) (Finset.card { val := l, nodup := hl... | [
226,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Order/Lattice.lean | sup_sup_distrib_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeSup α\na✝ b✝ c✝ d a b c : α\n⊢ a ⊔ b ⊔ c = a ⊔ c ⊔ (b ⊔ c)",
"tactic": "rw [sup_sup_sup_comm, sup_idem]"
}
] | [
290,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
1
] |
Mathlib/Combinatorics/Composition.lean | List.join_splitWrtComposition | [] | [
768,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Data/List/Sigma.lean | List.NodupKeys.kerase | [] | [
477,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/RingTheory/WittVector/MulP.lean | WittVector.bind₁_wittMulN_wittPolynomial | [
{
"state_after": "case zero\np : ℕ\nR : Type ?u.51070\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nk : ℕ\n⊢ ↑(bind₁ (wittMulN p Nat.zero)) (wittPolynomial p ℤ k) = ↑Nat.zero * wittPolynomial p ℤ k\n\ncase succ\np : ℕ\nR : Type ?u.51070\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nk n : ℕ\nih : ↑(bind₁ (wittMu... | [
84,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Topology/MetricSpace/ThickenedIndicator.lean | thickenedIndicatorAux_mono | [] | [
110,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | ContinuousLinearMap.comp_analyticOn | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_1\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf g✝ : E → F\np pf pg : For... | [
641,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Topology/UniformSpace/Equiv.lean | UniformEquiv.symm_comp_self | [] | [
210,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.ball_antitone | [] | [
746,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/CategoryTheory/Limits/Constructions/Pullbacks.lean | CategoryTheory.Limits.hasPushouts_of_hasBinaryCoproducts_of_hasCoequalizers | [] | [
100,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Real/Hyperreal.lean | Hyperreal.infinitesimal_zero | [] | [
685,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Combinatorics/Catalan.lean | Tree.coe_treesOfNumNodesEq | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ ∀ (x : Tree Unit), x ∈ ↑(treesOfNumNodesEq n) ↔ x ∈ {x | numNodes x = n}",
"tactic": "simp"
}
] | [
209,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_def | [
{
"state_after": "case h\nι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝² : (i : ι) → Zero (β i)\ninst✝¹ : (i : ι) → (x : β i) → Decidable (x ≠ 0)\np : ι → Prop\ninst✝ : DecidablePred p\nf : Π₀ (i : ι), β i\ni : ι\n⊢ ↑(filter p f) i = ↑(mk (Finset.filter p... | [
1251,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1250,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.sq_mul_squarefree_of_pos' | [
{
"state_after": "case intro.intro.intro.intro.intro\nn : ℕ\nh : 0 < n\na₁ b₁ : ℕ\nha₁ : 0 < a₁\nhb₁ : 0 < b₁\nhab₁ : b₁ ^ 2 * a₁ = n\nhab₂ : Squarefree a₁\n⊢ ∃ a b, (b + 1) ^ 2 * (a + 1) = n ∧ Squarefree (a + 1)",
"state_before": "n : ℕ\nh : 0 < n\n⊢ ∃ a b, (b + 1) ^ 2 * (a + 1) = n ∧ Squarefree (a + 1)",
... | [
358,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableAt_id | [] | [
1008,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
] |
Mathlib/RingTheory/FiniteType.lean | Subalgebra.fg_iff_finiteType | [] | [
184,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Analysis/Calculus/Deriv/Basic.lean | deriv_zero_of_not_differentiableAt | [
{
"state_after": "𝕜 : Type u\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type v\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type w\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₀ f₁ g : 𝕜 → F\nf' f₀' f₁' g' : F\nx : 𝕜\ns t : Set 𝕜\nL L₁ L₂ : Filter 𝕜\nh : ¬DifferentiableAt �... | [
244,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Logic/Basic.lean | exists_unique_false | [] | [
863,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
9
] |
Mathlib/Analysis/Calculus/MeanValue.lean | image_le_of_deriv_right_lt_deriv_boundary | [] | [
213,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Topology/Support.lean | HasCompactMulSupport.isCompact_range | [
{
"state_after": "case inl\nX : Type ?u.12625\nα : Type u_2\nα' : Type ?u.12631\nβ : Type u_1\nγ : Type ?u.12637\nδ : Type ?u.12640\nM : Type ?u.12643\nE : Type ?u.12646\nR : Type ?u.12649\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace α'\ninst✝³ : One β\ninst✝² : One γ\ninst✝¹ : One δ\ng : β → γ\nf : ... | [
184,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift'_map_le | [] | [
302,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Category/Ring/Basic.lean | SemiRingCat.ofHom_apply | [] | [
130,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Ring/CompTypeclasses.lean | RingHom.surjective | [] | [
168,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInf | [
{
"state_after": "case inl\nR : Type u_3\nM : Type u_2\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ns : Set R\na : R\nι : Type u_1\np : ι → Ideal R\nS : Finset ι\nhp : Set.Pairwise ↑S fun i j => p i ⊔ p j = ⊤\ninst✝ : DecidableEq ι\nh : S = ∅\n⊢ (⨆ (i : ι) (_ : i ∈ S), torsionBySet R... | [
431,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
396,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_mkPiField | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι)... | [
908,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.map_comp | [
{
"state_after": "case h.mk\nK : Type u_3\nV : Type u_5\ninst✝⁹ : DivisionRing K\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module K V\nL : Type u_4\nW : Type u_6\ninst✝⁶ : DivisionRing L\ninst✝⁵ : AddCommGroup W\ninst✝⁴ : Module L W\nF : Type u_1\nU : Type u_2\ninst✝³ : Field F\ninst✝² : AddCommGroup U\ninst✝¹ : Modul... | [
232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/CategoryTheory/Sites/Whiskering.lean | CategoryTheory.Presheaf.IsSheaf.comp | [
{
"state_after": "C : Type u₁\ninst✝³ : Category C\nA : Type u₂\ninst✝² : Category A\nB : Type u₃\ninst✝¹ : Category B\nJ : GrothendieckTopology C\nU : C\nR : Presieve U\nF : A ⥤ B\ninst✝ :\n (X : C) →\n (S : GrothendieckTopology.Cover J X) →\n (P : Cᵒᵖ ⥤ A) → PreservesLimit (MulticospanIndex.multicosp... | [
129,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | LinearIsometryEquiv.coe_toAffineIsometryEquiv | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_3\nV : Type u_1\nV₁ : Type ?u.380007\nV₂ : Type u_2\nV₃ : Type ?u.380013\nV₄ : Type ?u.380016\nP₁ : Type ?u.380019\nP : Type ?u.380022\nP₂ : Type ?u.380025\nP₃ : Type ?u.380028\nP₄ : Type ?u.380031\ninst✝²⁰ : NormedField 𝕜\ninst✝¹⁹ : SeminormedAddCo... | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_le_one_div_of_neg | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.179667\nα : Type u_1\nβ : Type ?u.179673\ninst✝ : LinearOrderedField α\na b c d : α\nn : ℤ\nha : a < 0\nhb : b < 0\n⊢ 1 / a ≤ 1 / b ↔ b ≤ a",
"tactic": "simpa [one_div] using inv_le_inv_of_neg ha hb"
}
] | [
885,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
884,
1
] |
Mathlib/Algebra/GroupWithZero/Defs.lean | mul_left_injective₀ | [] | [
90,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.RespectsIso.diagonal | [
{
"state_after": "case left\nC : Type u\ninst✝² : Category C\nD : Type ?u.69245\ninst✝¹ : Category D\ninst✝ : HasPullbacks C\nP : MorphismProperty C\nhP : RespectsIso P\n⊢ ∀ {X Y Z : C} (e : X ≅ Y) (f : Y ⟶ Z), MorphismProperty.diagonal P f → MorphismProperty.diagonal P (e.hom ≫ f)\n\ncase right\nC : Type u\nin... | [
539,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Topology/Order.lean | TopologicalSpace.isOpen_top_iff | [
{
"state_after": "case basic\nα✝ : Type ?u.11392\nt t₁ t₂ : TopologicalSpace α✝\ns : Set α✝\nα : Type u_1\nU s✝ : Set α\na✝ : s✝ ∈ ↑OrderDual.ofDual (↑OrderDual.ofDual ⊥)\n⊢ s✝ = ∅ ∨ s✝ = univ\n\ncase univ\nα✝ : Type ?u.11392\nt t₁ t₂ : TopologicalSpace α✝\ns : Set α✝\nα : Type u_1\nU : Set α\n⊢ univ = ∅ ∨ univ... | [
265,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ioc_toReal | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\ninst✝ : Fintype ι\na b : ι → ℝ\nh : a ≤ b\n⊢ ENNReal.toReal (↑↑volume (Set.pi univ fun i => Ioc (a i) (b i))) = ∏ i : ι, (b i - a i)",
"tactic": "simp only [volume_pi_Ioc, ENNReal.toReal_prod, ENNReal.toReal_ofReal (sub_nonneg.2 (h _))]"
}
] | [
245,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Topology/Algebra/GroupCompletion.lean | UniformSpace.Completion.continuous_toCompl | [] | [
192,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/RingTheory/GradedAlgebra/HomogeneousLocalization.lean | HomogeneousLocalization.NumDenSameDeg.num_smul | [] | [
271,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/NumberTheory/VonMangoldt.lean | Nat.ArithmeticFunction.vonMangoldt_apply_prime | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Prime p\n⊢ ↑Λ p = Real.log ↑p",
"tactic": "rw [vonMangoldt_apply, Prime.minFac_eq hp, if_pos hp.prime.isPrimePow]"
}
] | [
94,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Algebra/CharP/Basic.lean | RingHom.charP_iff_charP | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.80816\nK : Type u_1\nL : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : Semiring L\ninst✝ : Nontrivial L\nf : K →+* L\np : ℕ\n⊢ CharP K p ↔ CharP L p",
"tactic": "simp only [charP_iff, ← f.injective.eq_iff, map_natCast f, f.map_zero]"
}
] | [
327,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_pow | [] | [
350,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
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