file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.toPrefunctor_comp | [] | [
112,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.pullbackIsoPullback_inv_snd | [] | [
606,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snorm_one_smul_measure | [
{
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643,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
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Mathlib/CategoryTheory/Limits/Comma.lean | CategoryTheory.CostructuredArrow.epi_iff_epi_left | [] | [
300,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
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Mathlib/NumberTheory/Padics/PadicVal.lean | padicValInt_self | [] | [
527,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.biInf_apply' | [
{
"state_after": "no goals",
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"tactic": "simp only [← iInf_subty... | [
1219,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1217,
1
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Mathlib/LinearAlgebra/Prod.lean | LinearEquiv.skewProd_apply | [] | [
819,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_sqrt | [] | [
1570,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1569,
1
] |
Mathlib/Algebra/GradedMonoid.lean | SetLike.coe_gOne | [] | [
509,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
507,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.X_inv | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type ?u.2011299\nk : Type u_2\ninst✝ : Field k\ns : σ\n⊢ (X s)⁻¹ = 0",
"tactic": "rw [inv_eq_zero, constantCoeff_X]"
}
] | [
1040,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1039,
1
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Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.eqToHom_f | [
{
"state_after": "C : Type u_1\ninst✝ : Category C\nP : Karoubi C\n⊢ (eqToHom (_ : P = P)).f = P.p ≫ eqToHom (_ : P.X = P.X)",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nh : P = Q\n⊢ (eqToHom h).f = P.p ≫ eqToHom (_ : P.X = Q.X)",
"tactic": "subst h"
},
{
"state_after": ... | [
150,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.cokernel_not_iso_of_nonzero | [
{
"state_after": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasCokernel f\nw : f ≠ 0\nI : IsIso (cokernel.π f)\n⊢ Mono (cokernel.π f)",
"state_before": "C : Type u\ninst✝² : Category C\ninst✝¹ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ninst✝ : HasCokernel f\nw ... | [
868,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Data/Nat/Squarefree.lean | Nat.minSqFac_prime | [
{
"state_after": "n d : ℕ\nh : minSqFac n = some d\nthis : MinSqFacProp n (minSqFac n)\n⊢ Prime d",
"state_before": "n d : ℕ\nh : minSqFac n = some d\n⊢ Prime d",
"tactic": "have := minSqFac_has_prop n"
},
{
"state_after": "n d : ℕ\nh : minSqFac n = some d\nthis : MinSqFacProp n (some d)\n⊢ Prim... | [
222,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.mapsTo_iInter₂ | [] | [
1460,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1458,
1
] |
Mathlib/Order/CompleteBooleanAlgebra.lean | sSup_inf_eq | [
{
"state_after": "no goals",
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"tactic": "simpa only [inf_comm] using @inf_sSup_eq α _ s b"
}
] | [
98,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.continuousAt_of_comp_right | [
{
"state_after": "ι : Type ?u.42663\nB : Type u_2\nF : Type u_3\nE : B → Type ?u.42674\nZ : Type u_4\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace F\nproj : Z → B\ninst✝² : TopologicalSpace Z\ninst✝¹ : TopologicalSpace (TotalSpace E)\ne✝ : Trivialization F proj\nx : Z\nX : Type u_1\ninst✝ : Topologica... | [
542,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
535,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.integral_add' | [] | [
869,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
867,
1
] |
Mathlib/Topology/Category/TopCat/Limits/Products.lean | TopCat.sigmaIsoSigma_hom_ι | [
{
"state_after": "no goals",
"state_before": "J : Type v\ninst✝ : SmallCategory J\nι : Type v\nα : ι → TopCatMax\ni : ι\n⊢ Sigma.ι α i ≫ (sigmaIsoSigma α).hom = sigmaι α i",
"tactic": "simp [sigmaIsoSigma]"
}
] | [
127,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | norm_expSeries_div_summable | [] | [
588,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_snd | [] | [
650,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.closure_iUnion | [] | [
1002,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1001,
1
] |
Mathlib/Topology/Algebra/Module/Basic.lean | ContinuousLinearMap.coe_copy | [] | [
482,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
] |
Mathlib/Topology/Sheaves/PUnit.lean | TopCat.Presheaf.isSheaf_of_isTerminal_of_indiscrete | [
{
"state_after": "case inl\nC : Type u\ninst✝ : Category C\nX : TopCat\nhind : X.str = ⊤\nF : Presheaf C X\nit : IsTerminal (F.obj ⊥.op)\nc : C\ns : Sieve ⊥\nhs : s ∈ GrothendieckTopology.sieves (Opens.grothendieckTopology ↑X) ⊥\n⊢ Presieve.IsSheafFor (F ⋙ coyoneda.obj c.op) s.arrows\n\ncase inr\nC : Type u\nin... | [
45,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.transposeLinearEquiv_symm | [] | [
2069,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2067,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval₂_map | [
{
"state_after": "no goals",
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1328,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1326,
1
] |
Mathlib/Computability/Primrec.lean | Nat.Primrec'.prim_iff₂ | [
{
"state_after": "no goals",
"state_before": "f : ℕ → ℕ → ℕ\nh : Primrec fun v => f (Vector.head v) (Vector.head (Vector.tail v))\nv : ℕ × ℕ\n⊢ f (Vector.head (v.fst ::ᵥ v.snd ::ᵥ nil)) (Vector.head (Vector.tail (v.fst ::ᵥ v.snd ::ᵥ nil))) = f v.fst v.snd",
"tactic": "simp"
}
] | [
1559,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1555,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.eq_zero_of_le_div | [
{
"state_after": "m n k l : ℕ\nhn : 2 ≤ n\nh : m ≤ m / n\n⊢ m * n ≤ m",
"state_before": "m n k l : ℕ\nhn : 2 ≤ n\nh : m ≤ m / n\n⊢ n * m ≤ m",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m n k l : ℕ\nhn : 2 ≤ n\nh : m ≤ m / n\n⊢ m * n ≤ m",
"tactic": "exact... | [
409,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_hasFDerivWithinAt_iff' | [] | [
336,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Analysis/VonNeumannAlgebra/Basic.lean | VonNeumannAlgebra.coe_commutant | [] | [
135,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/FieldTheory/Separable.lean | isSeparable_tower_bot_of_isSeparable | [
{
"state_after": "F : Type u_1\nK : Type u_3\nE : Type u_2\ninst✝⁶ : Field F\ninst✝⁵ : Field K\ninst✝⁴ : Field E\ninst✝³ : Algebra F K\ninst✝² : Algebra F E\ninst✝¹ : Algebra K E\ninst✝ : IsScalarTower F K E\nh : IsSeparable F E\nx : K\nhs : Separable (minpoly F (↑(algebraMap K E) x))\n⊢ Separable (minpoly F x)... | [
556,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Data/Fintype/Pi.lean | Fintype.piFinset_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : Fintype α\nδ : α → Type u_2\ninst✝ : Nonempty α\nx✝ : (a : α) → δ a\n⊢ ¬x✝ ∈ piFinset fun x => ∅",
"tactic": "simp"
}
] | [
62,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Order/OrdContinuous.lean | LeftOrdContinuous.iterate | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\ng : β → γ\nf✝ : α → β\nf : α → α\nhf : LeftOrdContinuous f\nn : ℕ\n⊢ LeftOrdContinuous (f^[n])",
"tactic": "induction n with\n| zero => exact LeftOr... | [
88,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
11
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_mul_neg | [
{
"state_after": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x ≤ x_1\na : α\n⊢ abs a = a ⊔ a⁻¹ ⊔ 1",
"state_before": "α : Type u\ninst✝² : Lattice α\ninst✝¹ : CommGroup α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 =>... | [
382,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.prod.lift_fst_snd | [
{
"state_after": "case h₁\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ lift fst snd ≫ fst = 𝟙 (X ⨯ Y) ≫ fst\n\ncase h₂\nC : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryProduct X Y\n⊢ lift fst snd ≫ snd = 𝟙 (X ⨯ Y) ≫ snd",
"state_before": "C : Type u\nin... | [
734,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
733,
1
] |
Mathlib/CategoryTheory/GlueData.lean | CategoryTheory.GlueData.ι_gluedIso_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nC' : Type u₂\ninst✝² : Category C'\nD : GlueData C\nF : C ⥤ C'\nH : (i j k : D.J) → PreservesLimit (cospan (f D i j) (f D i k)) F\ninst✝¹ : HasMulticoequalizer (diagram D)\ninst✝ : PreservesColimit (MultispanIndex.multispan (dia... | [
376,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/Homology/Exact.lean | CategoryTheory.kernel_comp_cokernel | [
{
"state_after": "V : Type u\ninst✝⁴ : Category V\ninst✝³ : HasImages V\nA B C D : V\nf : A ⟶ B\ng : B ⟶ C\nh✝ : C ⟶ D\ninst✝² : HasZeroMorphisms V\ninst✝¹ : HasEqualizers V\ninst✝ : HasCokernels V\nh : Exact f g\n⊢ Subobject.arrow (kernelSubobject g) ≫ cokernel.π f = 0",
"state_before": "V : Type u\ninst✝⁴... | [
280,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Data/Nat/Bitwise.lean | Nat.lt_lxor'_cases | [] | [
320,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/LinearAlgebra/Dual.lean | LinearMap.dualPairing_nondegenerate | [] | [
1345,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1344,
1
] |
Mathlib/Order/Concept.lean | Concept.snd_injective | [] | [
210,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.ssubset_toFinset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.84731\nγ : Type ?u.84734\ns✝ t : Set α\ns : Finset α\ninst✝ : Fintype ↑t\n⊢ s ⊂ toFinset t ↔ ↑s ⊂ t",
"tactic": "rw [← Finset.coe_ssubset, coe_toFinset]"
}
] | [
668,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
667,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_mul | [] | [
137,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Data/Set/Semiring.lean | SetSemiring.down_zero | [] | [
111,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.le_self_pow | [] | [
44,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.mem_map_range | [] | [
931,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Order/Cover.lean | wcovby_of_le_of_le | [] | [
66,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Algebra/Lie/IdealOperations.lean | LieIdeal.map_comap_incl | [
{
"state_after": "R : Type u\nL : Type v\nL' : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\ninst✝¹ : LieRing L'\ninst✝ : LieAlgebra R L'\nf : L →ₗ⁅R⁆ L'\nI : LieIdeal R L\nJ : LieIdeal R L'\nI₁ I₂ : LieIdeal R L\n⊢ map (incl I₁) (comap (incl I₁) I₂) = LieHom.idealRange (incl I₁) ⊓ ... | [
303,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero | [
{
"state_after": "case h.h\nX✝ : LocallyRingedSpace\nX : LocallyRingedSpace\nU : Opens ↑↑X.toPresheafedSpace\nx : ↑↑(toRingedSpace X).toPresheafedSpace\n⊢ x ∈ ↑(RingedSpace.basicOpen (toRingedSpace X) 0) ↔ x ∈ ↑⊥",
"state_before": "X✝ : LocallyRingedSpace\nX : LocallyRingedSpace\nU : Opens ↑↑X.toPresheafedS... | [
333,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.uncurry0_norm | [
{
"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)... | [
1682,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1682,
1
] |
Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_comp_mulHom | [] | [
276,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Order/Closure.lean | ClosureOperator.closure_inf_le | [] | [
245,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_of_subset | [] | [
2068,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2067,
1
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Mathlib/Data/Set/Lattice.lean | Set.surjOn_iUnion | [] | [
1587,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
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Mathlib/SetTheory/Game/PGame.lean | LE.le.not_gf | [] | [
414,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.exists_simpleFunc_forall_lintegral_sub_lt_of_pos | [
{
"state_after": "α : Type u_1\nβ : Type ?u.85282\nγ : Type ?u.85285\nδ : Type ?u.85288\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nh : (⨆ (φ : α →ₛ ℝ≥0) (_ : ∀ (x : α), ↑(↑φ x) ≤ f x), SimpleFunc.lintegral (SimpleFunc.map ENNReal.some φ) μ) ≠ ⊤\nε : ℝ≥0∞\nhε : ε ≠ 0\n⊢ ∃ φ,\n (∀ (x : α), ↑(↑φ x) ... | [
268,
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252,
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Mathlib/Data/QPF/Univariate/Basic.lean | Qpf.Wequiv.symm | [
{
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"state_before": "F : Type u → Type u\ninst✝ : Functor F\nq : Qpf F\nx y : PFunctor.W (P F)\n⊢ Wequiv x y → Wequiv y x",
"tactic": "intro h"
},
{
"state_after": "case ind\nF... | [
224,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.comp_contLinear | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
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Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.arsinh_neg_iff | [] | [
179,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
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src/lean/Init/Core.lean | cast_eq | [] | [
554,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
553,
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Mathlib/Analysis/Calculus/FDeriv/Mul.lean | fderiv_smul_const | [] | [
270,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
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Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.PullbackCone.mono_of_isLimitMkIdId | [
{
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720,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
716,
1
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Std/Data/Int/Lemmas.lean | Int.one_mul | [
{
"state_after": "no goals",
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"tactic": "rw [Nat.one_mul]"
},
{
"state_after": "no goals",
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}
] | [
522,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
520,
19
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Mathlib/Data/Finset/MulAntidiagonal.lean | Finset.mem_mulAntidiagonal | [
{
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"tactic": "simp only [mulAntidiagonal... | [
77,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.sub_one_lt_floor | [] | [
498,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
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Std/Data/Int/Lemmas.lean | Int.subNatNat_elim | [
{
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112,
35
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101,
1
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Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Cycle.support_formPerm | [
{
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... | [
174,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.bot_ne_top | [
{
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774,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
1
] |
Mathlib/Topology/Connected.lean | IsPreconnected.subset_connectedComponent | [] | [
641,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
640,
1
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Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_symm_zero | [] | [
152,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Concrete.lean | Equiv.Perm.formPerm_toList | [
{
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392,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Order/FixedPoints.lean | OrderHom.le_nextFixed | [] | [
219,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
] |
Mathlib/Data/Analysis/Filter.lean | Filter.Realizer.top_F | [] | [
192,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.wOppSide_of_right_mem | [] | [
273,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_list_prod | [] | [
1120,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1119,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | reflection_symm | [] | [
658,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Combinatorics/SimpleGraph/Partition.lean | SimpleGraph.Partition.partOfVertex_mem | [
{
"state_after": "case intro\nV : Type u\nG : SimpleGraph V\nP : Partition G\nv : V\nh : Exists.choose (_ : ∃! b x, v ∈ b) ∈ P.parts\n⊢ partOfVertex P v ∈ P.parts",
"state_before": "V : Type u\nG : SimpleGraph V\nP : Partition G\nv : V\n⊢ partOfVertex P v ∈ P.parts",
"tactic": "obtain ⟨h, -⟩ := (P.isPar... | [
93,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.copy_eq | [] | [
583,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
582,
1
] |
Mathlib/Data/Polynomial/Inductions.lean | Polynomial.natDegree_ne_zero_induction_on | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝ : Semiring R\np q : R[X]\nM : R[X] → Prop\nf : R[X]\nf0 : natDegree f ≠ 0\nh_C_add : ∀ {a : R} {p : R[X]}, M p → M (↑C a + p)\nh_add : ∀ {p q : R[X]}, M p → M q → M (p + q)\nh_monomial : ∀ {n : ℕ} {a : R}, a ≠ 0 → n ≠ 0 → M ... | [
181,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
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Mathlib/Order/Atoms.lean | bot_covby_top | [] | [
497,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/Analysis/NormedSpace/AddTorsor.lean | eventually_homothety_mem_of_mem_interior | [
{
"state_after": "α : Type ?u.85021\nV : Type ?u.85024\nP : Type ?u.85027\nW : Type u_3\nQ : Type u_1\ninst✝⁸ : SeminormedAddCommGroup V\ninst✝⁷ : PseudoMetricSpace P\ninst✝⁶ : NormedAddTorsor V P\ninst✝⁵ : NormedAddCommGroup W\ninst✝⁴ : MetricSpace Q\ninst✝³ : NormedAddTorsor W Q\n𝕜 : Type u_2\ninst✝² : Norme... | [
250,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.mk | [
{
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"state_before": "α : Type u_1\nm0 : MeasurableSpace α\nμ μ₁ μ₂ ν ν₁ ν₂ : Measure α\ns t : Set α\nhs : ↑↑μ s = 0\nht : ↑↑ν t = ... | [
56,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ico_diff_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.37269\ninst✝ : PartialOrder α\na b c x : α\n⊢ x ∈ Ico a b \\ {a} ↔ x ∈ Ioo a b",
"tactic": "simp [and_right_comm, ← lt_iff_le_and_ne, eq_comm]"
}
] | [
786,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubVSubWeights_apply_left | [
{
"state_after": "no goals",
"state_before": "k : Type u_2\nV : Type ?u.420383\nP : Type ?u.420386\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.421042\ns₂ : Finset ι₂\ninst✝ : DecidableEq ι\ni j : ι\nh : i ≠ j\n⊢ weightedVSubVS... | [
686,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.embDomain_smul | [
{
"state_after": "case coeff.h\nΓ : Type u_1\nR : Type u_3\ninst✝⁴ : PartialOrder Γ\ninst✝³ : Semiring R\nV : Type ?u.831652\ninst✝² : AddCommMonoid V\ninst✝¹ : Module R V\nΓ' : Type u_2\ninst✝ : PartialOrder Γ'\nf : Γ ↪o Γ'\nr : R\nx : HahnSeries Γ R\ng : Γ'\n⊢ coeff (embDomain f (r • x)) g = coeff (r • embDom... | [
573,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
567,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.Ioc_filter_dvd_card_eq_div | [
{
"state_after": "case zero\np : ℕ\n⊢ card (Finset.filter (fun x => p ∣ x) (Ioc 0 zero)) = zero / p\n\ncase succ\np n : ℕ\nIH : card (Finset.filter (fun x => p ∣ x) (Ioc 0 n)) = n / p\n⊢ card (Finset.filter (fun x => p ∣ x) (Ioc 0 (succ n))) = succ n / p",
"state_before": "n p : ℕ\n⊢ card (Finset.filter (fu... | [
964,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
955,
1
] |
Mathlib/Control/Functor/Multivariate.lean | MvFunctor.exists_iff_exists_of_mono | [
{
"state_after": "case mp.intro\nn : ℕ\nα β γ : TypeVec n\nF : TypeVec n → Type v\ninst✝¹ : MvFunctor F\nP✝ : α ⟹ TypeVec.repeat n Prop\nR : α ⊗ α ⟹ TypeVec.repeat n Prop\ninst✝ : LawfulMvFunctor F\nP : F α → Prop\nq : F β → Prop\nf : α ⟹ β\ng : β ⟹ α\nh₀ : f ⊚ g = TypeVec.id\nh₁ : ∀ (u : F α), P u ↔ q (f <$$> ... | [
136,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Summable.matrix_blockDiagonal' | [] | [
426,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
424,
1
] |
Mathlib/Topology/Homeomorph.lean | HasCompactMulSupport.comp_homeomorph | [] | [
370,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_deleteMin | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nle : α → α → Bool\na : α\ns' s : Heap α\nh : NoSibling s\neq : deleteMin le s = some (a, s')\n⊢ size s = size s' + 1",
"tactic": "cases h with cases eq | node a c => rw [size_combine, size, size]"
},
{
"state_after": "no goals",
"st... | [
141,
68
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
139,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | rank_eq_of_injective | [] | [
206,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | inv_lt_of_inv_lt | [] | [
292,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.ofRat_intCast | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_ncard_iff_ncard_diff_le_ncard_diff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.129077\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\nht : autoParam (Set.Finite t) _auto✝\n⊢ ncard s ≤ ncard t ↔ ncard (s \\ t) ≤ ncard (t \\ s)",
"tactic": "rw [← ncard_inter_add_ncard_diff_eq_ncard s ... | [
557,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
554,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.filter_eq_self_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.425326\nγ : Type ?u.425329\nι : Type ?u.425332\nM : Type u_2\nM' : Type ?u.425338\nN : Type ?u.425341\nP : Type ?u.425344\nG : Type ?u.425347\nH : Type ?u.425350\nR : Type ?u.425353\nS : Type ?u.425356\ninst✝ : Zero M\np : α → Prop\nf :... | [
910,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
908,
1
] |
Mathlib/Algebra/Module/Submodule/Basic.lean | Submodule.coe_sub | [] | [
579,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
11
] |
Std/Data/List/Basic.lean | List.takeD_zero | [] | [
588,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
588,
9
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasStrictDerivAt.real_of_complex | [
{
"state_after": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasStrictDerivAt e e' ↑z\nA : HasStrictFDerivAt ofReal' ofRealClm z\n⊢ HasStrictDerivAt (fun x => (e ↑x).re) e'.re z",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nh : HasStrictDerivAt e e' ↑z\n⊢ HasStrictDerivAt (fun x => (e ↑x).re) e'.re z",
"tactic": "hav... | [
65,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/RingTheory/IsTensorProduct.lean | Algebra.pushoutDesc_left | [
{
"state_after": "R : Type u_1\nM : Type v₁\nN : Type v₂\nS : Type v₃\ninst✝³³ : AddCommMonoid M\ninst✝³² : AddCommMonoid N\ninst✝³¹ : CommRing R\ninst✝³⁰ : CommRing S\ninst✝²⁹ : Algebra R S\ninst✝²⁸ : Module R M\ninst✝²⁷ : Module R N\ninst✝²⁶ : Module S N\ninst✝²⁵ : IsScalarTower R S N\nf✝ : M →ₗ[R] N\nh : IsB... | [
494,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Path.mapEmbedding_injective | [] | [
1664,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | isLittleO_exp_neg_mul_rpow_atTop | [
{
"state_after": "case hgf\na : ℝ\nha : 0 < a\nb : ℝ\n⊢ ∀ᶠ (x : ℝ) in atTop, x ^ b = 0 → exp (-a * x) = 0\n\ncase a\na : ℝ\nha : 0 < a\nb : ℝ\n⊢ Tendsto (fun x => exp (-a * x) / x ^ b) atTop (𝓝 0)",
"state_before": "a : ℝ\nha : 0 < a\nb : ℝ\n⊢ (fun x => exp (-a * x)) =o[atTop] fun x => x ^ b",
"tactic"... | [
282,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/Topology/Algebra/Equicontinuity.lean | equicontinuous_of_equicontinuousAt_one | [
{
"state_after": "ι : Type u_1\nG : Type u_2\nM : Type u_3\nhom : Type u_4\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : UniformSpace M\ninst✝⁴ : Group G\ninst✝³ : Group M\ninst✝² : TopologicalGroup G\ninst✝¹ : UniformGroup M\ninst✝ : MonoidHomClass hom G M\nF : ι → hom\nhf : EquicontinuousAt (FunLike.coe ∘ F) 1\n⊢ Co... | [
34,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
23,
1
] |
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