file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
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Mathlib/RingTheory/Ideal/Quotient.lean | Ideal.exists_sub_one_mem_and_mem | [
{
"state_after": "R : Type u\ninst✝ : CommRing R\nI : Ideal R\na b : R\nS ι : Type v\ns : Finset ι\nf : ι → Ideal R\nhf : ∀ (i : ι), i ∈ s → ∀ (j : ι), j ∈ s → i ≠ j → f i ⊔ f j = ⊤\ni : ι\nhis : i ∈ s\nj : ι\nhjs : j ∈ s\nhji : j ≠ i\n⊢ ∃ r x, r ∈ f j",
"state_before": "R : Type u\ninst✝ : CommRing R\nI : ... | [
446,
26
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405,
1
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Mathlib/Data/Nat/Lattice.lean | Nat.iInf_lt_succ | [] | [
190,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Logic/Basic.lean | ne_of_apply_ne | [] | [
510,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
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Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernel_not_iso_of_nonzero | [
{
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397,
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394,
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Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.IsThreeCycle.sign | [
{
"state_after": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : IsThreeCycle σ\n⊢ (-1) ^ (sum {3} + ↑card {3}) = 1",
"state_before": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nh : IsThreeCycle σ\n⊢ ↑Perm.sign σ = 1",
"tactic": "rw [Equiv.Perm.sign_of... | [
599,
6
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597,
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src/lean/Init/Data/List/Control.lean | List.forM_nil | [] | [
191,
6
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190,
9
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.hasBinaryBiproducts_of_finite_biproducts | [] | [
1239,
91
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1234,
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Mathlib/Data/Sum/Order.lean | Sum.inl_mono | [] | [
188,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Order/RelIso/Basic.lean | RelEmbedding.wellFounded | [] | [
400,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
11
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Mathlib/Topology/MetricSpace/Basic.lean | Prod.dist_eq | [] | [
1751,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1751,
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Mathlib/CategoryTheory/Preadditive/Mat.lean | CategoryTheory.Mat.comp_apply | [] | [
616,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
614,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_restrict_of_restrict_compl | [] | [
606,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.ne_zero_of_not_isOrtho_self | [] | [
773,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
772,
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Mathlib/Data/Int/Order/Basic.lean | Int.toNat_le | [
{
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"state_before": "a✝ b : ℤ\nn✝ : ℕ\na : ℤ\nn : ℕ\n⊢ toNat a ≤ n ↔ a ≤ ↑n",
"tactic": "rw [ofNat_le.symm, toNat_eq_max, max_le_iff]"
},
{
"state_after": "no goals",
"state_before": "a✝ b : ℤ\nn✝ : ℕ\na : ℤ\nn : ℕ\n⊢... | [
502,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.mono | [] | [
54,
55
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Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | map_lt_lineMap_iff_slope_lt_slope_left | [] | [
232,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/Algebra/GCDMonoid/Multiset.lean | Multiset.gcd_dedup | [
{
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"tactic": "simp"
},
{
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206,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/Topology/Algebra/Module/FiniteDimension.lean | LinearEquiv.toLinearEquiv_toContinuousLinearEquiv | [
{
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394,
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Mathlib/Analysis/Normed/Group/Basic.lean | NormedCommGroup.tendsto_nhds_one | [
{
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744,
61
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Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_append | [
{
"state_after": "no goals",
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"tactic": "induction p <;> simp [*]"
}
] | [
709,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
707,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.symm_coe_proj | [] | [
587,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
585,
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Mathlib/ModelTheory/Substructures.lean | FirstOrder.Language.Substructure.comap_surjective_of_injective | [] | [
572,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
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Mathlib/RepresentationTheory/Action.lean | Action.rightDual_ρ | [
{
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748,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Convex/Between.lean | wbtw_one_zero_iff | [
{
"state_after": "no goals",
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453,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Algebra/Order/Group/Abs.lean | le_abs_self | [] | [
61,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Order/Concept.lean | extentClosure_empty | [] | [
92,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.lhom_ext' | [] | [
825,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/RingTheory/PowerSeries/Basic.lean | MvPolynomial.coe_eq_one_iff | [
{
"state_after": "no goals",
"state_before": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nφ ψ : MvPolynomial σ R\n⊢ ↑φ = 1 ↔ φ = 1",
"tactic": "rw [← coe_one, coe_inj]"
}
] | [
1154,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1154,
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Mathlib/CategoryTheory/MorphismProperty.lean | CategoryTheory.MorphismProperty.diagonal_iff | [] | [
527,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
526,
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Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.ofSet_target | [] | [
658,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
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Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FinitePresentation.comp_surjective | [] | [
516,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
514,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.ElementarilyEquivalent.trans | [] | [
1107,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1106,
8
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.coe_one | [] | [
605,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
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Mathlib/CategoryTheory/Sites/SheafOfTypes.lean | CategoryTheory.Presieve.isAmalgamation_sieveExtend | [
{
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408,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
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Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformlyOn.congr | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝¹ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx✝ : α\np : Filter ι\np' : Filter α\ng : ι → α\ninst✝ : TopologicalSpace α\nG : ι → α → β\nhf : TendstoLocallyUniformlyOn F f p s\nhg : ∀ (n : ι), EqOn (F n) (G n) s\nu : Set (β × β... | [
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
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Mathlib/MeasureTheory/Function/SimpleFuncDense.lean | MeasureTheory.SimpleFunc.nearestPt_zero | [] | [
86,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
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Mathlib/Algebra/Order/Floor.lean | Int.ceil_zero | [
{
"state_after": "no goals",
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"tactic": "rw [← cast_zero, ceil_intCast]"
}
] | [
1196,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.sub_eq_sInf | [] | [
1096,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1095,
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_eq_self_iff | [
{
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594,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_insert | [
{
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164,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | DifferentiableOn.csin | [] | [
399,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.mem_factorSet_top | [
{
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1334,
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Mathlib/Data/Finset/Pointwise.lean | Finset.zero_smul_finset_subset | [] | [
2117,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2116,
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Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.xy_coprime | [
{
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"tactic": ... | [
401,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
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Mathlib/Algebra/FreeAlgebra.lean | FreeAlgebra.lift_ι_apply | [
{
"state_after": "R : Type u_2\ninst✝² : CommSemiring R\nX : Type u_3\nA : Type u_1\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nf : X → A\nx : X\n⊢ ↑(↑{ toFun := FreeAlgebra.liftAux R, invFun := fun F => ↑F ∘ ι R,\n left_inv := (_ : ∀ (f : X → A), (fun F => ↑F ∘ ι R) (FreeAlgebra.liftAux R f) = f),\... | [
349,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
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Mathlib/Data/Finset/Pointwise.lean | Finset.image_mul_product | [] | [
319,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
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Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.span_empty | [] | [
735,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
734,
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Mathlib/Data/Nat/Parity.lean | Nat.div_two_mul_two_of_even | [] | [
227,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
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Mathlib/Algebra/Lie/Submodule.lean | LieSubalgebra.exists_lieIdeal_coe_eq_iff | [
{
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327,
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Mathlib/GroupTheory/GroupAction/Group.lean | smul_inv | [
{
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"tactic": "rw [inv_eq_iff_mul_eq_one, smul_mul_smul, mul_right_... | [
125,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/MeasureTheory/Measure/AEMeasurable.lean | AEMeasurable.add_measure | [] | [
130,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Nat/PartENat.lean | PartENat.lt_add_one_iff_lt | [
{
"state_after": "x y : PartENat\nhx : x ≠ ⊤\nh : x ≤ y\n⊢ x < y + 1",
"state_before": "x y : PartENat\nhx : x ≠ ⊤\n⊢ x < y + 1 ↔ x ≤ y",
"tactic": "refine ⟨le_of_lt_add_one, fun h => ?_⟩"
},
{
"state_after": "case intro\ny : PartENat\nm : ℕ\nhx : ↑m ≠ ⊤\nh : ↑m ≤ y\n⊢ ↑m < y + 1",
"state_be... | [
522,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
515,
1
] |
Mathlib/Algebra/DirectSum/Module.lean | DirectSum.coeLinearMap_of | [] | [
324,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_sub | [
{
"state_after": "m n : Nat\n⊢ toNat (subNatNat m n) = m - n",
"state_before": "m n : Nat\n⊢ toNat (↑m - ↑n) = m - n",
"tactic": "rw [← Int.subNatNat_eq_coe]"
},
{
"state_after": "case refine_1\nm n✝ i n : Nat\n⊢ (fun m n i => toNat i = m - n) (n + i) n ↑i\n\ncase refine_2\nm n✝ i n : Nat\n⊢ (fu... | [
518,
80
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
514,
1
] |
Mathlib/Data/Option/Basic.lean | Option.join_pmap_eq_pmap_join | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.13574\nδ : Type ?u.13577\np : α → Prop\nf✝ : (a : α) → p a → β\nx✝ : Option α\nf : (a : α) → p a → β\nx : Option (Option α)\nH : ∀ (a : Option α), a ∈ x → ∀ (a_2 : α), a_2 ∈ a → p a_2\n⊢ join (pmap (pmap f) x H) = pmap f (... | [
259,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.isPredLimit_of_pred_ne | [] | [
340,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
339,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.range_val | [] | [
2980,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2979,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.ofNat_re | [] | [
283,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.getLeft_inr | [] | [
100,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
9
] |
Mathlib/Topology/MetricSpace/Baire.lean | dense_iUnion_interior_of_closed | [] | [
349,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Order/Lattice.lean | toDual_inf | [] | [
963,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
962,
1
] |
Mathlib/Algebra/QuadraticDiscriminant.lean | quadratic_eq_zero_iff | [
{
"state_after": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NeZero 2\na b c x✝ : K\nha : a ≠ 0\ns : K\nh : discrim a b c = s * s\nx : K\n⊢ s = 2 * a * x + b ∨ s = -(2 * a * x + b) ↔ x = (-b + s) / (2 * a) ∨ x = (-b - s) / (2 * a)",
"state_before": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NeZero 2\na b c x✝ : ... | [
95,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.vsub_subset_vsub_right | [] | [
1527,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1526,
1
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.leadingCoeff_divByMonic_of_monic | [
{
"state_after": "R✝ : Type u\nS : Type v\nT : Type w\na b : R✝\nn : ℕ\ninst✝² : CommRing R✝\ninst✝¹ : IsDomain R✝\np✝ q✝ : R✝[X]\nR : Type u\ninst✝ : CommRing R\np q : R[X]\nhmonic : Monic q\nhdegree : degree q ≤ degree p\n✝ : Nontrivial R\n⊢ leadingCoeff (p /ₘ q) = leadingCoeff p",
"state_before": "R✝ : T... | [
1014,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_lt_coeff_mul | [] | [
163,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Order/CompactlyGenerated.lean | CompleteLattice.IsSupClosedCompact.wellFounded | [
{
"state_after": "ι : Sort ?u.27269\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : IsSupClosedCompact α\na : (fun x x_1 => x > x_1) ↪r fun x x_1 => x > x_1\n⊢ False",
"state_before": "ι : Sort ?u.27269\nα : Type u_1\ninst✝ : CompleteLattice α\nf : ι → α\nh : IsSupClosedCompact α\n⊢ WellFounded fun... | [
246,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.intervalIntegral_tendsto_integral_Iic | [
{
"state_after": "ι : Type u_2\nE : Type u_1\nμ : Measure ℝ\nl : Filter ι\ninst✝³ : IsCountablyGenerated l\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\na b✝ : ι → ℝ\nf : ℝ → E\nb : ℝ\nhfi : IntegrableOn f (Iic b)\nha : Tendsto a l atBot\nφ : ι → Set ℝ := fun i => Ioi (a i)\... | [
642,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
634,
1
] |
Mathlib/Topology/MetricSpace/Polish.lean | Equiv.polishSpace_induced | [] | [
169,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/LinearAlgebra/Dimension.lean | LinearMap.lift_rank_comp_le_right | [
{
"state_after": "K : Type u\nV V₁ V₂ V₃ : Type v\nV' V'₁ : Type v'\nV'' : Type v''\nι : Type w\nι' : Type w'\nη : Type u₁'\nφ : η → Type ?u.1114972\ninst✝⁸ : Ring K\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module K V\ninst✝⁵ : AddCommGroup V₁\ninst✝⁴ : Module K V₁\ninst✝³ : AddCommGroup V'\ninst✝² : Module K V'\nins... | [
1341,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1339,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.norm_map_cons_le | [
{
"state_after": "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) → NormedAddCommGroup (E i)\nins... | [
1307,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.Subsingleton.congr | [
{
"state_after": "case h\nα : Type u_1\ns : Cycle α\nh✝ : Subsingleton s\nl : List α\nh : Subsingleton (Quot.mk Setoid.r l)\n⊢ ∀ ⦃x : α⦄, x ∈ Quot.mk Setoid.r l → ∀ ⦃y : α⦄, y ∈ Quot.mk Setoid.r l → x = y",
"state_before": "α : Type u_1\ns : Cycle α\nh : Subsingleton s\n⊢ ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s... | [
614,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Algebra/Tropical/Basic.lean | Tropical.succ_nsmul | [
{
"state_after": "case zero\nR✝ : Type u\ninst✝² : LinearOrderedAddCommMonoidWithTop R✝\nR : Type u_1\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\nx : Tropical R\n⊢ (Nat.zero + 1) • x = x\n\ncase succ\nR✝ : Type u\ninst✝² : LinearOrderedAddCommMonoidWithTop R✝\nR : Type u_1\ninst✝¹ : LinearOrder R\ninst✝ : Orde... | [
571,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Data/Fintype/Sum.lean | Set.MapsTo.exists_equiv_extend_of_card_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝ : Fintype α\nt : Finset β\nhαt : Fintype.card α = card t\ns : Set α\nf : α → β\nhfst : MapsTo f s ↑t\nhfs : InjOn f s\n⊢ ∃ g, ∀ (i : α), i ∈ s → ↑(↑g i) = f i",
"tactic": "classical\n let s' : Finset α := s.toFinset\n have... | [
118,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Algebra/Module/Injective.lean | Module.Baer.extensionOfMax_adjoin.aux1 | [
{
"state_after": "R : Type u\ninst✝⁷ : Ring R\nQ : TypeMax\ninst✝⁶ : AddCommGroup Q\ninst✝⁵ : Module R Q\nM N : Type (max u v)\ninst✝⁴ : AddCommGroup M\ninst✝³ : AddCommGroup N\ninst✝² : Module R M\ninst✝¹ : Module R N\ni : M →ₗ[R] N\nf : M →ₗ[R] Q\ninst✝ : Fact (Function.Injective ↑i)\ny : N\nx : { x // x ∈ su... | [
268,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
9
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.card_classes_ker_le | [
{
"state_after": "no goals",
"state_before": "α✝ : Type ?u.1538\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype β\nf : α → β\ninst✝ : Fintype ↑(classes (ker f))\n⊢ Fintype.card ↑(classes (ker f)) ≤ Fintype.card β",
"tactic": "classical exact\n le_trans (Set.card_le_of_subset (classes_ker_subset_fiber_s... | [
95,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Algebra/Associated.lean | Associates.bot_eq_one | [] | [
786,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.U_eq_X_mul_U_add_T | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.12813\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ U R (0 + 1) = X * U R 0 + T R (0 + 1)",
"tactic": "simp only [T, U, two_mul, mul_one]"
},
{
"state_after": "R : Type u_1\nS : Type ?u.12813\ninst✝¹ : CommRing R\ninst✝ : Comm... | [
135,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.lt_succ_iff_eq_or_lt_of_not_isMax | [] | [
445,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | Seminorm.const_isBounded | [
{
"state_after": "case mp\n𝕜 : Type u_2\n𝕜₂ : Type u_4\n𝕝 : Type ?u.123266\n𝕝₂ : Type ?u.123269\nE : Type u_3\nF : Type u_5\nG : Type ?u.123278\nι✝ : Type ?u.123281\nι' : Type u_6\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : NormedField 𝕜₂\ninst✝³ : AddCommGroup F\ninst... | [
243,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
237,
1
] |
Mathlib/Data/Int/Bitwise.lean | Int.bodd_zero | [] | [
31,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
30,
1
] |
Mathlib/CategoryTheory/Sites/Closed.lean | CategoryTheory.topology_eq_iff_same_sheaves | [
{
"state_after": "case mp\nC : Type u\ninst✝ : Category C\nJ₁✝ J₂✝ J₁ J₂ : GrothendieckTopology C\n⊢ J₁ = J₂ → ∀ (P : Cᵒᵖ ⥤ Type (max v u)), Presieve.IsSheaf J₁ P ↔ Presieve.IsSheaf J₂ P\n\ncase mpr\nC : Type u\ninst✝ : Category C\nJ₁✝ J₂✝ J₁ J₂ : GrothendieckTopology C\n⊢ (∀ (P : Cᵒᵖ ⥤ Type (max v u)), Presiev... | [
287,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.smul | [
{
"state_after": "case refine'_2\nα : Type u_1\nβ : Type ?u.584464\nE : Type ?u.584467\nF : Type ?u.584470\nG : Type ?u.584473\nE' : Type u_4\nF' : Type u_5\nG' : Type ?u.584482\nE'' : Type ?u.584485\nF'' : Type ?u.584488\nG'' : Type ?u.584491\nR : Type ?u.584494\nR' : Type ?u.584497\n𝕜 : Type u_2\n𝕜' : Type ... | [
1777,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1774,
1
] |
Mathlib/Algebra/Module/Submodule/Bilinear.lean | Submodule.map₂_sup_left | [] | [
133,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.smul_extend | [
{
"state_after": "case h\nα : Type u_2\nP : α → Prop\nm : (s : α) → P s → ℝ≥0∞\nR : Type u_1\ninst✝³ : Zero R\ninst✝² : SMulWithZero R ℝ≥0∞\ninst✝¹ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\ninst✝ : NoZeroSMulDivisors R ℝ≥0∞\nc : R\nhc : c ≠ 0\ns : α\n⊢ (c • extend m) s = extend (fun s h => c • m s h) s",
"state_before":... | [
1335,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1328,
1
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.Term.relabel_comp_relabel | [] | [
135,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Analysis/PSeries.lean | NNReal.summable_rpow | [
{
"state_after": "no goals",
"state_before": "p : ℝ\n⊢ (Summable fun n => ↑n ^ p) ↔ p < -1",
"tactic": "simp [← NNReal.summable_coe]"
}
] | [
281,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Algebra/Module/Basic.lean | Convex.combo_eq_smul_sub_add | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.85204\nR : Type u_1\nk : Type ?u.85210\nS : Type ?u.85213\nM : Type u_2\nM₂ : Type ?u.85219\nM₃ : Type ?u.85222\nι : Type ?u.85225\ninst✝² : Semiring R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nx y : M\na b : R\nh : a + b = 1\n⊢ a • x + b • y = b... | [
282,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Topology/Basic.lean | isClosed_empty | [] | [
208,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
9
] |
Mathlib/CategoryTheory/Limits/EssentiallySmall.lean | CategoryTheory.Limits.hasColimitsOfShape_of_essentiallySmall | [] | [
39,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Algebra/BigOperators/Finsupp.lean | Finsupp.liftAddHom_apply_single | [] | [
489,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
487,
1
] |
Mathlib/Algebra/CharP/Basic.lean | CharP.char_is_prime_or_zero | [] | [
551,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
547,
1
] |
Mathlib/Topology/Constructions.lean | openEmbedding_sigmaMk | [] | [
1489,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1487,
1
] |
Mathlib/Analysis/Convex/Hull.lean | convexHull_singleton | [] | [
131,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.isEquivalent_of_tendsto_one' | [] | [
222,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/Data/Finset/Image.lean | Equiv.finsetCongr_symm | [] | [
796,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/Topology/LocallyFinite.lean | LocallyFinite.comp_injOn | [
{
"state_after": "ι : Type u_1\nι' : Type u_3\nα : Type ?u.1343\nX : Type u_2\nY : Type ?u.1349\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf g✝ : ι → Set X\ng : ι' → ι\nhf : LocallyFinite f\nhg : InjOn g {i | Set.Nonempty (f (g i))}\nx : X\nt : Set X\nhtx : t ∈ 𝓝 x\nhtf : Set.Finite {i | Set.Non... | [
54,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/CategoryTheory/Extensive.lean | CategoryTheory.FinitaryExtensive.isPullback_initial_to_binaryCofan | [] | [
273,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
270,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | le_mul_of_one_le_of_le_of_nonneg | [] | [
930,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.mem_of_span_eq_top_of_smul_pow_mem | [] | [
1464,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1460,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.seq_sub | [] | [
320,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
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