file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
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values | start list |
|---|---|---|---|---|---|---|
Mathlib/Order/Lattice.lean | inf_le_iff | [] | [
874,
26
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873,
1
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Mathlib/CategoryTheory/Limits/EssentiallySmall.lean | CategoryTheory.Limits.hasCoproductsOfShape_of_small | [] | [
49,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
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Mathlib/Combinatorics/Pigeonhole.lean | Fintype.exists_card_fiber_le_of_card_le_nsmul | [] | [
445,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
442,
1
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Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.affineCombinationSingleWeights_apply_self | [
{
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659,
89
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658,
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Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.SatelliteConfig.centerAndRescale_center | [
{
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}
] | [
119,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
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Mathlib/Topology/Algebra/Monoid.lean | isClosed_setOf_map_one | [] | [
314,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
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Mathlib/RingTheory/HahnSeries.lean | HahnSeries.ofPowerSeries_X | [
{
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"state_before": "Γ : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\ninst✝ : StrictOrderedSemiring Γ\n⊢ ↑(ofPowerSe... | [
1219,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1209,
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Mathlib/Topology/Order.lean | map_nhds_induced_eq | [
{
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"tactic": "rw [nhds_induced, Filter.map_comap, nhdsWithin]"
}
] | [
875,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
874,
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Mathlib/Order/RelClasses.lean | superset_antisymm_iff | [] | [
661,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
660,
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Mathlib/LinearAlgebra/Prod.lean | LinearMap.prod_eq_sup_map | [
{
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490,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
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Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.le_kernelSubobject | [
{
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"tactic": "simp"
}
] | [
202,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_sum | [] | [
440,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Data/Set/Intervals/Basic.lean | IsBot.Ici_eq | [] | [
703,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
702,
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Mathlib/Order/RelIso/Basic.lean | RelHom.map_rel | [] | [
117,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
11
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Mathlib/Topology/Algebra/StarSubalgebra.lean | StarSubalgebra.topologicalClosure_minimal | [] | [
102,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
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Std/Data/List/Lemmas.lean | List.tail_eq_tailD | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : List α\n⊢ tail l = tailD l []",
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}
] | [
450,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
450,
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Mathlib/Topology/Connected.lean | IsPreconnected.subset_closure | [] | [
294,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
11
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Mathlib/Order/RelClasses.lean | IsRefl.swap | [] | [
72,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Set/Ncard.lean | Set.ncard_coe_Finset | [
{
"state_after": "no goals",
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"tactic": "rw [ncard_eq_toFinset_card _, Finset.finite_toSet_toFinset]"
}
] | [
93,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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Mathlib/Data/Set/Image.lean | Subtype.range_val_subtype | [] | [
1417,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1416,
1
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Mathlib/Topology/UniformSpace/UniformEmbedding.lean | isComplete_image_iff | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nm : α → β\ns : Set α\nhm : UniformInducing m\nc : IsComplete s\n⊢ IsComplete (m '' s)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ninst✝² : UniformSpace α\ninst✝¹ : Unifo... | [
304,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
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Mathlib/FieldTheory/SplittingField/IsSplittingField.lean | Polynomial.IsSplittingField.of_algEquiv | [
{
"state_after": "case splits'\nF : Type u\nK : Type v\nL : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Field F\ninst✝² : Algebra K L\ninst✝¹ : Algebra K F\np : K[X]\nf : F ≃ₐ[K] L\ninst✝ : IsSplittingField K F p\n⊢ Splits (algebraMap K L) p\n\ncase adjoin_roots'\nF : Type u\nK : Type v\nL : Type w\nin... | [
147,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
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Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_sq | [
{
"state_after": "no goals",
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"tactic": "rw [derivative_pow_succ, Nat.cast_one, one_add_one_eq_two, pow_one]"
}
] | [
491,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
490,
1
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Mathlib/Data/Complex/Exponential.lean | Complex.cosh_zero | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cosh 0 = 1",
"tactic": "simp [cosh]"
}
] | [
619,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
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Mathlib/Algebra/Hom/Centroid.lean | CentroidHom.coe_nsmul | [] | [
315,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_injective | [] | [
134,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Std/Data/Array/Init/Lemmas.lean | Array.push_data | [
{
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"state_before": "α : Type u_1\narr : Array α\na : α\n⊢ (push arr a).data = arr.data ++ [a]",
"tactic": "simp [push, List.concat_eq_append]"
}
] | [
76,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
75,
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.openSegment_subset | [] | [
62,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biprod.fstKernelFork_ι | [] | [
1683,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1682,
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Mathlib/RingTheory/Subring/Basic.lean | Subring.InClosure.recOn | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ns : Set R\nC : R → Prop\nx : R\nhx : x ∈ closure s\nh1 : C 1\nhneg1 : C (-1)\nhs : ∀ (z : R), z ∈ s → ∀ (n : R), C n → C (z * n)\nha : ∀ {x y : R}, C x → C y → C (x + y)\nh0 : C 0\n⊢ C x",
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1397,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1354,
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Mathlib/Analysis/Calculus/ContDiff.lean | contDiffWithinAt_snd | [] | [
846,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
844,
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Mathlib/Algebra/Field/Basic.lean | sub_div' | [
{
"state_after": "no goals",
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"tactic": "simpa using div_sub_div b a one_ne_zero hc"
}
] | [
241,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
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Mathlib/Order/Filter/Basic.lean | Filter.Tendsto.if | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.319862\nι : Sort x\nl₁ : Filter α\nl₂ : Filter β\nf g : α → β\np : α → Prop\ninst✝ : (x : α) → Decidable (p x)\nh₀ : ∀ (s : Set β), s ∈ l₂ → {x | x ∈ {x | p x} → x ∈ f ⁻¹' s} ∈ l₁\nh₁ : ∀ (s : Set β), s ∈ l₂ → {x | x ∈ {x | ¬p x} → x ∈ g ⁻¹' s} ∈... | [
3095,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3086,
11
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasStrictDerivAt_sinh | [
{
"state_after": "x : ℂ\n⊢ HasStrictDerivAt sinh ((exp x + exp (-x)) * 2⁻¹) x",
"state_before": "x : ℂ\n⊢ HasStrictDerivAt sinh (cosh x) x",
"tactic": "simp only [cosh, div_eq_mul_inv]"
},
{
"state_after": "case h.e'_7\nx : ℂ\n⊢ (exp x + exp (-x)) * 2⁻¹ = (exp x - exp (-id x) * -1) * 2⁻¹",
"... | [
110,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Data/Int/Log.lean | Int.log_mono_right | [
{
"state_after": "case inl\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr₁ r₂ : R\nh₀ : 0 < r₁\nh : r₁ ≤ r₂\nhb : b ≤ 1\n⊢ log b r₁ ≤ log b r₂\n\ncase inr\nR : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr₁ r₂ : R\nh₀ : 0 < r₁\nh : r₁ ≤ r₂\nh... | [
157,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/Algebra/ContinuedFractions/Translations.lean | GeneralizedContinuedFraction.zeroth_convergent_eq_h | [
{
"state_after": "no goals",
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"tactic": "simp [convergent_eq_num_div_denom, num_eq_conts_a, denom_eq_conts_b, div_one]"
}
] | [
148,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Integral/IntegralEqImproper.lean | MeasureTheory.AECover.biUnion_Iic_aecover | [] | [
340,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
337,
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Mathlib/FieldTheory/Subfield.lean | Subfield.mem_toSubmonoid | [] | [
431,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Analysis/NormedSpace/Ray.lean | sameRay_iff_of_norm_eq | [
{
"state_after": "case inl\nE : Type ?u.245331\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nx : F\nh : ‖x‖ = ‖0‖\n⊢ SameRay ℝ x 0 ↔ x = 0\n\ncase inr\nE : Type ?u.245331\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpac... | [
106,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.salient_strictlyPositive | [] | [
626,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
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] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.derivWithin_integral_left | [] | [
979,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
974,
1
] |
Mathlib/Algebra/Module/LocalizedModule.lean | LocalizedModule.one_smul' | [
{
"state_after": "case h\nR : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\nm : M\ns : { x // x ∈ S }\n⊢ 1 • mk m s = mk m s",
"state_before": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Mo... | [
343,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
341,
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] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_congr_subtype | [
{
"state_after": "no goals",
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"tactic": "rw [h]"
}
] | [
460,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/Algebra/CharP/Basic.lean | add_pow_prime_pow_eq | [] | [
74,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
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Mathlib/FieldTheory/Subfield.lean | Subfield.coe_inv | [] | [
392,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
391,
1
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Mathlib/Order/CompleteLattice.lean | isLUB_iSup | [] | [
775,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
1
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Mathlib/FieldTheory/IntermediateField.lean | IntermediateField.one_mem | [] | [
167,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
11
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Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.comap_mono | [
{
"state_after": "no goals",
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201,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/AlgebraicTopology/SimplicialObject.lean | CategoryTheory.CosimplicialObject.δ_comp_σ_of_le | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX : CosimplicialObject C\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nH : i ≤ ↑Fin.castSucc j\n⊢ X.map (SimplexCategory.δ (↑Fin.castSucc i)) ≫ X.map (SimplexCategory.σ (Fin.succ j)) =\n X.map (SimplexCategory.σ j) ≫ X.map (SimplexCategory.δ i)",
"state_befor... | [
524,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
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Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.submodule_eq | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nV : Type u_2\ninst✝² : DivisionRing K\ninst✝¹ : AddCommGroup V\ninst✝ : Module K V\nv : ℙ K V\n⊢ Projectivization.submodule v = Submodule.span K {Projectivization.rep v}",
"tactic": "conv_lhs => rw [← v.mk_rep]"
}
] | [
138,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
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Mathlib/Topology/Algebra/Order/Floor.lean | tendsto_floor_left | [
{
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"state_before": "α : Type u_1\nβ : Type ?u.16071\nγ : Ty... | [
136,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
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Mathlib/Order/Grade.lean | Covby.grade | [] | [
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27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
11
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Mathlib/MeasureTheory/Integral/CircleIntegral.lean | circleIntegral.integral_const_mul | [] | [
459,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
457,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.IsRegularOfDegree.compl | [
{
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Mathlib/Data/List/Forall2.lean | List.forall₂_take_append | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.131498\nδ : Type ?u.131501\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\nl : List α\nl₁ l₂ : List β\nh : Forall₂ R l (l₁ ++ l₂)\nh' : Forall₂ R (take (length l₁) l) (take (length l₁) (l₁ ++ l₂))\n⊢ Forall₂ R (take (length l₁) l) l₁",
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229,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
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Mathlib/Order/WithBot.lean | WithBot.coe_strictMono | [] | [
330,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_not | [] | [
272,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Measurable.ccos | [] | [
191,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | MonoidHomClass.lipschitz_of_bound | [
{
"state_after": "no goals",
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796,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
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Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.second_wallis_limit | [
{
"state_after": "a : ℝ\nhane : a ≠ 0\nha : Tendsto stirlingSeq atTop (𝓝 a)\n⊢ Tendsto (fun n => stirlingSeq n ^ 4 / stirlingSeq (2 * n) ^ 2 * (↑n / (2 * ↑n + 1))) atTop (𝓝 (a ^ 2 / 2))",
"state_before": "a : ℝ\nhane : a ≠ 0\nha : Tendsto stirlingSeq atTop (𝓝 a)\n⊢ Tendsto Wallis.W atTop (𝓝 (a ^ 2 / 2))... | [
263,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
254,
1
] |
Mathlib/MeasureTheory/Decomposition/SignedHahn.lean | MeasureTheory.SignedMeasure.exists_subset_restrict_nonpos' | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.39511\ninst✝³ : MeasurableSpace α\nM : Type ?u.39517\ninst✝² : AddCommMonoid M\ninst✝¹ : TopologicalSpace M\ninst✝ : OrderedAddCommMonoid M\ns : SignedMeasure α\ni j : Set α\nhi₁ : MeasurableSet i\nhi₂ : ↑s i < 0\nhn :\n ¬∀ (n : ℕ),\n ¬restrict s (i \\... | [
266,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
9
] |
Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsQF.liftAt | [] | [
733,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | differentiableOn_singleton | [] | [
1128,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1127,
1
] |
Mathlib/Data/Set/Basic.lean | Set.coe_inclusion | [] | [
2805,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2804,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.coe_castAddHom | [] | [
82,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Topology/Algebra/StarSubalgebra.lean | StarSubalgebra.le_topologicalClosure | [] | [
87,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Algebra/Homology/ShortExact/Preadditive.lean | CategoryTheory.Split.rightSplit | [] | [
139,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/CategoryTheory/Filtered.lean | CategoryTheory.IsCofiltered.of_isLeftAdjoint | [] | [
741,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableAt.cexp | [] | [
146,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_eq_fintype_total_apply | [
{
"state_after": "case h\nα : Type u_2\nM : Type u_1\nR : Type u_3\ninst✝⁶ : Fintype α\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nS : Type u_4\ninst✝² : Semiring S\ninst✝¹ : Module S M\ninst✝ : SMulCommClass R S M\nv : α → M\nx : α → R\n⊢ (↑(LinearEquiv.symm (linearEquivFunOnFinite R R... | [
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24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1071,
1
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.Lp.simpleFunc.add_toSimpleFunc | [
{
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657,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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Mathlib/Algebra/MonoidAlgebra/ToDirectSum.lean | DirectSum.toAddMonoidAlgebra_add | [] | [
174,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Data/Dfinsupp/Order.lean | Dfinsupp.le_iff' | [] | [
167,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
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Mathlib/Analysis/SpecialFunctions/Polynomials.lean | Polynomial.isEquivalent_atTop_div | [
{
"state_after": "case pos\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrderedField 𝕜\nP Q : 𝕜[X]\ninst✝ : OrderTopology 𝕜\nhP : P = 0\n⊢ (fun x => eval x P / eval x Q) ~[atTop] fun x =>\n leadingCoeff P / leadingCoeff Q * x ^ (↑(natDegree P) - ↑(natDegree Q))\n\ncase neg\n𝕜 : Type u_1\ninst✝¹ : NormedLinearOrd... | [
137,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.Measure.IsComplete.out | [] | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.flip_nondegenerate | [] | [
697,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/GroupTheory/SpecificGroups/Cyclic.lean | card_orderOf_eq_totient_aux₂ | [
{
"state_after": "α : Type u\na : α\ninst✝² : Group α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhn : ∀ (n : ℕ), 0 < n → card (filter (fun a => a ^ n = 1) univ) ≤ n\nd : ℕ\nhd : d ∣ Fintype.card α\nc : ℕ := Fintype.card α\n⊢ card (filter (fun a => orderOf a = d) univ) = φ d",
"state_before": "α : Type u\na... | [
395,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffWithinAt.sum | [
{
"state_after": "case empty\n𝕜 : Type u_2\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type uG\nins... | [
1351,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1343,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.coe_prod | [] | [
1543,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1542,
1
] |
Mathlib/Data/Set/Function.lean | Set.InjOn.cancel_left | [] | [
728,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
726,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_erase_lt_of_one_lt | [
{
"state_after": "ι : Type ?u.800477\nβ : Type u\nα : Type v\nγ✝ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nf✝ g : α → β\ninst✝³ : CommMonoid β\nγ : Type u_1\ninst✝² : DecidableEq α\ninst✝¹ : OrderedCommMonoid γ\ninst✝ : CovariantClass γ γ (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ns : Finset α\nd : α\nhd : d ∈ s\... | [
1701,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1696,
1
] |
Mathlib/Data/List/AList.lean | AList.empty_union | [] | [
433,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | RingHom.quotientKerEquivOfRightInverse.Symm.apply | [] | [
79,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_subset_inter_right | [] | [
1707,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1706,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.add_le_of_lt | [] | [
246,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero | [
{
"state_after": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : x ≠ 0\n⊢ 0 < ‖x‖ / Real.sqrt (‖x‖ * ‖x‖ + ‖y‖ * ‖y‖)",
"state_before": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nh : inner x y = 0\nh0 : ... | [
135,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Topology/PathConnected.lean | Path.ext | [
{
"state_after": "case mk.mk.mk.mk\nX : Type u_1\nY : Type ?u.11489\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx✝ y z : X\nι : Type ?u.11504\nx : ↑I → X\nh11 : Continuous x\nh12 : ContinuousMap.toFun (ContinuousMap.mk x) 0 = x✝\nh13 : ContinuousMap.toFun (ContinuousMap.mk x) 1 = y\nh21 : Continuo... | [
103,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
11
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | IsFiniteMeasure.lintegral_lt_top_of_bounded_to_eNNReal | [
{
"state_after": "case intro\nα✝ : Type ?u.1753837\nβ : Type ?u.1753840\nγ : Type ?u.1753843\nδ : Type ?u.1753846\nm : MeasurableSpace α✝\nμ✝ ν : Measure α✝\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nμ_fin : IsFiniteMeasure μ\nf : α → ℝ≥0∞\nc : ℝ≥0\nhc : ∀ (x : α), f x ≤ ↑c\n⊢ (∫⁻ (x : α), f x ∂μ)... | [
1538,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1532,
1
] |
Mathlib/Data/List/AList.lean | AList.lookup_union_left | [] | [
457,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
456,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousAffineMap.lean | ContinuousAffineMap.decomp | [
{
"state_after": "case mk\n𝕜 : Type ?u.87212\nR : Type u_1\nV : Type u_2\nW : Type u_3\nW₂ : Type ?u.87224\nP : Type ?u.87227\nQ : Type ?u.87230\nQ₂ : Type ?u.87233\ninst✝¹⁶ : NormedAddCommGroup V\ninst✝¹⁵ : MetricSpace P\ninst✝¹⁴ : NormedAddTorsor V P\ninst✝¹³ : NormedAddCommGroup W\ninst✝¹² : MetricSpace Q\n... | [
159,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.verts_inf | [] | [
375,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Topology/ContinuousOn.lean | IsOpen.nhdsWithin_eq | [] | [
225,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/WithBot.lean | WithBot.toDual_symm_apply | [] | [
924,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sigmaFinite_of_le | [] | [
3785,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3784,
1
] |
Mathlib/Algebra/Order/Ring/Abs.lean | abs_one | [] | [
28,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Analysis/Calculus/Deriv/Comp.lean | HasDerivWithinAt.comp_hasFDerivWithinAt | [] | [
157,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/SetTheory/Cardinal/Continuum.lean | Cardinal.lift_continuum | [
{
"state_after": "no goals",
"state_before": "⊢ lift 𝔠 = 𝔠",
"tactic": "rw [← two_power_aleph0, lift_two_power, lift_aleph0, two_power_aleph0]"
}
] | [
46,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.mono | [] | [
227,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.isCountablyGenerated_biInf_principal | [] | [
1162,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/Data/Set/Sups.lean | Set.sups_infs_subset_left | [] | [
378,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
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