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/Algebra/Order/Sub/Canonical.lean | tsub_min | [
{
"state_after": "case inl\nα : Type u_1\ninst✝² : CanonicallyLinearOrderedAddMonoid α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nh : a ≤ b\n⊢ a - min a b = a - b\n\ncase inr\nα : Type u_1\ninst✝² : CanonicallyLinearOrderedAddMonoid α\ninst✝¹ : Sub α\ninst✝ : OrderedSub α\na b c d : α\nh : b ≤ a\n⊢ a -... | [
507,
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504,
1
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Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.LocallyIntegrableOn.integrableOn_isCompact | [] | [
71,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Data/Set/NAry.lean | Set.image2_image_left_comm | [] | [
369,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
366,
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Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.totalDegree_add | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.397208\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q a b : MvPolynomial σ R\nn : σ →₀ ℕ\nhn : n ∈ support (a + b)\nthis : n ∈ a.support ∪ b.support\n⊢ (sum n fun x e => e) ≤ max (totalDegree a) (totalDegree b)",
"state_be... | [
652,
50
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644,
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Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.natDegree_hasseDeriv | [
{
"state_after": "case inl\nR : Type u_1\ninst✝¹ : Semiring R\nk : ℕ\nf : R[X]\ninst✝ : NoZeroSMulDivisors ℕ R\np : R[X]\nn : ℕ\nhn : natDegree p < n\n⊢ natDegree (↑(hasseDeriv n) p) = natDegree p - n\n\ncase inr\nR : Type u_1\ninst✝¹ : Semiring R\nk : ℕ\nf : R[X]\ninst✝ : NoZeroSMulDivisors ℕ R\np : R[X]\nn : ... | [
228,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
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Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.mk_proj_snd' | [] | [
372,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
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Mathlib/Topology/Homeomorph.lean | Homeomorph.comp_continuous_iff' | [] | [
416,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
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Mathlib/Data/IsROrC/Basic.lean | IsROrC.normSq_nonneg | [] | [
484,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
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Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_right_hasFDerivAt_iff | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace ... | [
222,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
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Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_powerset | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\nb : β\nf✝ g : α → β\ninst✝ : CommMonoid β\ns : Finset α\nf : Finset α → β\n⊢ ∏ t in powerset s, f t = ∏ j in range (card s + 1), ∏ t in powersetLen j s, f t",
"tactic": "rw [powerset_card_disjiU... | [
268,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Topology/Category/Compactum.lean | Compactum.lim_eq_str | [
{
"state_after": "X : Compactum\nF : Ultrafilter X.A\n⊢ ∀ (s : Set X.A), str X F ∈ s → IsOpen s → s ∈ ↑F",
"state_before": "X : Compactum\nF : Ultrafilter X.A\n⊢ Ultrafilter.lim F = str X F",
"tactic": "rw [Ultrafilter.lim_eq_iff_le_nhds, le_nhds_iff]"
},
{
"state_after": "no goals",
"state_... | [
374,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
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Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.mk₂'ₛₗ_apply | [] | [
97,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Endofunctor/Algebra.lean | CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm | [
{
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"state_before": "C : Type u\ninst✝ : Category C\nF G : C ⥤ C\nadj : F ⊣ G\nV₁ V₂ : Coalgebra G\nf : V₁ ⟶ V₂\n⊢ F.map f.f ≫ ↑(Adjunction.homEquiv adj V₂.V V₂.V).symm V₂.str = ↑(Adjunction.homEquiv adj V₁.V V₁.V).symm V₁.str ≫ f.f",
"tactic": "rw [← Adjunction.homEquiv_natural... | [
466,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
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Mathlib/Algebra/GroupPower/Ring.lean | zero_pow_eq_zero | [
{
"state_after": "case mp\nR : Type ?u.47966\nS : Type ?u.47969\nM : Type u_1\ninst✝¹ : MonoidWithZero M\ninst✝ : Nontrivial M\nn : ℕ\nh : 0 ^ n = 0\n⊢ 0 < n\n\ncase mpr\nR : Type ?u.47966\nS : Type ?u.47969\nM : Type u_1\ninst✝¹ : MonoidWithZero M\ninst✝ : Nontrivial M\nn : ℕ\nh : 0 < n\n⊢ 0 ^ n = 0",
"sta... | [
105,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
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Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.X_pow_add_C_ne_zero | [
{
"state_after": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\na : R\n⊢ ↑n ≠ ⊥",
"state_before": "R : Type u\nS : Type v\na✝ b c d : R\nn✝ m : ℕ\ninst✝¹ : Nontrivial R\ninst✝ : Semiring R\nn : ℕ\nhn : 0 < n\na : R\n⊢ degree (X ^ n + ↑C a) ≠ ⊥"... | [
1388,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
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Mathlib/Deprecated/Submonoid.lean | Monoid.mem_closure_union_iff | [
{
"state_after": "no goals",
"state_before": "M✝ : Type ?u.75380\ninst✝² : Monoid M✝\ns✝ : Set M✝\nA : Type ?u.75389\ninst✝¹ : AddMonoid A\nt✝ : Set A\nM : Type u_1\ninst✝ : CommMonoid M\ns t : Set M\nx : M\nhx : x ∈ Closure (s ∪ t)\nL : List M\nHL1✝ : ∀ (x : M), x ∈ L → x ∈ s ∪ t\nHL2 : List.prod L = x\nhd... | [
416,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
395,
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Mathlib/Order/JordanHolder.lean | CompositionSeries.top_snoc | [] | [
560,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.card_atomise_le | [] | [
576,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_range_mul_prod_Ico | [] | [
94,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
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Mathlib/Order/SupIndep.lean | CompleteLattice.Independent.disjoint_biSup | [] | [
357,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
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Mathlib/RingTheory/UniqueFactorizationDomain.lean | Associates.prime_pow_dvd_iff_le | [
{
"state_after": "case intro.intro\nα : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ndec_irr : (p : Associates α) → Decidable (Irreducible p)\ninst✝¹ : UniqueFactorizationMonoid α\ndec : DecidableEq α\ndec' : DecidableEq (Associates α)\ninst✝ : Nontrivial α\np : Associates α\nh₂ : Irreducible p\nk : ℕ\na : α\... | [
1690,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_comp_map | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹⁴ : CommSemiring R\nR' : Type ?u.1289962\ninst✝¹³ : Monoid R'\nR'' : Type ?u.1289968\ninst✝¹² : Semiring R''\nM : Type u_4\nN : Type u_5\nP : Type u_2\nQ : Type u_6\nS : Type u_3\ninst✝¹¹ : AddCommMonoid M\ninst✝¹⁰ : AddCommMonoid N\ninst✝⁹ :... | [
1143,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
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Mathlib/Algebra/Order/Module.lean | smul_nonneg_of_nonpos_of_nonpos | [] | [
98,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | DifferentiableOn.cexp | [] | [
150,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Topology/Bornology/Hom.lean | LocallyBoundedMap.comp_apply | [] | [
175,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | isUnit_exp | [] | [
476,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
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Mathlib/Computability/Primrec.lean | Primrec.comp₂ | [] | [
479,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContinuousLinearMap.iteratedFDerivWithin_comp_left | [] | [
244,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ioc_subset_Ioc | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12902\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nha : a₂ ≤ a₁\nhb : b₁ ≤ b₂\n⊢ Ioc a₁ b₁ ⊆ Ioc a₂ b₂",
"tactic": "simpa [← coe_subset] using Set.Ioc_subset_Ioc ha hb"
}
] | [
171,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/Partition/Finpartition.lean | Finpartition.biUnion_filter_atomise | [
{
"state_after": "case a\nα : Type u_1\ninst✝ : DecidableEq α\ns t : Finset α\nP : Finpartition s\nF : Finset (Finset α)\nht : t ∈ F\nhts : t ⊆ s\na : α\n⊢ a ∈ Finset.biUnion (filter (fun u => u ⊆ t ∧ Finset.Nonempty u) (atomise s F).parts) id ↔ a ∈ t",
"state_before": "α : Type u_1\ninst✝ : DecidableEq α\n... | [
587,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Algebra.top_toSubmodule | [] | [
790,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
790,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.countable_not_continuousWithinAt_Ioi | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝⁶ : LinearOrder α\ninst✝⁵ : ConditionallyCompleteLinearOrder β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : OrderTopology β\nf : α → β\nhf : Monotone f\nx y : α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\ninst✝ : TopologicalSpace.SecondCountableTopology β... | [
269,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Data/List/Basic.lean | List.bind_singleton' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.21722\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ l : List α\n⊢ (List.bind l fun x => [x]) = l",
"tactic": "induction l <;> simp [*]"
}
] | [
504,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
9
] |
Mathlib/RingTheory/Polynomial/Basic.lean | Polynomial.toSubring_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type ?u.95871\ninst✝¹ : Ring R\ninst✝ : Semiring S\nf : R →+* S\nx : S\np : R[X]\nT : Subring R\nhp : ↑(frange p) ⊆ ↑T\n⊢ ↑(frange 0) ⊆ ↑T",
"tactic": "simp [frange_zero]"
},
{
"state_after": "case a.a\nR : Type u\nS : Type ?u.95871\n... | [
395,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
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Mathlib/Data/Set/Function.lean | Set.MapsTo.mem_iff | [] | [
542,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.cos_arccos | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx₁ : -1 ≤ x\nhx₂ : x ≤ 1\n⊢ cos (arccos x) = x",
"tactic": "rw [arccos, cos_pi_div_two_sub, sin_arcsin hx₁ hx₂]"
}
] | [
362,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
361,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.div_add_mod' | [
{
"state_after": "R : Type u\ninst✝ : EuclideanDomain R\nm k : R\n⊢ k * (m / k) + m % k = m",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\nm k : R\n⊢ m / k * k + m % k = m",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDom... | [
139,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Order/Antichain.lean | IsAntichain.image_relIso | [] | [
136,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | euler_four_squares | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : CommRing R\na b c d x y z w : R\n⊢ (a * x - b * y - c * z - d * w) ^ 2 + (a * y + b * x + c * w - d * z) ^ 2 + (a * z - b * w + c * x + d * y) ^ 2 +\n (a * w + b * z - c * y + d * x) ^ 2 =\n (a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2) * (x ^ 2 ... | [
39,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
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Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.quotientMulEquivOfEq_mk | [] | [
450,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
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Mathlib/Algebra/GCDMonoid/Basic.lean | normalize_eq_normalize | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\na b : α\nhab : a ∣ b\nhba : b ∣ a\n✝ : Nontrivial α\n⊢ ↑normalize a = ↑normalize b",
"state_before": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizationMonoid α\na b : α\nhab : a ∣ b\nhb... | [
184,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Analysis/NormedSpace/Ray.lean | SameRay.norm_eq_iff | [] | [
120,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/Bases.lean | QuotientMap.secondCountableTopology | [
{
"state_after": "case intro.intro.intro\nα : Type u\nt : TopologicalSpace α\nX : Type u_1\ninst✝² : TopologicalSpace X\nY : Type u_2\ninst✝¹ : TopologicalSpace Y\nπ : X → Y\ninst✝ : SecondCountableTopology X\nh' : QuotientMap π\nh : IsOpenMap π\nV : Set (Set X)\nV_countable : Set.Countable V\nV_generates : IsT... | [
860,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
855,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | Associates.out_mk | [] | [
223,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.write_nth | [] | [
674,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
670,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.ofReal_real_eq_id | [] | [
864,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
863,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.le_zero_iff | [
{
"state_after": "n✝ m n : ℕ\ninst✝ : NeZero n\nk : Fin n\nh : k ≤ 0\n⊢ 0 = ↑0",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\nk : Fin n\nh : k ≤ 0\n⊢ ↑k = ↑0",
"tactic": "rw [Nat.eq_zero_of_le_zero h]"
},
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\nk : Fin n... | [
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99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
988,
1
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.inv_comp_eq_id | [] | [
490,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/AlgebraicGeometry/Stalks.lean | AlgebraicGeometry.PresheafedSpace.stalkMap.congr | [
{
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"tactic": "rw [h₂]"
},
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ ... | [
169,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
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Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_unique | [
{
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585,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
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Mathlib/Analysis/Convex/Basic.lean | Convex.lineMap_mem | [] | [
481,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.inducedOuterMeasure_exists_set | [
{
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1513,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1502,
1
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Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | NNReal.pow_nat_rpow_nat_inv | [
{
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},
{
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268,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Mathlib/CategoryTheory/Conj.lean | CategoryTheory.Iso.homCongr_apply | [
{
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] | [
54,
6
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52,
1
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Mathlib/Data/List/Cycle.lean | Cycle.mk''_eq_coe | [] | [
478,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
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Mathlib/Order/Heyting/Basic.lean | codisjoint_hnot_right | [] | [
1037,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
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Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.rTensor_smul | [] | [
1063,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1062,
1
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Mathlib/MeasureTheory/Function/Jacobian.lean | MeasureTheory.measurableEmbedding_of_fderivWithin | [] | [
793,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
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Mathlib/Data/Set/Lattice.lean | Set.iInter₂_comm | [] | [
803,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
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Mathlib/Algebra/Order/Field/Basic.lean | div_le_one_iff | [
{
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860,
49
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856,
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Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.eq_comp_inv | [] | [
234,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
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Mathlib/Data/Real/ENNReal.lean | ENNReal.toReal_add | [
{
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1948,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1945,
1
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Mathlib/Tactic/NormNum/Basic.lean | Mathlib.Meta.NormNum.isNat_ofScientific_of_false | [
{
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"state_before": "α : Type u_1\ninst✝ : DivisionRing α\nσα : OfScientific... | [
603,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
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Mathlib/SetTheory/Game/PGame.lean | PGame.lf_of_moveRight_le | [] | [
482,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
481,
1
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Mathlib/Topology/ContinuousOn.lean | nhdsWithin_pi_eq' | [
{
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319,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
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Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.pf_sub_c | [] | [
40,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
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Mathlib/Dynamics/Ergodic/MeasurePreserving.lean | MeasureTheory.MeasurePreserving.exists_mem_image_mem | [
{
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167,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasDerivWithinAt.cosh | [] | [
867,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
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Mathlib/Topology/MetricSpace/Holder.lean | HolderOnWith.ediam_image_le | [] | [
164,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
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Mathlib/Analysis/Convex/Strict.lean | StrictConvex.sub | [] | [
391,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
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Mathlib/Data/Finset/NAry.lean | Finset.image_subset_image₂_left | [] | [
95,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
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Mathlib/Data/List/Basic.lean | List.splitAt_eq_take_drop | [
{
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2897,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2866,
1
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Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.coe_bit1 | [] | [
139,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.splitting_iso_hom_eq_id | [] | [
261,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubalgebra.ideal_in_normalizer | [
{
"state_after": "R : Type u_2\nL : Type u_1\nM : Type ?u.56361\nM' : Type ?u.56364\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : Lie... | [
158,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
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Mathlib/Data/ZMod/Basic.lean | ZMod.nat_cast_zmod_eq_zero_iff_dvd | [
{
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"tactic": "rw [← Nat.cast_zero, ZMod.nat_cast_eq_nat_cast_iff, Nat.modEq_zero_iff_dvd]"
}
] | [
483,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.div_mul_le_self | [
{
"state_after": "no goals",
"state_before": "m : Nat\n⊢ m / 0 * 0 ≤ m",
"tactic": "simp"
}
] | [
562,
69
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
560,
1
] |
Mathlib/Analysis/Normed/Group/Pointwise.lean | IsCompact.div_closedBall_one | [
{
"state_after": "no goals",
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"tactic": "simp [div_eq_mul_inv, hs.mul_closedBall_one hδ]"
}
] | [
266,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_congr_measure_of_add_left | [
{
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1669,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1662,
1
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Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.map_comp_inl | [
{
"state_after": "no goals",
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300,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
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Mathlib/Data/Set/Image.lean | Set.range_subtype_map | [
{
"state_after": "case h.mk\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.88408\nι : Sort ?u.88411\nι' : Sort ?u.88414\nf✝ : ι → α\ns t : Set α\np : α → Prop\nq : β → Prop\nf : α → β\nh : ∀ (x : α), p x → q (f x)\nx : β\nhx : q x\n⊢ { val := x, property := hx } ∈ range (Subtype.map f h) ↔\n { val := x, property :... | [
1018,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1005,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.disjoint_iUnion_left | [] | [
2076,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2074,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.empty_vecAlt1 | [
{
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"tactic": "simp"
}
] | [
425,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivAtFilter.const_add | [] | [
127,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.algebraMap_fst | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean | TensorAlgebra.algebraMap_eq_zero_iff | [] | [
213,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.isCauSeq_abs | [] | [
1262,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1258,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.neighborSet_bot | [] | [
511,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
511,
1
] |
Mathlib/Computability/Partrec.lean | Nat.rfind_min' | [
{
"state_after": "no goals",
"state_before": "p : ℕ → Bool\nm : ℕ\npm : p m = true\nthis : true ∈ ↑p m\nn : ℕ\nhn : n ∈ rfind ↑p\nh : m < n\n⊢ False",
"tactic": "injection mem_unique this (rfind_min hn h)"
}
] | [
118,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
] |
Mathlib/Topology/Algebra/WithZeroTopology.lean | WithZeroTopology.Iio_mem_nhds_zero | [] | [
72,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Std/Data/List/Lemmas.lean | List.ne_and_not_mem_of_not_mem_cons | [] | [
104,
61
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
103,
1
] |
Mathlib/Algebra/Quandle.lean | Rack.assoc_iff_id | [
{
"state_after": "R✝ : Type ?u.30897\ninst✝¹ : Rack R✝\nR : Type u_1\ninst✝ : Rack R\nx y z : R\n⊢ (x ◃ y) ◃ x ◃ z = (x ◃ y) ◃ z ↔ x ◃ z = z",
"state_before": "R✝ : Type ?u.30897\ninst✝¹ : Rack R✝\nR : Type u_1\ninst✝ : Rack R\nx y z : R\n⊢ x ◃ y ◃ z = (x ◃ y) ◃ z ↔ x ◃ z = z",
"tactic": "rw [self_distr... | [
355,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Analysis/Convex/Basic.lean | convex_iInter₂ | [] | [
112,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_zero_one | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\np : α\nhp : 0 < p\nb : α\n⊢ toIcoDiv (_ : 0 < 1) 0 b = ⌊b⌋",
"tactic": "simp [toIcoDiv_eq_floor]"
}
] | [
1015,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1014,
1
] |
Mathlib/Analysis/BoxIntegral/Basic.lean | BoxIntegral.HasIntegral.mcShane_of_forall_isLittleO | [
{
"state_after": "no goals",
"state_before": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI J : Box ι\nπ : TaggedPrepartition I\ninst✝ : Fintype ι\nl : IntegrationParams\nf g✝ : (ι → ℝ) → E\nvol : ι →ᵇᵃ... | [
849,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
843,
1
] |
Mathlib/Order/Hom/Basic.lean | OrderHom.fst_prod_snd | [
{
"state_after": "case h.h.mk\nF : Type ?u.52049\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.52058\nδ : Type ?u.52061\ninst✝³ : Preorder α\ninst✝² : Preorder β\ninst✝¹ : Preorder γ\ninst✝ : Preorder δ\nx : α\ny : β\n⊢ ↑(OrderHom.prod fst snd) (x, y) = ↑id (x, y)",
"state_before": "F : Type ?u.52049\nα : Type u... | [
460,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
458,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.degree_interpolate_erase_lt | [
{
"state_after": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ninst✝ : DecidableEq ι\ns t : Finset ι\ni j : ι\nv r r' : ι → F\nhvs : Set.InjOn v ↑s\nhi : i ∈ s\n⊢ degree (↑(interpolate (Finset.erase s i) v) r) < ↑(card (Finset.erase s i))",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\nins... | [
356,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Data/List/Forall2.lean | List.forall₂_zip | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.33435\nδ : Type ?u.33438\nR S : α → β → Prop\nP : γ → δ → Prop\nRₐ : α → α → Prop\na✝ : α\nb✝ : β\nl₁✝ : List α\nl₂✝ : List β\nh₁ : R a✝ b✝\nh₂ : Forall₂ R l₁✝ l₂✝\nx : α\ny : β\nhx : (x, y) = (a✝, b✝) ∨ (x, y) ∈ zipWith Prod.mk l₁✝ l₂✝\n⊢ R x y",
"s... | [
194,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/Control/Traversable/Equiv.lean | Equiv.id_map | [
{
"state_after": "no goals",
"state_before": "t t' : Type u → Type u\neqv : (α : Type u) → t α ≃ t' α\ninst✝¹ : Functor t\ninst✝ : LawfulFunctor t\nα : Type u\nx : t' α\n⊢ Equiv.map eqv id x = x",
"tactic": "simp [Equiv.map, id_map]"
}
] | [
61,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
11
] |
Mathlib/GroupTheory/NielsenSchreier.lean | IsFreeGroupoid.SpanningTree.treeHom_eq | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝² : Groupoid G\ninst✝¹ : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\na : G\np : Path (root (WideSubquiver.toType (Symmetrify (Generators G)) T)) a\n⊢... | [
182,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
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