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/RingTheory/Coprime/Basic.lean | isCoprime_mul_unit_left | [] | [
261,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
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Mathlib/Algebra/ModEq.lean | AddCommGroup.not_modEq_iff_ne_mod_zmultiples | [] | [
307,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
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Mathlib/Topology/UniformSpace/Cauchy.lean | Cauchy.mono' | [] | [
82,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
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Mathlib/Topology/MetricSpace/Baire.lean | Dense.inter_of_Gδ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.23922\nγ : Type ?u.23925\nι : Type ?u.23928\ninst✝¹ : TopologicalSpace α\ninst✝ : BaireSpace α\ns t : Set α\nhs : IsGδ s\nht : IsGδ t\nhsc : Dense s\nhtc : Dense t\n⊢ Dense (⋂ (b : Bool), bif b then s else t)",
"state_before": "α : Type u_1\nβ : Type ?u.23922\nγ :... | [
288,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
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Mathlib/Algebra/IndicatorFunction.lean | Set.comp_mulIndicator_const | [] | [
286,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
284,
1
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Mathlib/Algebra/Lie/Solvable.lean | LieAlgebra.derivedSeriesOfIdeal_antitone | [] | [
118,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nonpos_of_pi_div_two_le_of_le | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx₁ : π / 2 ≤ x\nhx₂ : x ≤ π + π / 2\n⊢ -(π / 2) ≤ π - x",
"tactic": "linarith"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx₁ : π / 2 ≤ x\nhx₂ : x ≤ π + π / 2\n⊢ π - x ≤ π / 2",
"tactic": "linarith"
}
] | [
484,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
482,
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Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.index_elim | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK V : Set G\nhK : IsCompact K\nhV : Set.Nonempty (interior V)\nthis :\n sInf (Finset.card '' {t | K ⊆ ⋃ (g : G) (_ : g ∈ t), (fun h => g * h) ⁻¹' V}) ∈\n Finset.card '' {t | K ⊆ ⋃ (g : G) (_ : g ∈ t), ... | [
183,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
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Mathlib/Analysis/Normed/Group/Basic.lean | Pi.sum_norm_apply_le_norm' | [] | [
2549,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2548,
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Mathlib/CategoryTheory/Limits/Cones.lean | CategoryTheory.Limits.coconeOfConeLeftOp_ι_app | [
{
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"state_before": "J : Type u₁\ninst✝³ : Category J\nK : Typ... | [
955,
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952,
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.basis_toMatrix_basisFun_mul | [
{
"state_after": "p : ℝ≥0∞\n𝕜 : Type u_2\n𝕜' : Type ?u.557496\nι : Type u_1\nα : ι → Type ?u.557504\nβ : ι → Type ?u.557509\ninst✝⁸ : Fintype ι\ninst✝⁷ : Fact (1 ≤ p)\ninst✝⁶ : NormedField 𝕜\ninst✝⁵ : NormedField 𝕜'\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (β i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (β i)\nc... | [
1005,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
997,
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Mathlib/Data/List/Intervals.lean | List.Ico.mem | [
{
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"state_before": "n m l : ℕ\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"tactic": "suffices n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m by simp [Ico, this]"
},
{
"state_after": "case inl\nn m l : ℕ\nhnm : n ≤ m\n⊢ n ≤ l ∧ l < n + (m - n) ↔... | [
72,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.tendsto_integral_filter_of_dominated_convergence | [
{
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1023,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_smul_assoc | [
{
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1957,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
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Mathlib/Data/Nat/Interval.lean | Nat.card_Ico | [] | [
103,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
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Mathlib/Topology/LocalExtr.lean | IsLocalMax.congr | [] | [
600,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
598,
8
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Mathlib/Data/Fin/Basic.lean | Fin.mul_comm | [
{
"state_after": "no goals",
"state_before": "n m : ℕ\na b : Fin n\n⊢ ↑(a * b) = ↑(b * a)",
"tactic": "rw [mul_def, mul_def, mul_comm]"
}
] | [
2528,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2527,
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Mathlib/Data/Sum/Basic.lean | Sum.map_id_id | [] | [
241,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
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Mathlib/Analysis/Calculus/FDerivSymmetric.lean | Convex.second_derivative_within_at_symmetric | [
{
"state_after": "case intro\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns✝ : Set E\ns_conv✝ : Convex ℝ s✝\nf✝ : E → F\nf'✝ : E → E →L[ℝ] F\nf''✝ : E →L[ℝ] E →L[ℝ] F\nhf✝ : ∀ (x : E), x ∈ interior s✝ → HasFDerivAt ... | [
306,
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261,
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Mathlib/Topology/SubsetProperties.lean | isCompact_iff_compactSpace | [] | [
919,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
918,
1
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Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_mul_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c : α\nha : a = 0\n⊢ (fun x => x * a) '' [[b, c]] = [[b * a, c * a]]",
"tactic": "simp [ha]"
},
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\na✝ a b c ... | [
716,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
710,
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Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.exists_iso_map | [] | [
690,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
689,
1
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Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_sInter | [] | [
1708,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1707,
1
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Mathlib/Data/Finset/PImage.lean | Finset.pimage_eq_image_filter | [
{
"state_after": "case a\nα : Type u_2\nβ : Type u_1\ninst✝² : DecidableEq β\nf g : α →. β\ninst✝¹ : (x : α) → Decidable (f x).Dom\ninst✝ : (x : α) → Decidable (g x).Dom\ns t : Finset α\nb x : β\n⊢ x ∈ pimage f s ↔ x ∈ image (fun x => Part.get (f ↑x) (_ : (f ↑x).Dom)) (attach (filter (fun x => (f x).Dom) s))",
... | [
100,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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] |
Mathlib/RingTheory/Localization/Integral.lean | IsIntegral.exists_multiple_integral_of_isLocalization | [
{
"state_after": "case inl\nR : Type u_3\ninst✝¹¹ : CommRing R\nM : Submonoid R\nS : Type u_2\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nP : Type ?u.431142\ninst✝⁸ : CommRing P\nRₘ : Type u_1\nSₘ : Type ?u.431151\ninst✝⁷ : CommRing Rₘ\ninst✝⁶ : CommRing Sₘ\ninst✝⁵ : Algebra R Rₘ\ninst✝⁴ : IsLocalization M Rₘ\... | [
305,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
289,
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] |
Mathlib/Data/Set/Image.lean | Function.Injective.exists_unique_of_mem_range | [] | [
1339,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1337,
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] |
Mathlib/Combinatorics/DoubleCounting.lean | Finset.card_mul_le_card_mul' | [] | [
104,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
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] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_add_sin_I | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos x + sin x * I = exp (x * I)",
"tactic": "rw [← cosh_add_sinh, sinh_mul_I, cosh_mul_I]"
}
] | [
1010,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1009,
1
] |
Mathlib/Combinatorics/SetFamily/Intersecting.lean | Set.Intersecting.exists_mem_finset | [] | [
145,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/FunLike/Basic.lean | FunLike.ne_iff | [] | [
192,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/NumberTheory/ArithmeticFunction.lean | Nat.ArithmeticFunction.intCoe_int | [] | [
179,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Order.lean | continuous_induced_rng | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type u_1\nf : α → β\nι : Sort ?u.36895\ng : γ → α\nt₂ : TopologicalSpace β\nt₁ : TopologicalSpace γ\n⊢ Continuous g ↔ Continuous (f ∘ g)",
"tactic": "simp only [continuous_iff_le_induced, induced_compose]"
}
] | [
711,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Topology/Constructions.lean | continuous_apply_apply | [] | [
1205,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1203,
1
] |
Mathlib/GroupTheory/Submonoid/Membership.lean | Submonoid.iSup_induction' | [
{
"state_after": "M : Type u_2\nA : Type ?u.48124\nB : Type ?u.48127\ninst✝ : MulOneClass M\nι : Sort u_1\nS : ι → Submonoid M\nC : (x : M) → (x ∈ ⨆ (i : ι), S i) → Prop\nhp : ∀ (i : ι) (x : M) (hxS : x ∈ S i), C x (_ : x ∈ ⨆ (i : ι), S i)\nh1 : C 1 (_ : 1 ∈ ⨆ (i : ι), S i)\nhmul :\n ∀ (x y : M) (hx : x ∈ ⨆ (i... | [
299,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
290,
1
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Mathlib/Data/Vector/Zip.lean | Vector.zipWith_get | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nn : ℕ\nf : α → β → γ\nx : Vector α n\ny : Vector β n\ni : Fin n\n⊢ List.nthLe (List.zipWith f ↑x ↑y) ↑i (_ : ↑i < List.length (List.zipWith f ↑x ↑y)) =\n f\n (match x, i with\n | { val := l, property := h }, i => List.nthLe l ↑i (_ : ↑i < ... | [
40,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
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Mathlib/Algebra/Group/Ext.lean | CancelCommMonoid.ext | [] | [
119,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_ge_inter_gt | [] | [
412,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | EsakiaHom.comp_assoc | [] | [
337,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/GroupTheory/Finiteness.lean | Group.fg_iff | [] | [
308,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
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] |
Mathlib/Data/Stream/Init.lean | Stream'.corec_id_id_eq_const | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\na : α\n⊢ corec id id a = const a",
"tactic": "rw [corec_def, map_id, iterate_id]"
}
] | [
383,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
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] |
Mathlib/FieldTheory/IntermediateField.lean | toSubalgebra_toIntermediateField' | [
{
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324,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/CategoryTheory/Preadditive/HomOrthogonal.lean | CategoryTheory.HomOrthogonal.equiv_of_iso | [
{
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223,
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208,
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Mathlib/Algebra/CharZero/Lemmas.lean | bit1_eq_one | [
{
"state_after": "no goals",
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"tactic": "rw [show (1 : R) = bit1 0 by simp, bit1_eq_bit1]"
},
{
"state_after": "no goals",
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147,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/Analysis/Convex/Gauge.lean | le_gauge_of_not_mem | [
{
"state_after": "𝕜 : Type ?u.88359\nE : Type u_1\nF : Type ?u.88365\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns t : Set E\na : ℝ\nx : E\nhs₀ : ∀ ⦃x : E⦄, x ∈ s → ∀ ⦃a : ℝ⦄, 0 ≤ a → a ≤ 1 → a • x ∈ s\nhs₂ : Absorbs ℝ s {x}\nhx : ¬x ∈ a • s\n⊢ a ≤ gauge s x",
"state_before": "𝕜 : Type ?u.88359\nE : Typ... | [
233,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.comp_contDiffAt | [] | [
734,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
732,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.map_swap_divisorsAntidiagonal | [
{
"state_after": "n : ℕ\n⊢ Prod.swap ⁻¹' ↑(divisorsAntidiagonal n) = ↑(divisorsAntidiagonal n)",
"state_before": "n : ℕ\n⊢ map (Equiv.toEmbedding (Equiv.prodComm ℕ ℕ)) (divisorsAntidiagonal n) = divisorsAntidiagonal n",
"tactic": "rw [← coe_inj, coe_map, Equiv.coe_toEmbedding, Equiv.coe_prodComm,\n Set... | [
248,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
243,
1
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Mathlib/Topology/Order.lean | isClosed_discrete | [] | [
286,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
285,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_bot | [
{
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142,
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Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.Γ_obj | [] | [
278,
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277,
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Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_union_eq_adjoin_adjoin | [] | [
316,
71
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308,
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.reduce.eq_of_red | [] | [
1221,
49
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Mathlib/Data/List/Basic.lean | List.get_set_of_ne | [
{
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{
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1579,
87
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.continuous_const_mul | [] | [
412,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
411,
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Mathlib/AlgebraicTopology/SimplexCategory.lean | SimplexCategory.const_comp | [] | [
173,
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171,
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Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.apply_symm_apply | [] | [
524,
37
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523,
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Mathlib/MeasureTheory/Constructions/Polish.lean | Continuous.measurableEmbedding | [] | [
626,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
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Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.nontrivial_iff_exists_ne_one | [
{
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Mathlib/Data/Multiset/Basic.lean | Multiset.map_eq_map | [
{
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24
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Mathlib/Logic/Function/Conjugate.lean | Function.Semiconj₂.isAssociative_left | [
{
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171,
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Mathlib/GroupTheory/GroupAction/Quotient.lean | MulAction.card_eq_sum_card_group_div_card_stabilizer' | [
{
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282,
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.left_vsub_lineMap | [
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641,
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640,
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Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_constantsVarsEquiv | [
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486,
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477,
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Mathlib/Data/Set/Sigma.lean | Set.mk_preimage_sigma_eq_if | [
{
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192,
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Mathlib/Algebra/Field/Power.lean | Odd.neg_zpow | [
{
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38,
26
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36,
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Mathlib/Order/UpperLower/Basic.lean | LowerSet.compl_iSup | [
{
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917,
86
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Mathlib/Topology/ContinuousFunction/T0Sierpinski.lean | TopologicalSpace.productOfMemOpens_injective | [
{
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61,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
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Mathlib/Data/Real/Sqrt.lean | Real.sqrt_eq_zero_of_nonpos | [
{
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] | [
192,
101
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192,
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Mathlib/Algebra/CubicDiscriminant.lean | Cubic.natDegree_of_b_eq_zero' | [] | [
417,
33
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416,
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Mathlib/RingTheory/Localization/Away/Basic.lean | selfZpow_of_nonpos | [
{
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238,
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Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.stepAux_write | [
{
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1801,
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Mathlib/CategoryTheory/Limits/HasLimits.lean | CategoryTheory.Limits.colimit.pre_map' | [
{
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32
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1122,
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Mathlib/Data/Finsupp/Defs.lean | Finsupp.support_update_ne_zero | [
{
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Mathlib/Analysis/Complex/Circle.lean | circle.toUnits_apply | [] | [
102,
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100,
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Mathlib/RingTheory/WittVector/Defs.lean | WittVector.wittOne_pos_eq_zero | [
{
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262,
48
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247,
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Std/Data/List/Lemmas.lean | List.exists_or_eq_self_of_replaceF | [] | [
1343,
62
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1335,
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Mathlib/Topology/MetricSpace/MetrizableUniformity.lean | PseudoMetricSpace.dist_ofPreNNDist | [] | [
95,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
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Mathlib/Topology/Order.lean | nhdsAdjoint_nhds_of_ne | [
{
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46
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614,
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Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.maximal_iff | [
{
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586,
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567,
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Mathlib/Topology/Order/Basic.lean | closure_interior_Icc | [] | [
2309,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2304,
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Mathlib/Algebra/Ring/AddAut.lean | AddAut.mulRight_apply | [] | [
44,
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43,
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Mathlib/LinearAlgebra/Orientation.lean | Orientation.eq_or_eq_neg | [
{
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341,
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Mathlib/AlgebraicGeometry/PresheafedSpace.lean | CategoryTheory.Functor.mapPresheaf_map_c | [] | [
562,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
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Mathlib/Data/Fintype/Card.lean | Fintype.induction_subsingleton_or_nontrivial | [
{
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1215,
40
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1202,
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Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.nil_append | [] | [
775,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
774,
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Mathlib/GroupTheory/Commensurable.lean | Commensurable.symm | [] | [
54,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
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Mathlib/Topology/Order/Basic.lean | Dense.orderDual | [] | [
106,
5
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
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Mathlib/Data/List/AList.lean | AList.mem_lookup_union | [] | [
468,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
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Mathlib/Order/SuccPred/Limit.lean | Order.isSuccLimitRecOn_succ | [] | [
198,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
196,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.edge_comp_symm | [] | [
757,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
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] |
Mathlib/Data/Bool/Basic.lean | Bool.cond_eq_ite | [
{
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}
] | [
126,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
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Mathlib/Computability/Encoding.lean | Computability.Encoding.card_le_aleph0 | [
{
"state_after": "α : Type u\ne : Encoding α\ninst✝ : Encodable e.Γ\n⊢ lift (#List e.Γ) ≤ lift ℵ₀",
"state_before": "α : Type u\ne : Encoding α\ninst✝ : Encodable e.Γ\n⊢ (#α) ≤ ℵ₀",
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},
{
"state_after": "α : Type u\ne : Encoding... | [
256,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
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Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isClosed_range_comap_of_surjective | [
{
"state_after": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nS' : Type ?u.417705\ninst✝ : CommRing S'\nf : R →+* S\nhf : Surjective ↑f\n⊢ IsClosed (zeroLocus ↑(ker f))",
"state_before": "R : Type u\nS : Type v\ninst✝² : CommRing R\ninst✝¹ : CommRing S\nS' : Type ?u.417705\ninst✝ : Com... | [
749,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Data/Int/Parity.lean | Int.odd_coe_nat | [
{
"state_after": "no goals",
"state_before": "m n✝ : ℤ\nn : ℕ\n⊢ Odd ↑n ↔ Odd n",
"tactic": "rw [odd_iff_not_even, Nat.odd_iff_not_even, even_coe_nat]"
}
] | [
208,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Computability/Partrec.lean | Partrec.map | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.61762\nσ : Type u_3\ninst✝³ : Primcodable α\ninst✝² : Primcodable β\ninst✝¹ : Primcodable γ\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β → σ\nhf : Partrec f\nhg : Computable₂ g\n⊢ Partrec fun a => Part.map (g a) (f a)",
... | [
465,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.cast_zero | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\na : R\ne : a = ↑0\n⊢ a = 0",
"tactic": "simp [e]"
}
] | [
835,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
834,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.sup_pure | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.43512\nγ : Type ?u.43515\nι : Sort u_2\nι' : Sort ?u.43521\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nhl : HasBasis l p s\nx : α\n⊢ HasBasis (l ⊔ pure x) p fun i => s i ∪ {... | [
617,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.roots_ne_zero_of_splits | [] | [
300,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/Set/Image.lean | Set.preimage_eq_empty | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.121366\nf : α → β\ns✝ t : Set α\ns : Set β\nh : Disjoint s (range f)\n⊢ f ⁻¹' s = ∅",
"tactic": "simpa using h.preimage f"
}
] | [
1618,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1616,
1
] |
Mathlib/Data/List/Cycle.lean | List.next_mem | [] | [
249,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | PowerSeries.rescale_mul | [
{
"state_after": "case a.h\nR : Type u_1\ninst✝ : CommSemiring R\na b : R\nx✝ : PowerSeries R\nn✝ : ℕ\n⊢ ↑(coeff R n✝) (↑(rescale (a * b)) x✝) = ↑(coeff R n✝) (↑(RingHom.comp (rescale b) (rescale a)) x✝)",
"state_before": "R : Type u_1\ninst✝ : CommSemiring R\na b : R\n⊢ rescale (a * b) = RingHom.comp (resc... | [
1799,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1797,
1
] |
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