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/CategoryTheory/Sites/Types.lean | CategoryTheory.typesGlue_eval | [
{
"state_after": "S : Type uᵒᵖ ⥤ Type u\nhs : IsSheaf typesGrothendieckTopology S\nα : Type u\ns : S.obj α.op\n⊢ ∀ ⦃Y : Type u⦄ ⦃f : Y ⟶ α⦄, discretePresieve α f → S.map f.op (typesGlue S hs α (eval S α s)) = S.map f.op s",
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120,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_ofNat_add_one | [] | [
1376,
85
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1376,
9
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Std/Data/Nat/Lemmas.lean | Nat.sub_le_sub_right_iff | [] | [
132,
74
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
131,
11
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Mathlib/Logic/Basic.lean | Fact.elim | [] | [
128,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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] |
Mathlib/Topology/Order/Basic.lean | nhdsWithin_Ico_eq_nhdsWithin_Ici | [] | [
549,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
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Mathlib/Topology/Connected.lean | IsPreconnected.biUnion_of_reflTransGen | [
{
"state_after": "α : Type u\nβ : Type v\nι✝ : Type ?u.5558\nπ : ι✝ → Type ?u.5563\ninst✝ : TopologicalSpace α\ns✝ t✝ u v : Set α\nι : Type u_1\nt : Set ι\ns : ι → Set α\nH : ∀ (i : ι), i ∈ t → IsPreconnected (s i)\nK : ∀ (i : ι), i ∈ t → ∀ (j : ι), j ∈ t → ReflTransGen (fun i j => Set.Nonempty (s i ∩ s j) ∧ i ... | [
200,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
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Std/Logic.lean | or_rotate | [
{
"state_after": "no goals",
"state_before": "a b c : Prop\n⊢ a ∨ b ∨ c ↔ b ∨ c ∨ a",
"tactic": "simp only [or_left_comm, Or.comm]"
}
] | [
287,
82
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
287,
1
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Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.eq_of_empty | [] | [
128,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
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Mathlib/Data/Fin/Basic.lean | Fin.cast_val_eq_self | [
{
"state_after": "n✝ m n : ℕ\ninst✝ : NeZero n\na : Fin n\n⊢ ↑↑↑a = ↑a",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\na : Fin n\n⊢ ↑↑a = a",
"tactic": "rw [Fin.eq_iff_veq]"
},
{
"state_after": "no goals",
"state_before": "n✝ m n : ℕ\ninst✝ : NeZero n\na : Fin n\n⊢ ↑↑↑a = ↑a",
"tactic":... | [
809,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/Algebra/Order/WithZero.lean | le_mul_inv_iff₀ | [] | [
159,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/CategoryTheory/Adjunction/Limits.lean | CategoryTheory.Adjunction.hasColimitsOfShape_of_equivalence | [] | [
155,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/RingTheory/Coprime/Lemmas.lean | exists_sum_eq_one_iff_pairwise_coprime | [
{
"state_after": "case refine'_1\nR : Type u\nI : Type v\ninst✝¹ : CommSemiring R\nx y z : R\ns : I → R\nt : Finset I\ninst✝ : DecidableEq I\nh : Finset.Nonempty t\n⊢ ∀ (a : I), (∃ μ, ∑ i in {a}, μ i * ∏ j in {a} \\ {i}, s j = 1) ↔ Pairwise (IsCoprime on fun i => s ↑i)\n\ncase refine'_2\nR : Type u\nI : Type v\... | [
168,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
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Mathlib/Data/List/Intervals.lean | List.Ico.filter_lt_of_ge | [
{
"state_after": "case inl\nn m l : ℕ\nhlm : l ≤ m\nhnl : n ≤ l\n⊢ filter (fun x => decide (x < l)) (Ico n m) = Ico n l\n\ncase inr\nn m l : ℕ\nhlm : l ≤ m\nhln : l ≤ n\n⊢ filter (fun x => decide (x < l)) (Ico n m) = Ico n l",
"state_before": "n m l : ℕ\nhlm : l ≤ m\n⊢ filter (fun x => decide (x < l)) (Ico ... | [
176,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.tsupport_eq | [
{
"state_after": "no goals",
"state_before": "E : Type u_1\nX : Type ?u.87643\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup X\ninst✝¹ : NormedSpace ℝ X\ninst✝ : HasContDiffBump E\nc : E\nf : ContDiffBump c\nx : E\nn : ℕ∞\n⊢ tsupport ↑f = closedBall c f.rOut",
"tac... | [
411,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
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Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.mk_neg | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → AddGroup (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni : ι\n⊢ (if H : i ∈ s then (-x) { val := i, property := H } else 0) = -if H : i ∈ s then x { val := i, property := H } else 0"... | [
1049,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1047,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.coe_Iic | [] | [
1180,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1179,
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Mathlib/Topology/MetricSpace/Infsep.lean | Set.Finite.einfsep_pos | [] | [
313,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Std/Data/List/Lemmas.lean | List.map_filterMap_some_eq_filter_map_is_some | [
{
"state_after": "case cons\nα : Type u_1\nβ : Type u_2\nf : α → Option β\nhead✝ : α\ntail✝ : List α\ntail_ih✝ : map some (filterMap f tail✝) = filter (fun b => Option.isSome b) (map f tail✝)\n⊢ map some\n (match f head✝ with\n | none => filterMap f tail✝\n | some b => b :: filterMap f tail✝) =\n... | [
1205,
43
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1203,
1
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Mathlib/Topology/ContinuousOn.lean | dense_pi | [
{
"state_after": "no goals",
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426,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
423,
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Mathlib/LinearAlgebra/DirectSum/Finsupp.lean | finsuppTensorFinsupp_single | [
{
"state_after": "no goals",
"state_before": "R✝ : Type u\nM✝ : Type v\nN✝ : Type w\ninst✝⁹ : Ring R✝\ninst✝⁸ : AddCommGroup M✝\ninst✝⁷ : Module R✝ M✝\ninst✝⁶ : AddCommGroup N✝\ninst✝⁵ : Module R✝ N✝\nR : Type u_1\nM : Type u_2\nN : Type u_3\nι : Type u_4\nκ : Type u_5\ninst✝⁴ : CommRing R\ninst✝³ : AddComm... | [
53,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.power_mul | [
{
"state_after": "α β : Type u\na b c : Cardinal\n⊢ a ^ (c * b) = (a ^ b) ^ c",
"state_before": "α β : Type u\na b c : Cardinal\n⊢ a ^ (b * c) = (a ^ b) ^ c",
"tactic": "rw [mul_comm b c]"
},
{
"state_after": "no goals",
"state_before": "α β : Type u\na b c : Cardinal\n⊢ a ^ (c * b) = (a ^ b... | [
594,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.coproductIso_mk_comp_inv | [] | [
377,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_eq_pi_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ toReal θ = π ↔ θ = ↑π",
"tactic": "rw [← toReal_inj, toReal_pi]"
}
] | [
604,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | IntervalIntegrable.refl | [
{
"state_after": "no goals",
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"tactic": "constructor <;> simp"
}
] | [
147,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/Order.lean | continuous_Prop | [
{
"state_after": "α : Type u_1\ninst✝ : TopologicalSpace α\np : α → Prop\n⊢ (∀ (x : α), p x → ∀ᶠ (x : α) in 𝓝 x, p x) ↔ ∀ (a : α), a ∈ {x | p x} → {x | p x} ∈ 𝓝 a",
"state_before": "α : Type u_1\ninst✝ : TopologicalSpace α\np : α → Prop\n⊢ Continuous p ↔ IsOpen {x | p x}",
"tactic": "simp only [contin... | [
923,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
922,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.mul_succ | [] | [
163,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
162,
1
] |
Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.polar_smul_left_of_tower | [
{
"state_after": "no goals",
"state_before": "S : Type u_3\nR : Type u_1\nR₁ : Type ?u.185856\nM : Type u_2\ninst✝⁷ : Ring R\ninst✝⁶ : CommRing R₁\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nQ : QuadraticForm R M\ninst✝³ : CommSemiring S\ninst✝² : Algebra S R\ninst✝¹ : Module S M\ninst✝ : IsScalarTower S... | [
331,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
1
] |
Mathlib/CategoryTheory/Monoidal/FunctorCategory.lean | CategoryTheory.Monoidal.tensorUnit_obj | [] | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/Algebra/Group/Basic.lean | one_div | [] | [
320,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Equalizers.lean | CategoryTheory.Limits.map_π_preserves_coequalizer_inv_colimMap_desc | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nG : C ⥤ D\nX Y Z : C\nf g : X ⟶ Y\nh✝ : Y ⟶ Z\nw : f ≫ h✝ = g ≫ h✝\ninst✝³ : HasCoequalizer f g\ninst✝² : HasCoequalizer (G.map f) (G.map g)\ninst✝¹ : PreservesColimit (parallelPair f g) G\nX' Y' : D\nf' g' : X' ⟶ Y'\ninst✝ : ... | [
239,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/Topology/ContinuousOn.lean | Filter.Tendsto.if_nhdsWithin | [] | [
358,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Topology/FiberBundle/Constructions.lean | Pullback.continuous_lift | [
{
"state_after": "B : Type u\nF : Type v\nE : B → Type w₁\nB' : Type w₂\nf✝ : B' → B\ninst✝¹ : TopologicalSpace B'\ninst✝ : TopologicalSpace (TotalSpace E)\nf : B' → B\n⊢ induced TotalSpace.proj inst✝¹ ⊓ induced (Pullback.lift f) inst✝ ≤ induced (Pullback.lift f) inst✝",
"state_before": "B : Type u\nF : Typ... | [
327,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
325,
1
] |
Mathlib/Topology/Constructions.lean | nhds_ne_subtype_neBot_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.13040\nδ : Type ?u.13043\nε : Type ?u.13046\nζ : Type ?u.13049\ninst✝ : TopologicalSpace α\nS : Set α\nx : ↑S\n⊢ NeBot (𝓝[{x}ᶜ] x) ↔ NeBot (𝓝[{↑x}ᶜ] ↑x ⊓ 𝓟 S)",
"tactic": "rw [neBot_iff, neBot_iff, not_iff_not, nhds_ne_... | [
246,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Data/List/Indexes.lean | List.foldrIdxSpec_cons | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Algebra/Module/Basic.lean | zsmul_eq_smul_cast | [
{
"state_after": "case h1\nα : Type ?u.146146\nR : Type u_2\nk : Type ?u.146152\nS : Type ?u.146155\nM : Type u_1\nM₂ : Type ?u.146161\nM₃ : Type ?u.146164\nι : Type ?u.146167\ninst✝⁴ : Semiring S\ninst✝³ : Ring R\ninst✝² : AddCommGroup M\ninst✝¹ : Module S M\ninst✝ : Module R M\nn : ℤ\nb : M\n⊢ ↑(↑(AddMonoidHo... | [
435,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/Topology/Algebra/Ring/Basic.lean | RingTopology.coinduced_continuous | [] | [
351,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/Algebra/Group/Basic.lean | continuous_div_left' | [] | [
1115,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1114,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toNonUnitalRingHomm_comp_symm_toNonUnitalRingHom | [
{
"state_after": "case a\nF : Type ?u.86101\nα : Type ?u.86104\nβ : Type ?u.86107\nR : Type u_1\nS : Type u_2\nS' : Type ?u.86116\ninst✝² : NonUnitalNonAssocSemiring R\ninst✝¹ : NonUnitalNonAssocSemiring S\ninst✝ : NonUnitalNonAssocSemiring S'\ne : R ≃+* S\nx✝ : S\n⊢ ↑(NonUnitalRingHom.comp (toNonUnitalRingHom ... | [
655,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
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] |
Mathlib/Data/Nat/Pow.lean | Nat.sq_sub_sq | [
{
"state_after": "a b : ℕ\n⊢ a * a - b * b = (a + b) * (a - b)",
"state_before": "a b : ℕ\n⊢ a ^ 2 - b ^ 2 = (a + b) * (a - b)",
"tactic": "rw [sq, sq]"
},
{
"state_after": "no goals",
"state_before": "a b : ℕ\n⊢ a * a - b * b = (a + b) * (a - b)",
"tactic": "exact Nat.mul_self_sub_mul_s... | [
152,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
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Mathlib/Data/Matrix/Basic.lean | Matrix.map_injective | [] | [
169,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Lie/Basic.lean | LieHom.map_sub | [] | [
317,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
316,
1
] |
Mathlib/Data/List/Range.lean | List.nodup_finRange | [] | [
147,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableEquiv.ext | [] | [
1236,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1236,
8
] |
Mathlib/Data/Int/GCD.lean | Int.gcd_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "i j : ℤ\n⊢ gcd i j = 0 ↔ i = 0 ∧ j = 0",
"tactic": "rw [gcd, Nat.gcd_eq_zero_iff, natAbs_eq_zero, natAbs_eq_zero]"
}
] | [
320,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
319,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.coeAddMonoidHom_of | [] | [
368,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
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Mathlib/Logic/Function/Iterate.lean | Function.Iterate.rec_zero | [] | [
202,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.map_smul | [
{
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230,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | AddSubmonoid.le_pointwise_smul_iff₀ | [] | [
476,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Data/Nat/PrimeFin.lean | Nat.pow_factors_toFinset | [
{
"state_after": "case zero\nn : ℕ\nhk : zero ≠ 0\n⊢ List.toFinset (factors (n ^ zero)) = List.toFinset (factors n)\n\ncase succ\nn n✝ : ℕ\nhk : succ n✝ ≠ 0\n⊢ List.toFinset (factors (n ^ succ n✝)) = List.toFinset (factors n)",
"state_before": "n k : ℕ\nhk : k ≠ 0\n⊢ List.toFinset (factors (n ^ k)) = List.t... | [
48,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
44,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.ofReal_sub | [
{
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"tactic": "simp [ofReal']"
}
] | [
710,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Order/WellFoundedSet.lean | Set.partiallyWellOrderedOn_iff_finite_antichains | [
{
"state_after": "ι : Type ?u.81761\nα : Type u_1\nβ : Type ?u.81767\nr : α → α → Prop\nr' : β → β → Prop\nf : α → β\ns t : Set α\na : α\ninst✝¹ : IsRefl α r\ninst✝ : IsSymm α r\n⊢ (∀ (t : Set α), t ⊆ s → IsAntichain r t → Set.Finite t) → PartiallyWellOrderedOn s r",
"state_before": "ι : Type ?u.81761\nα : ... | [
343,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.le_ofReal_iff_toReal_le | [
{
"state_after": "case intro\nα : Type ?u.811667\nβ : Type ?u.811670\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\nb : ℝ\nhb : 0 ≤ b\na : ℝ≥0\n⊢ ↑a ≤ ENNReal.ofReal b ↔ ENNReal.toReal ↑a ≤ b",
"state_before": "α : Type ?u.811667\nβ : Type ?u.811670\na✝ b✝ c d : ℝ≥0∞\nr p q : ℝ≥0\na : ℝ≥0∞\nb : ℝ\nha : a ≠ ⊤\nhb : 0 ≤ b\n... | [
2152,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2149,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotEquivQuotOfLEₐ_symm_toRingEquiv | [] | [
840,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
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Mathlib/Order/Filter/Basic.lean | Filter.mem_biInf_of_directed | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.96376\nι : Sort x\nf✝ g : Filter α\ns✝ t✝ : Set α\nf : β → Filter α\ns : Set β\nh : DirectedOn (f ⁻¹'o fun x x_1 => x ≥ x_1) s\nne : Set.Nonempty s\nt : Set α\nthis : Nonempty ↑s\n⊢ (t ∈ ⨅ (i : β) (_ : i ∈ s), f i) ↔ ∃ i, i ∈ s ∧ t ∈ f i",
"s... | [
828,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
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Mathlib/Data/Finset/Pointwise.lean | Finset.pow_subset_pow_of_one_mem | [
{
"state_after": "case base\nF : Type ?u.352257\nα : Type u_1\nβ : Type ?u.352263\nγ : Type ?u.352266\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq β\ninst✝ : Monoid α\ns t : Finset α\na : α\nm n : ℕ\nhs : 1 ∈ s\n⊢ s ^ m ⊆ s ^ m\n\ncase succ\nF : Type ?u.352257\nα : Type u_1\nβ : Type ?u.352263\nγ : Type ?u.352... | [
903,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
898,
1
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Mathlib/Logic/IsEmpty.lean | isEmpty_plift | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort ?u.3700\nβ : Sort ?u.3703\nγ : Sort ?u.3706\nα : Sort u_1\n⊢ IsEmpty (PLift α) ↔ IsEmpty α",
"tactic": "simp only [← not_nonempty_iff, nonempty_plift]"
}
] | [
196,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Tactic/PushNeg.lean | Mathlib.Tactic.PushNeg.not_ne_eq | [] | [
26,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
26,
1
] |
Mathlib/Data/Setoid/Partition.lean | Setoid.rel_iff_exists_classes | [
{
"state_after": "α : Type u_1\nr : Setoid α\nx y : α\nx✝ : ∃ c, c ∈ classes r ∧ x ∈ c ∧ y ∈ c\nz : α\nhx : x ∈ {x | Rel r x z}\nhy : y ∈ {x | Rel r x z}\n⊢ Rel r x y",
"state_before": "α : Type u_1\nr : Setoid α\nx y : α\nx✝ : ∃ c, c ∈ classes r ∧ x ∈ c ∧ y ∈ c\nc : Set α\nz : α\nhz : c = {x | Rel r x z}\n... | [
107,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.add | [] | [
1072,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.image_closure | [
{
"state_after": "case intro.intro\nG : Type u_2\nH : Type u_1\nA : Type ?u.130329\na a₁ a₂ b c : G\ninst✝¹ : Group G\ns✝ : Set G\ninst✝ : Group H\nf : G → H\nhf : IsGroupHom f\ns : Set G\nx : G\nhx : x ∈ closure s\n⊢ f x ∈ closure (f '' s)",
"state_before": "G : Type u_2\nH : Type u_1\nA : Type ?u.130329\n... | [
610,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.filter_mono | [] | [
261,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.fst_sub | [] | [
279,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
278,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | cauchySeq_of_le_geometric | [] | [
384,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Logic/Nontrivial.lean | exists_pair_lt | [
{
"state_after": "case intro.intro\nα✝ : Type ?u.565\nβ : Type ?u.568\nα : Type u_1\ninst✝¹ : Nontrivial α\ninst✝ : LinearOrder α\nx y : α\nhxy : x ≠ y\n⊢ ∃ x y, x < y",
"state_before": "α✝ : Type ?u.565\nβ : Type ?u.568\nα : Type u_1\ninst✝¹ : Nontrivial α\ninst✝ : LinearOrder α\n⊢ ∃ x y, x < y",
"tact... | [
72,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.eval₂Hom_bind₂ | [] | [
328,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/LinearAlgebra/Contraction.lean | transpose_dualTensorHom | [
{
"state_after": "case h.h\nι : Type w\nR : Type u\nM : Type v₁\nN : Type v₂\nP : Type v₃\nQ : Type v₄\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : AddCommMonoid M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : AddCommMonoid P\ninst✝⁶ : AddCommMonoid Q\ninst✝⁵ : Module R M\ninst✝⁴ : Module R N\ninst✝³ : Module R P\ninst✝² : Module... | [
96,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.bounded_singleton | [
{
"state_after": "α : Type u_1\nβ : Type ?u.105149\nγ : Type ?u.105152\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝ : IsWellOrder α r\nhr : IsLimit (type r)\nx : α\n⊢ ∀ (b : α), b ∈ {x} → r b (enum r (succ (typein r x)) (_ : succ (typein r x) < type r))",
"state_before": "... | [
375,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.coe_prodComm | [] | [
124,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.inits_core_eq | [
{
"state_after": "α : Type u\nβ : Type v\nδ : Type w\nl : List α\ns : Stream' α\n⊢ corec\n (fun x =>\n match x with\n | (a, snd) => a)\n (fun p =>\n match p with\n | (l', s') => (l' ++ [head s'], tail s'))\n (l, s) =\n l ::\n corec\n (fun x =>\n ... | [
688,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/CategoryTheory/CommSq.lean | CategoryTheory.Functor.map_commSq | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝¹ : Category C\nD : Type u_3\ninst✝ : Category D\nF : C ⥤ D\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ns : CommSq f g h i\n⊢ F.map f ≫ F.map h = F.map g ≫ F.map i",
"tactic": "simpa using congr_arg (fun k : W ⟶ Z => F.map k)... | [
86,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.mono | [] | [
493,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Algebra/Squarefree.lean | not_squarefree_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : MonoidWithZero R\ninst✝ : Nontrivial R\n⊢ ∃ x, ¬(x * x ∣ 0 → IsUnit x)",
"state_before": "R : Type u_1\ninst✝¹ : MonoidWithZero R\ninst✝ : Nontrivial R\n⊢ ¬Squarefree 0",
"tactic": "erw [not_forall]"
},
{
"state_after": "no goals",
"state_before": "R ... | [
56,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_int_cast | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Ring R\nn : ℤ\n⊢ ↑derivative (↑C ↑n) = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\nA : Type z\na b : R\nn✝ : ℕ\ninst✝ : Ring R\nn : ℤ\n⊢ ↑derivative ↑n = 0",
"tactic": "rw [← C... | [
620,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
618,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_add_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIocMod hp a (p + b) = toIocMod hp a b",
"tactic": "rw [add_comm, toIocMod_add_right]"
}
] | [
504,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
] |
Mathlib/Order/Monotone/Basic.lean | strictMonoOn_toDual_comp_iff | [] | [
212,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | bit0_strictMono | [] | [
1691,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1689,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_image | [] | [
280,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_sq | [] | [
1302,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1301,
1
] |
Mathlib/Order/OmegaCompletePartialOrder.lean | OmegaCompletePartialOrder.ContinuousHom.id_comp | [
{
"state_after": "case h\nα : Type u\nα' : Type ?u.65785\nβ : Type v\nβ' : Type ?u.65790\nγ : Type u_1\nφ : Type ?u.65796\ninst✝⁵ : OmegaCompletePartialOrder α\ninst✝⁴ : OmegaCompletePartialOrder β\ninst✝³ : OmegaCompletePartialOrder γ\ninst✝² : OmegaCompletePartialOrder φ\ninst✝¹ : OmegaCompletePartialOrder α'... | [
725,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
725,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.optionEquivSumPUnit_symm_inr | [] | [
445,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
444,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | gcd_pow_right_dvd_pow_gcd | [
{
"state_after": "case pos\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b : α\nk : ℕ\nhg : gcd a b = 0\n⊢ gcd a (b ^ k) ∣ gcd a b ^ k\n\ncase neg\nα : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b : α\nk : ℕ\nhg : ¬gcd a b = 0\n⊢ gcd a (b ^ k) ∣ gcd a b ^ ... | [
578,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
564,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.const_add | [] | [
259,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
] |
Mathlib/Topology/Basic.lean | frontier_subset_closure | [] | [
715,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
714,
1
] |
Mathlib/Analysis/InnerProductSpace/Orientation.lean | OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation | [
{
"state_after": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nne : Nonempty ι\ne f : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\nh : ↑(Basis.det (OrthonormalBasis.toBasis e)) ↑f ≠ -1\n⊢ Basis.orientation (OrthonormalBas... | [
72,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_of_le_of_lt' | [] | [
238,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Set/Intervals/Monotone.lean | Monotone.Ioo | [] | [
166,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
11
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.not_one_le_div_iff | [] | [
866,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
865,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.prod | [] | [
904,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
901,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.centralizer_univ | [] | [
1421,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1420,
1
] |
Mathlib/Topology/ContinuousOn.lean | continuousOn_piecewise_ite' | [
{
"state_after": "case ht\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.399126\nδ : Type ?u.399129\ninst✝⁴ : TopologicalSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : TopologicalSpace γ\ninst✝¹ : TopologicalSpace δ\ns s' t : Set α\nf f' : α → β\ninst✝ : (x : α) → Decidable (x ∈ t)\nh : ContinuousOn f (s ∩ closure t)... | [
1247,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1240,
1
] |
Mathlib/LinearAlgebra/Matrix/BilinearForm.lean | BilinForm.nondegenerate_of_det_ne_zero | [] | [
615,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Data/Seq/Computation.lean | Computation.mem_bind | [] | [
812,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aevalTower_ofId | [
{
"state_after": "case h.hf\nR : Type u\nS₁ : Type v\nS₂ : Type w\nS₃ : Type x\nσ : Type u_1\na a' a₁ a₂ : R\ne : ℕ\nn m : σ\ns : σ →₀ ℕ\ninst✝⁷ : CommSemiring R\ninst✝⁶ : CommSemiring S₁\np q : MvPolynomial σ R\nS : Type u_2\nA : Type u_3\nB : Type ?u.5318782\ninst✝⁵ : CommSemiring S\ninst✝⁴ : CommSemiring A\n... | [
1643,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1640,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.coe_toLinearIsometry | [] | [
624,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
623,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_eq_zero | [] | [
127,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/Analysis/InnerProductSpace/Dual.lean | InnerProductSpace.toDual_symm_apply | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : CompleteSpace E\nx : E\ny : NormedSpace.Dual 𝕜 E\n⊢ ↑(↑(toDual 𝕜 E) (↑(LinearIsometryEquiv.symm (toDual 𝕜 E)) y)) x = ↑y x",
"state_before": "𝕜 : Type u_1\nE : Type ... | [
163,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Std/Data/List/Lemmas.lean | List.get?_append_right | [
{
"state_after": "α : Type u_1\na : α\nl x✝ : List α\nn : Nat\nh₁ : length (a :: l) ≤ n + 1\n⊢ get? (a :: (l ++ x✝)) (n + 1) = get? x✝ (n + 1 - length (a :: l))",
"state_before": "α : Type u_1\na : α\nl x✝ : List α\nn : Nat\nh₁ : length (a :: l) ≤ n + 1\n⊢ get? (a :: l ++ x✝) (n + 1) = get? x✝ (n + 1 - leng... | [
598,
89
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
595,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | tendsto_nat_ceil_div_atTop | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.528297\nβ : Type ?u.528300\nι : Type ?u.528303\nR : Type u_1\ninst✝³ : TopologicalSpace R\ninst✝² : LinearOrderedField R\ninst✝¹ : OrderTopology R\ninst✝ : FloorRing R\n⊢ Tendsto (fun x => ↑⌈x⌉₊ / x) atTop (𝓝 1)",
"tactic": "simpa using tendsto_... | [
614,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforward_eq' | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝ : Category C\nX Y : TopCat\nf g : X ⟶ Y\nh : f = g\nℱ : Presheaf C X\n⊢ f _* ℱ = g _* ℱ",
"tactic": "rw [h]"
}
] | [
166,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.hasStrictFDerivAt | [
{
"state_after": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type u_4\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.16148\ninst✝¹... | [
84,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
1
] |
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