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/Data/Seq/WSeq.lean | Stream'.WSeq.seq_destruct_nil | [] | [
644,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Data/Real/Cardinality.lean | Cardinal.cantorFunctionAux_zero | [
{
"state_after": "no goals",
"state_before": "c : ℝ\nf✝ g : ℕ → Bool\nn : ℕ\nf : ℕ → Bool\n⊢ cantorFunctionAux c f 0 = bif f 0 then 1 else 0",
"tactic": "cases h : f 0 <;> simp [h]"
}
] | [
86,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.comp_symmCompOfNondegenerate_apply | [
{
"state_after": "no goals",
"state_before": "R : Type ?u.1833309\nM : Type ?u.1833312\ninst✝¹⁷ : Semiring R\ninst✝¹⁶ : AddCommMonoid M\ninst✝¹⁵ : Module R M\nR₁ : Type ?u.1833348\nM₁ : Type ?u.1833351\ninst✝¹⁴ : Ring R₁\ninst✝¹³ : AddCommGroup M₁\ninst✝¹² : Module R₁ M₁\nR₂ : Type ?u.1833960\nM₂ : Type ?u.... | [
1555,
79
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1552,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.comap_top | [
{
"state_after": "k : Type u_1\nV₁ : Type u_2\nP₁ : Type u_3\nV₂ : Type u_4\nP₂ : Type u_5\nV₃ : Type ?u.601866\nP₃ : Type ?u.601869\ninst✝⁹ : Ring k\ninst✝⁸ : AddCommGroup V₁\ninst✝⁷ : Module k V₁\ninst✝⁶ : AffineSpace V₁ P₁\ninst✝⁵ : AddCommGroup V₂\ninst✝⁴ : Module k V₂\ninst✝³ : AffineSpace V₂ P₂\ninst✝² : ... | [
1634,
31
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1632,
1
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Mathlib/RingTheory/Filtration.lean | Ideal.Filtration.Stable.inter_right | [] | [
420,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
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Mathlib/Data/Rel.lean | Rel.image_core_gc | [] | [
257,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iic_union_Ico_eq_Iio | [] | [
1485,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1483,
1
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Mathlib/Algebra/Group/WithOne/Basic.lean | WithOne.lift_coe | [] | [
77,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
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Mathlib/RingTheory/TensorProduct.lean | Algebra.TensorProduct.productMap_apply_tmul | [
{
"state_after": "R : Type u_2\nA : Type u_3\nB : Type u_4\nS : Type u_1\ninst✝⁶ : CommSemiring R\ninst✝⁵ : Semiring A\ninst✝⁴ : Semiring B\ninst✝³ : CommSemiring S\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\ninst✝ : Algebra R S\nf : A →ₐ[R] S\ng : B →ₐ[R] S\na : A\nb : B\n⊢ ↑(AlgHom.comp\n (algHomOfL... | [
966,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
964,
1
] |
Mathlib/NumberTheory/ADEInequality.lean | ADEInequality.admissible_E'3 | [] | [
139,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.volume_pi_pi | [] | [
682,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
680,
1
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Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingIso.coe_toRingEquiv | [] | [
420,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/RingTheory/Int/Basic.lean | multiplicity.finite_int_iff | [
{
"state_after": "no goals",
"state_before": "a b : ℤ\n⊢ Finite a b ↔ _root_.Int.natAbs a ≠ 1 ∧ b ≠ 0",
"tactic": "rw [finite_int_iff_natAbs_finite, finite_nat_iff, pos_iff_ne_zero, Int.natAbs_ne_zero]"
}
] | [
341,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.inl_nat_cast | [] | [
533,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
532,
1
] |
Mathlib/GroupTheory/Subsemigroup/Basic.lean | Subsemigroup.ext | [] | [
139,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
] |
Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.NullMeasurable.congr | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.25082\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.25091\ninst✝² : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nf : α → β\nμ : Measure α\ng : α → β\nhf : NullMeasurable f\nhg : f =ᵐ[μ] g\ns : Set β\nhs : MeasurableSet s\nx : ... | [
438,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
435,
1
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Mathlib/Data/Complex/Basic.lean | Complex.I_im | [] | [
308,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.rpow_logb | [
{
"state_after": "b x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\nhx : 0 < x\n⊢ abs x = x",
"state_before": "b x y : ℝ\nb_pos : 0 < b\nb_ne_one : b ≠ 1\nhx : 0 < x\n⊢ b ^ logb b x = x",
"tactic": "rw [rpow_logb_eq_abs b_pos b_ne_one hx.ne']"
},
{
"state_after": "no goals",
"state_before": "b x y... | [
107,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean | SimpleGraph.IsSRGWith.compl | [] | [
178,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Algebra/CovariantAndContravariant.lean | rel_of_act_rel_act | [] | [
225,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
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Mathlib/Data/Matrix/Basis.lean | Matrix.StdBasisMatrix.mul_left_apply_same | [
{
"state_after": "no goals",
"state_before": "l : Type ?u.31097\nm : Type ?u.31100\nn : Type u_1\nR : Type ?u.31106\nα : Type u_2\ninst✝⁴ : DecidableEq l\ninst✝³ : DecidableEq m\ninst✝² : DecidableEq n\ninst✝¹ : Semiring α\ni j : n\nc : α\ni' j' : n\ninst✝ : Fintype n\nb : n\nM : Matrix n n α\n⊢ (stdBasisMa... | [
178,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
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] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.conj_eq_iff_re | [] | [
429,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
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Mathlib/Data/UnionFind.lean | UnionFind.rank_lt | [
{
"state_after": "α : Type u_1\nself : UnionFind α\ni : ℕ\nh : i < Array.size self.arr\nm : UFModel (Array.size self.arr)\nhm : UFModel.Models self.arr m\n⊢ self.arr[i].parent ≠ i → rank self i < rank self self.arr[i].parent",
"state_before": "α : Type u_1\nself : UnionFind α\ni : ℕ\nh : i < Array.size self... | [
204,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
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Mathlib/Logic/Function/Conjugate.lean | Function.Commute.symm | [] | [
111,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Topology/Sequences.lean | subset_seqClosure | [] | [
85,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/List/Basic.lean | List.reduceOption_cons_of_some | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.348712\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\nx : α\nl : List (Option α)\n⊢ reduceOption (some x :: l) = x :: reduceOption l",
"tactic": "simp only [reduceOption, filterMap, id.def, eq_self_iff_true, and_self_iff]"
}
] | [
3420,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3418,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_of_le_of_lt_one_of_pos | [] | [
714,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
712,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_lt | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.137301\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ a b c : α\n⊢ filter (fun x => x < c) (Ico a b) = Ico a (min b c)",
"tactic": "cases le_total b c with\n| inl h => rw [Ico_filter_lt_of_right_le h, min_eq_left h]\n|... | [
791,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
788,
1
] |
Std/Data/RBMap/Lemmas.lean | Std.RBNode.WF.depth_bound | [] | [
92,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
91,
1
] |
Mathlib/Order/WithBot.lean | WithTop.some_lt_some | [] | [
1061,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1060,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | Submonoid.map_strictMono_of_injective | [] | [
432,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/RingTheory/MvPolynomial/Tower.lean | MvPolynomial.aeval_algebraMap_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "R : Type u_4\nA : Type u_1\nB : Type u_2\nσ : Type u_3\ninst✝⁸ : CommSemiring R\ninst✝⁷ : CommSemiring A\ninst✝⁶ : CommSemiring B\ninst✝⁵ : Algebra R A\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra R B\ninst✝² : IsScalarTower R A B\ninst✝¹ : NoZeroSMulDivisors A B\nin... | [
67,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_one_lt_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na b c d : α\ninst✝³ : MulOneClass α\ninst✝² : Zero α\ninst✝¹ : Preorder α\ninst✝ : PosMulStrictMono α\nha : 0 < a\nh : 1 < b\n⊢ a < a * b",
"tactic": "simpa only [mul_one] using mul_lt_mul_of_pos_left h ha"
}
] | [
698,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
697,
1
] |
Mathlib/Algebra/Module/Submodule/Lattice.lean | AddSubgroup.toIntSubmodule_toAddSubgroup | [] | [
412,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
410,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_max | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1029220\nγ : Type ?u.1029223\nδ : Type ?u.1029226\nm : MeasurableSpace α\nμ ν : Measure α\nf g : α → ℝ≥0∞\nhf : Measurable f\nhg : Measurable g\nhm : MeasurableSet {x | f x ≤ g x}\n⊢ (∫⁻ (x : α), max (f x) (g x) ∂μ) = (∫⁻ (x : α) in {x | f x ≤ g x}, g x ∂μ) + ∫⁻ (x : ... | [
1250,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1242,
1
] |
Mathlib/Data/Int/Cast/Lemmas.lean | Int.cast_ite | [] | [
70,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
68,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_le_iff | [] | [
904,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_smul | [] | [
241,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
1
] |
Mathlib/Algebra/Order/Rearrangement.lean | MonovaryOn.sum_mul_comp_perm_le_sum_mul | [] | [
355,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/CategoryTheory/Sites/Sheafification.lean | CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift | [
{
"state_after": "case a\nC : Type u\ninst✝³ : Category C\nJ : GrothendieckTopology C\nD : Type w\ninst✝² : Category D\ninst✝¹ : ∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : Cover J X), HasMultiequalizer (Cover.index S P)\ninst✝ : ∀ (X : C), HasColimitsOfShape (Cover J X)ᵒᵖ D\nP Q R : Cᵒᵖ ⥤ D\nη : P ⟶ Q\nγ : Q ⟶ R\nhR : Preshe... | [
597,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Topology/Constructions.lean | Continuous.prod_map | [] | [
435,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Matrix/Block.lean | Matrix.toSquareBlockProp_def | [] | [
210,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_subset_iff | [] | [
477,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Order/Hom/Lattice.lean | InfHom.id_comp | [] | [
610,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
610,
9
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.mk_coe | [] | [
546,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Data/List/Perm.lean | List.replicate_perm | [] | [
205,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
203,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | pow_lt_one_iff | [] | [
256,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_zero_of_forall_eq_zero | [] | [
285,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
283,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.rel_nthLe_of_le | [] | [
129,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotLeftToQuotSupₐ_toRingHom | [] | [
685,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
683,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.map_floor | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedRing α\ninst✝³ : LinearOrderedRing β\ninst✝² : FloorRing α\ninst✝¹ : FloorRing β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\nn : ℤ\n⊢ ↑n ≤ ↑f a ↔ ↑n ≤ a",
"tact... | [
1535,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1534,
1
] |
Std/Data/RBMap/Alter.lean | Std.RBNode.Ordered.zoom | [] | [
292,
50
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
289,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValRat.div | [
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhq : q ≠ 0\nhr : r ≠ 0\n⊢ padicValRat p (q / r) = padicValRat p q - padicValRat p r",
"tactic": "rw [div_eq_mul_inv, padicValRat.mul hq (inv_ne_zero hr), padicValRat.inv r, sub_eq_add_neg]"
}
] | [
319,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
11
] |
Mathlib/Logic/Function/Basic.lean | Function.Injective2.left | [] | [
930,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
11
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.tendsto_self_div_two_mul_self_add_one | [
{
"state_after": "n : ℕ\nhn : n ≥ 1\n⊢ (2 + 1 / ↑n)⁻¹ = (fun n => ↑n / (2 * ↑n + 1)) n",
"state_before": "⊢ Tendsto (fun n => ↑n / (2 * ↑n + 1)) atTop (𝓝 (2 + 0)⁻¹)",
"tactic": "refine' (((tendsto_const_div_atTop_nhds_0_nat 1).const_add (2 : ℝ)).inv₀\n ((add_zero (2 : ℝ)).symm ▸ two_ne_zero)).congr' (... | [
229,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.eq_aleph'_of_eq_card_ord | [
{
"state_after": "no goals",
"state_before": "o : Ordinal\nho : ord (card o) = o\n⊢ ord (aleph' (↑alephIdx.relIso (card o))) = o",
"tactic": "simpa using ho"
}
] | [
365,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
364,
1
] |
Mathlib/Analysis/InnerProductSpace/Projection.lean | exists_norm_eq_iInf_of_complete_convex | [
{
"state_after": "𝕜 : Type ?u.9703\nE : Type ?u.9706\nF : Type u_1\ninst✝⁴ : IsROrC 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace ℝ F\nK : Set F\nne : Set.Nonempty K\nh₁ : IsComplete K\nh₂ : Convex ℝ K\nu : F\nδ : ℝ := ⨅ (w : ↑K), ‖... | [
198,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | SubgroupClass.coe_zpow | [] | [
306,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.add_def | [] | [
277,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Std/Data/String/Lemmas.lean | String.foldl_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nf : α → Char → α\ns : String\na : α\n⊢ foldl f a s = List.foldl f a s.data",
"tactic": "simpa using foldlAux_of_valid f [] s.1 [] a"
}
] | [
690,
46
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
689,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.semiconj_of_isUnit_of_translationNumber_eq | [
{
"state_after": "case intro.intro\nf g : CircleDeg1Lift\nf₁ f₂ : CircleDeg1Liftˣ\nh : τ ↑f₁ = τ ↑f₂\n⊢ ∃ F, Semiconj ↑F ↑↑f₁ ↑↑f₂",
"state_before": "f g f₁ f₂ : CircleDeg1Lift\nh₁ : IsUnit f₁\nh₂ : IsUnit f₂\nh : τ f₁ = τ f₂\n⊢ ∃ F, Semiconj ↑F ↑f₁ ↑f₂",
"tactic": "rcases h₁, h₂ with ⟨⟨f₁, rfl⟩, ⟨f₂, r... | [
1022,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1019,
1
] |
Mathlib/Order/Disjoint.lean | Prod.codisjoint_iff | [] | [
597,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
11
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.lintegral_piecewise | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.1467338\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ η : { x // x ∈ kernel α β }\ns : Set α\nhs : MeasurableSet s\ninst✝ : DecidablePred fun x => x ∈ s\na : α\ng : β → ℝ≥0∞\n⊢ (∫⁻ (b : β), g b ∂if a ∈ s then ↑κ a else ↑η a) = if a ∈ s then ∫⁻ (b : ... | [
650,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
648,
1
] |
Mathlib/Data/Set/Image.lean | Set.exists_subset_range_and_iff | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.75177\nι : Sort ?u.75180\nι' : Sort ?u.75183\nf✝ : ι → α\ns t : Set α\nf : α → β\np : Set β → Prop\n⊢ (∃ s, s ⊆ range f ∧ p s) ↔ ∃ a, a ∈ 𝒫 range f ∧ p a",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.75177\nι : Sort ?u.75180\nι' : Sort ... | [
809,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
807,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_of_measurable_union_cover | [
{
"state_after": "case h.e'_3\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.70127\nδ : Type ?u.70130\nδ' : Type ?u.70133\nι : Sort uι\ns✝ t✝ u✝ : Set α\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nf : α → β\ns t : Set α\nhs : MeasurableSet s\nht : MeasurableSet t\nh : univ ⊆ s ∪ t\nhc : Measurable fun a => f ↑a\n... | [
601,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.isCycleOn_one | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.1635260\nα : Type u_1\nβ : Type ?u.1635266\nf g : Perm α\ns t : Set α\na b x y : α\n⊢ IsCycleOn 1 s ↔ Set.Subsingleton s",
"tactic": "simp [IsCycleOn, Set.bijOn_id, Set.Subsingleton]"
}
] | [
764,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/Topology/UniformSpace/Compact.lean | compactSpace_uniformity | [] | [
68,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_induction | [
{
"state_after": "case empty\nF : Type ?u.75184\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.75193\nι : Type ?u.75196\nκ : Type ?u.75199\ninst✝¹ : SemilatticeSup α\ninst✝ : OrderBot α\ns s₁ s₂ : Finset β\nf g : β → α\na : α\np : α → Prop\nhb : p ⊥\nhp : ∀ (a₁ : α), p a₁ → ∀ (a₂ : α), p a₂ → p (a₁ ⊔ a₂)\nhs✝ : ∀ (b ... | [
245,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/NumberTheory/Padics/Hensel.lean | bound | [
{
"state_after": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nF : Polynomial ℤ_[p]\na : ℤ_[p]\nhnorm : ‖Polynomial.eval a F‖ < ‖Polynomial.eval a (↑Polynomial.derivative F)‖ ^ 2\nhnsol : Polynomial.eval a F ≠ 0\nthis : Tendsto (fun n => ‖Polynomial.eval a (↑Polynomial.derivative F)‖ * T_gen p F a ^ 2 ^ n) atTop (𝓝 0)\n... | [
363,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
356,
9
] |
Mathlib/Algebra/Group/Units.lean | Units.copy_eq | [] | [
175,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.top_adj | [] | [
360,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
359,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | MetricSpace.ext | [
{
"state_after": "case mk\nα✝ : Type u\nβ : Type v\nX : Type ?u.547543\nι : Type ?u.547546\ninst✝ : PseudoMetricSpace α✝\nα : Type u_1\nm' : MetricSpace α\ntoPseudoMetricSpace✝ : PseudoMetricSpace α\neq_of_dist_eq_zero✝ : ∀ {x y : α}, dist x y = 0 → x = y\nh : PseudoMetricSpace.toDist = PseudoMetricSpace.toDist... | [
2829,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2827,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.tendsto_diag | [] | [
213,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Std/Data/List/Lemmas.lean | List.subset_append_right | [] | [
251,
100
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
251,
9
] |
Mathlib/CategoryTheory/CofilteredSystem.lean | CategoryTheory.Functor.toEventualRanges_nonempty | [
{
"state_after": "J : Type u\ninst✝² : Category J\nF : J ⥤ Type v\ni✝ j✝ k : J\ns : Set (F.obj i✝)\ninst✝¹ : IsCofilteredOrEmpty J\nh✝ : IsMittagLeffler F\ninst✝ : ∀ (j : J), _root_.Nonempty (F.obj j)\nj i : J\nf : i ⟶ j\nh : eventualRange F j = range (F.map f)\n⊢ _root_.Nonempty ((toEventualRanges F).obj j)",
... | [
316,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.smul_integral_comp_mul_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.14827562\n𝕜 : Type ?u.14827565\nE : Type u_1\nF : Type ?u.14827571\nA : Type ?u.14827574\ninst✝² : NormedAddCommGroup E\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\na b c✝ d : ℝ\nf : ℝ → E\nc : ℝ\n⊢ (c • ∫ (x : ℝ) in a..b, f (x * c)) = ∫ (x :... | [
711,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
709,
1
] |
Mathlib/Data/List/Sigma.lean | List.exists_of_mem_keys | [] | [
66,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_neg_Iio | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : OrderedAddCommGroup α\na b c : α\n⊢ Neg.neg '' Iio a = Ioi (-a)",
"tactic": "simp"
}
] | [
300,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_of_singleton_coe | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.166144\nγ : Type ?u.166147\nι : Sort ?u.166150\nι' : Sort ?u.166153\nι₂ : Sort ?u.166156\nκ : ι → Sort ?u.166161\nκ₁ : ι → Sort ?u.166166\nκ₂ : ι → Sort ?u.166171\nκ' : ι' → Sort ?u.166176\ns : Set α\n⊢ (⋃ (i : ↑s), {↑i}) = s",
"tac... | [
1310,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1310,
1
] |
Mathlib/Data/Set/Prod.lean | Set.empty_prod | [
{
"state_after": "case h\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.6918\nδ : Type ?u.6921\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\nx✝ : α × β\n⊢ x✝ ∈ ∅ ×ˢ t ↔ x✝ ∈ ∅",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.6918\nδ : Type ?u.6921\ns s₁ s₂ : Set α\nt t₁ t₂ : Set β\na : α\nb : β\n⊢ ∅ ... | [
119,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
117,
1
] |
Mathlib/Init/Data/Nat/Bitwise.lean | Nat.shiftl_zero | [] | [
200,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | strictMono_iff_map_neg | [] | [
273,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/Module/Basic.lean | self_eq_neg | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.296154\nR : Type ?u.296157\nk : Type ?u.296160\nS : Type ?u.296163\nM : Type u_1\nM₂ : Type ?u.296169\nM₃ : Type ?u.296172\nι : Type ?u.296175\ninst✝⁴ : Semiring R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : NoZeroSMulDivisors R M\ninst✝ ... | [
694,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
693,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.map_sub | [] | [
573,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
572,
11
] |
Mathlib/Data/Set/Basic.lean | Set.nonempty_compl | [] | [
1692,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1691,
1
] |
Mathlib/GroupTheory/Commensurable.lean | Commensurable.refl | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ Commensurable H H",
"tactic": "simp [Commensurable]"
}
] | [
47,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
11
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.mul_integral_comp_mul_add | [] | [
267,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Algebra/Field/Basic.lean | neg_div_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.38671\nβ : Type ?u.38674\nK : Type u_1\ninst✝ : DivisionRing K\na✝ b c d a : K\nh : a ≠ 0\n⊢ -a / a = -1",
"tactic": "rw [neg_div, div_self h]"
}
] | [
149,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.isUnit_iff_norm_isUnit | [
{
"state_after": "no goals",
"state_before": "d✝ d : ℤ\nz : ℤ√d\n⊢ IsUnit z ↔ IsUnit (norm z)",
"tactic": "rw [Int.isUnit_iff_natAbs_eq, norm_eq_one_iff]"
}
] | [
604,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineEquiv.lean | AffineEquiv.toEquiv_refl | [] | [
313,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/CategoryTheory/Linear/Yoneda.lean | CategoryTheory.whiskering_linearYoneda | [] | [
75,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/MeasureTheory/Measure/Complex.lean | MeasureTheory.ComplexMeasure.absolutelyContinuous_eNNReal_iff | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type ?u.103329\nm : MeasurableSpace α\nc : ComplexMeasure α\nμ : VectorMeasure α ℝ≥0∞\nh : c ≪ᵥ μ\n⊢ ↑re c ≪ᵥ μ ∧ ↑im c ≪ᵥ μ\n\ncase mpr\nα : Type u_1\nβ : Type ?u.103329\nm : MeasurableSpace α\nc : ComplexMeasure α\nμ : VectorMeasure α ℝ≥0∞\nh : ↑re c ≪ᵥ μ ∧ ↑im c ≪... | [
125,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Algebra/BigOperators/Ring.lean | Finset.prod_add | [
{
"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✝ : CommSemiring β\nf g : α → β\ns : Finset α\n⊢ ∏ a in s, (f a + g a) = ∏ a in s, ∑ p in {True, False}, if p then f a else g a",
"tactic": "simp"
},
{
"state_a... | [
158,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.toOpposite_symm_apply | [] | [
410,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.comap_map_le | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\nL' : Type w₂\nM : Type w\nM' : Type w₁\ninst✝¹² : CommRing R\ninst✝¹¹ : LieRing L\ninst✝¹⁰ : LieAlgebra R L\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 :... | [
856,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Order/BooleanAlgebra.lean | sdiff_eq_symm | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type ?u.30443\nw x y z : α\ninst✝ : GeneralizedBooleanAlgebra α\nhy : y ≤ x\nh : x \\ y = z\n⊢ x \\ z = y",
"tactic": "rw [← h, sdiff_sdiff_eq_self hy]"
}
] | [
389,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.basicOpen_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf g : R\n⊢ ↑(basicOpen (f * g)) = ↑(basicOpen f ⊓ basicOpen g)",
"tactic": "simp [zeroLocus_singleton_mul]"
}
] | [
803,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
802,
1
] |
Mathlib/Topology/Separation.lean | RegularSpace.inf | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α\na : α\ns : Set α\nX : Type u_1\nt₁ t₂ : TopologicalSpace X\nh₁ : RegularSpace X\nh₂ : RegularSpace X\n⊢ RegularSpace X",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : TopologicalSpace α\ninst✝ : RegularSpace α... | [
1628,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1625,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.union_iUnion | [] | [
540,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
539,
1
] |
Mathlib/Order/Zorn.lean | IsChain.exists_maxChain | [
{
"state_after": "case refine_2\nα : Type u_1\nβ : Type ?u.18779\nr : α → α → Prop\nc : Set α\nhc : IsChain r c\nH : ∃ m, m ∈ {s | c ⊆ s ∧ IsChain r s} ∧ c ⊆ m ∧ ∀ (a : Set α), a ∈ {s | c ⊆ s ∧ IsChain r s} → m ⊆ a → a = m\n⊢ ∃ M, IsMaxChain r M ∧ c ⊆ M\n\ncase refine_1\nα : Type u_1\nβ : Type ?u.18779\nr : α →... | [
232,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
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