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/Analysis/SpecialFunctions/Stirling.lean | Stirling.stirlingSeq'_antitone | [] | [
201,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
200,
1
] |
Mathlib/MeasureTheory/PiSystem.lean | IsPiSystem.insert_univ | [
{
"state_after": "α : Type u_1\nS : Set (Set α)\nh_pi : IsPiSystem S\ns : Set α\nhs : s ∈ insert univ S\nt : Set α\nht : t ∈ insert univ S\nhst : Set.Nonempty (s ∩ t)\n⊢ s ∩ t ∈ insert univ S",
"state_before": "α : Type u_1\nS : Set (Set α)\nh_pi : IsPiSystem S\n⊢ IsPiSystem (insert univ S)",
"tactic": ... | [
104,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/LinearAlgebra/BilinearMap.lean | LinearMap.lcomp_apply | [] | [
282,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.closed_form | [
{
"state_after": "case zero\nq : ℕ+\n⊢ ↑(s zero) = ω ^ 2 ^ zero + ωb ^ 2 ^ zero\n\ncase succ\nq : ℕ+\ni : ℕ\nih : ↑(s i) = ω ^ 2 ^ i + ωb ^ 2 ^ i\n⊢ ↑(s (succ i)) = ω ^ 2 ^ succ i + ωb ^ 2 ^ succ i",
"state_before": "q : ℕ+\ni : ℕ\n⊢ ↑(s i) = ω ^ 2 ^ i + ωb ^ 2 ^ i",
"tactic": "induction' i with i ih"
... | [
391,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
380,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_div | [] | [
1687,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1686,
11
] |
Std/Data/Int/DivMod.lean | Int.emod_eq_emod_iff_emod_sub_eq_zero | [
{
"state_after": "no goals",
"state_before": "m n k : Int\n⊢ (m - k) % n = (k - k) % n ↔ (m - k) % n = 0",
"tactic": "simp [Int.sub_self]"
}
] | [
451,
65
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
450,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.factorization_one_right | [] | [
183,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Topology/UniformSpace/Basic.lean | UniformContinuous₂.bicompl | [] | [
1729,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
] |
Mathlib/Data/Polynomial/HasseDeriv.lean | Polynomial.hasseDeriv_coeff | [
{
"state_after": "R : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nn : ℕ\n⊢ (if n + k - k = n then ↑(choose (n + k) k) * coeff f (n + k) else 0) = ↑(choose (n + k) k) * coeff f (n + k)\n\ncase h₀\nR : Type u_1\ninst✝ : Semiring R\nk : ℕ\nf : R[X]\nn : ℕ\n⊢ ∀ (b : ℕ), b ∈ support f → b ≠ n + k → coeff (↑(monom... | [
85,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.homOfLe_injective | [
{
"state_after": "no goals",
"state_before": "R : Type u\nL : Type v\ninst✝⁴ : CommRing R\ninst✝³ : LieRing L\ninst✝² : LieAlgebra R L\nL₂ : Type w\ninst✝¹ : LieRing L₂\ninst✝ : LieAlgebra R L₂\nf : L →ₗ⁅R⁆ L₂\nK K' : LieSubalgebra R L\nK₂ : LieSubalgebra R L₂\nh : K ≤ K'\nx y : { x // x ∈ K }\n⊢ ↑(homOfLe ... | [
614,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
613,
1
] |
Mathlib/Order/Bounds/Basic.lean | not_bddBelow_iff | [] | [
143,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.sin_neg_of_neg_of_neg_pi_lt | [] | [
429,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Algebra/CharZero/Lemmas.lean | RingHom.charZero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝¹ : NonAssocSemiring R\ninst✝ : NonAssocSemiring S\nϕ : R →+* S\nhS : CharZero S\na b : ℕ\nh : ↑a = ↑b\n⊢ ↑a = ↑b",
"tactic": "rw [← map_natCast ϕ, ← map_natCast ϕ, h]"
}
] | [
192,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/GroupTheory/Submonoid/Pointwise.lean | Submonoid.pointwise_smul_le_pointwise_smul_iff₀ | [] | [
330,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
328,
1
] |
Std/Data/List/Lemmas.lean | List.append_eq_nil | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\np q : List α✝\n⊢ p ++ q = [] ↔ p = [] ∧ q = []",
"tactic": "cases p <;> simp"
}
] | [
111,
19
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
110,
9
] |
Mathlib/Data/List/Chain.lean | List.Chain'.right_of_append | [] | [
306,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_def | [] | [
2040,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2039,
1
] |
Mathlib/Algebra/GroupPower/Order.lean | one_lt_sq_iff | [] | [
597,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Std/Logic.lean | ne_of_mem_of_not_mem | [] | [
677,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
677,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_mul_norm | [
{
"state_after": "case h.h\nα : Type u_1\nE : Type ?u.398702\nF : Type u_2\nF' : Type u_3\nG : Type ?u.398711\n𝕜 : Type ?u.398714\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F... | [
587,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Combinatorics/SetFamily/LYM.lean | Finset.slice_subset_falling | [] | [
145,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/AdicCompletion.lean | adicCompletion.coe_eval | [] | [
235,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin.range_algebraMap_subset | [
{
"state_after": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\nx : E\nhx : x ∈ Set.range ↑(algebraMap F E)\n⊢ x ∈ ↑(adjoin F S)",
"state_before": "F : Type u_2\ninst✝² : Field F\nE : Type u_1\ninst✝¹ : Field E\ninst✝ : Algebra F E\nS : Set E\n⊢ Set.range ↑(... | [
314,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/LinearAlgebra/LinearIndependent.lean | LinearIndependent.not_mem_span_image | [
{
"state_after": "ι : Type u'\nι' : Type ?u.344052\nR : Type u_1\nK : Type ?u.344058\nM : Type u_2\nM' : Type ?u.344064\nM'' : Type ?u.344067\nV : Type u\nV' : Type ?u.344072\nv : ι → M\ninst✝⁷ : Ring R\ninst✝⁶ : AddCommGroup M\ninst✝⁵ : AddCommGroup M'\ninst✝⁴ : AddCommGroup M''\ninst✝³ : Module R M\ninst✝² : ... | [
628,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
620,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | finite_set_of_fin_dim_affineIndependent | [] | [
96,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.neg_pi_div_two_ne_zero | [
{
"state_after": "⊢ -π / 2 ≠ 0",
"state_before": "⊢ ↑(-π / 2) ≠ 0",
"tactic": "rw [← toReal_injective.ne_iff, toReal_neg_pi_div_two, toReal_zero]"
},
{
"state_after": "no goals",
"state_before": "⊢ -π / 2 ≠ 0",
"tactic": "exact div_ne_zero (neg_ne_zero.2 Real.pi_ne_zero) two_ne_zero"
}... | [
639,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/Real/EReal.lean | EReal.range_coe_ennreal | [] | [
547,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
543,
9
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.isCycle_copy | [
{
"state_after": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu' : V\np : Walk G u' u'\n⊢ IsCycle (Walk.copy p (_ : u' = u') (_ : u' = u')) ↔ IsCycle p",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\n... | [
914,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.sup_mem | [] | [
274,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Order/BoundedOrder.lean | exists_ge_and_iff_exists | [] | [
603,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
601,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inl_one | [] | [
386,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.type_fintype | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.240276\nγ : Type ?u.240279\nr✝ : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nr : α → α → Prop\ninst✝¹ : IsWellOrder α r\ninst✝ : Fintype α\n⊢ type r = ↑(Fintype.card α)",
"tactic": "rw [← card_eq_nat, card_type, mk_fintype]"
... | [
1587,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1586,
1
] |
Mathlib/Data/Fintype/Basic.lean | Fin.univ_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.103890\nβ : Type ?u.103893\nγ : Type ?u.103896\nn : ℕ\n⊢ ¬0 ∈ map { toFun := succ, inj' := (_ : Injective succ) } univ",
"tactic": "simp [map_eq_image]"
},
{
"state_after": "no goals",
"state_before": "α : Type ?u.103890\nβ : Type ?u.... | [
836,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
833,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | AddSubmonoid.mem_iSup_iff_exists_dfinsupp | [] | [
1981,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Std/Data/Int/DivMod.lean | Int.zero_mod | [
{
"state_after": "no goals",
"state_before": "b : Int\n⊢ mod 0 b = 0",
"tactic": "cases b <;> simp [mod]"
}
] | [
248,
78
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
248,
9
] |
Mathlib/Order/Cover.lean | Covby.ne' | [] | [
281,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Order/Monotone/Union.lean | StrictAntiOn.Iic_union_Ici | [] | [
76,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
11
] |
Mathlib/LinearAlgebra/Basis/Bilinear.lean | LinearMap.ext_basis | [] | [
48,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
1
] |
Mathlib/Data/Polynomial/Monic.lean | Polynomial.monic_of_isUnit_leadingCoeff_inv_smul | [
{
"state_after": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : IsUnit (leadingCoeff p)\n⊢ ↑(IsUnit.unit h)⁻¹ • leadingCoeff p = 1",
"state_before": "R : Type u\nS : Type v\na b : R\nm n : ℕ\nι : Type y\ninst✝ : Semiring R\np : R[X]\nh : IsUnit (leadingCoeff p)\n⊢ M... | [
521,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | span_eq_top_of_linearIndependent_of_card_eq_finrank | [
{
"state_after": "case pos\nK : Type u\nV : Type v\ninst✝³ : DivisionRing K\ninst✝² : AddCommGroup V\ninst✝¹ : Module K V\nι : Type u_1\nhι : Nonempty ι\ninst✝ : Fintype ι\nb : ι → V\nlin_ind : LinearIndependent K b\ncard_eq : Fintype.card ι = finrank K V\nfin : FiniteDimensional K V\n⊢ span K (Set.range b) = ⊤... | [
1185,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1167,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | MulEquiv.map_prod | [] | [
227,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
11
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_source' | [] | [
826,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
825,
1
] |
Mathlib/Tactic/LinearCombination.lean | Mathlib.Tactic.LinearCombination.c_div_pf | [] | [
49,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.cast_commute | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.6256\ninst✝ : NonAssocSemiring α\nn : ℕ\nx : α\n⊢ Commute (↑n) x",
"tactic": "induction n with\n| zero => rw [Nat.cast_zero]; exact Commute.zero_left x\n| succ n ihn => rw [Nat.cast_succ]; exact ihn.add_left (Commute.one_left x)"
... | [
70,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_add_sin_mul_I_pow | [
{
"state_after": "x y : ℂ\nn : ℕ\nz : ℂ\n⊢ exp (z * I) ^ n = exp (↑n * z * I)",
"state_before": "x y : ℂ\nn : ℕ\nz : ℂ\n⊢ (cos z + sin z * I) ^ n = cos (↑n * z) + sin (↑n * z) * I",
"tactic": "rw [← exp_mul_I, ← exp_mul_I]"
},
{
"state_after": "case zero\nx y z : ℂ\n⊢ exp (z * I) ^ Nat.zero = ex... | [
1121,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1116,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.closedBall_zero' | [] | [
692,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/Order/Filter/ENNReal.lean | ENNReal.limsup_liminf_le_liminf_limsup | [
{
"state_after": "α : Type u_2\nf✝ : Filter α\nβ : Type u_1\ninst✝¹ : Countable β\nf : Filter α\ninst✝ : CountableInterFilter f\ng : Filter β\nu : α → β → ℝ≥0∞\n⊢ ∀ (i : β), ∀ᶠ (x : α) in f, u x i ≤ limsup (fun a' => u a' i) f",
"state_before": "α : Type u_2\nf✝ : Filter α\nβ : Type u_1\ninst✝¹ : Countable ... | [
97,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/NNReal.lean | ENNReal.rpow_eq_pow | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.decomp | [
{
"state_after": "case h\nk : Type u_1\nV1 : Type u_2\nP1 : Type ?u.585564\nV2 : Type u_3\nP2 : Type ?u.585570\nV3 : Type ?u.585573\nP3 : Type ?u.585576\nV4 : Type ?u.585579\nP4 : Type ?u.585582\ninst✝¹² : Ring k\ninst✝¹¹ : AddCommGroup V1\ninst✝¹⁰ : Module k V1\ninst✝⁹ : AffineSpace V1 P1\ninst✝⁸ : AddCommGrou... | [
670,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Topology/Homotopy/HomotopyGroup.lean | genLoopOneEquivPathSelf_homotopic_iff | [
{
"state_after": "no goals",
"state_before": "X : Type u\ninst✝ : TopologicalSpace X\nn : ℕ\nx : X\nf g : GenLoop 1 x\n⊢ Path.Homotopic (↑genLoopOneEquivPathSelf f) (↑genLoopOneEquivPathSelf g) ↔ GenLoop.Homotopic f g",
"tactic": "rw [← genLoopOneEquivPathSelf_symm_homotopic_iff, Equiv.symm_apply_apply,... | [
278,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/EulerSineProd.lean | EulerSine.integral_cos_mul_cos_pow_even | [
{
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... | [
183,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | hasSum_extend_zero | [
{
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"state_before": "α : Type u_3\nβ : Type u_1\nγ : Type u_... | [
146,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
9
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_finite_isCompactElement | [] | [
626,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
625,
1
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Mathlib/Data/Set/Basic.lean | Set.diff_subset_comm | [] | [
1951,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1950,
1
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Mathlib/Algebra/Order/Field/Basic.lean | div_nonpos_iff | [
{
"state_after": "no goals",
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"tactic": "simp [division_def, mul_nonpos_iff]"
}
] | [
693,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
692,
1
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Mathlib/Logic/Equiv/Basic.lean | Function.piCongrLeft'_symm_update | [
{
"state_after": "no goals",
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1949,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1946,
1
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Mathlib/Data/Set/Finite.lean | Set.iUnion_pi_of_monotone | [
{
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1556,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1550,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.biUnion_null_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nR : Type ?u.7093\nR' : Type ?u.7096\nms : Set (OuterMeasure α)\nm✝ m : OuterMeasure α\ns : Set β\nhs : Set.Countable s\nt : β → Set α\nthis : Encodable ↑s\n⊢ ↑m (⋃ (i : β) (_ : i ∈ s), t i) = 0 ↔ ∀ (i : β), i ∈ s → ↑m (t i) = 0",
"state_before": "α : Type u_1\nβ... | [
141,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
138,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | Complex.hasDerivAt_sinh | [] | [
116,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
115,
1
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Mathlib/Order/Closure.lean | LowerAdjoint.idempotent | [] | [
371,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/Topology/Algebra/Field.lean | Filter.tendsto_cocompact_mul_left₀ | [] | [
30,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
28,
1
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Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.quot_lift_mk | [] | [
505,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
503,
1
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Mathlib/Topology/DiscreteQuotient.lean | DiscreteQuotient.ofLE_proj | [] | [
242,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
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Mathlib/Topology/PartitionOfUnity.lean | BumpCovering.locallyFinite_tsupport | [] | [
240,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.IsAlt.isRefl | [
{
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973,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
971,
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Mathlib/RingTheory/Ideal/Operations.lean | Ideal.map_isPrime_of_surjective | [
{
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2145,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2131,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.pi_ne_zero | [
{
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"tactic": "rw [← toReal_injective.ne_iff, toReal_pi, toReal_zero]"
},
{
"state_after": "no goals",
"state_before": "⊢ π ≠ 0",
"tactic": "exact Real.pi_ne_zero"
}
] | [
609,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
607,
1
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Mathlib/Algebra/Hom/Ring.lean | NonUnitalRingHom.coe_copy | [] | [
165,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.mul | [] | [
1393,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1391,
8
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Mathlib/CategoryTheory/Monoidal/Free/Basic.lean | CategoryTheory.FreeMonoidalCategory.mk_α_hom | [] | [
206,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
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Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean | IsCoercive.ker_eq_bot | [
{
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"state_before": "V : Type u\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace ... | [
85,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.tendsto_nhds_infty' | [
{
"state_after": "no goals",
"state_before": "X : Type u_2\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nα : Type u_1\nf : OnePoint X → α\nl : Filter α\n⊢ Tendsto f (𝓝 ∞) l ↔ Tendsto f (pure ∞) l ∧ Tendsto (f ∘ some) (coclosedCompact X) l",
"tactic": "simp [nhds_infty_eq, and_comm]"
}... | [
362,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Algebra/Support.lean | Function.nmem_mulSupport | [] | [
58,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
57,
1
] |
Mathlib/Data/Fintype/Card.lean | Fintype.card_quotient_lt | [] | [
882,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Init/Algebra/Order.lean | le_or_gt | [] | [
353,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/AlgebraicTopology/DoldKan/FunctorGamma.lean | AlgebraicTopology.DoldKan.Γ₀.Obj.map_on_summand' | [
{
"state_after": "case fac\nC : Type u_2\ninst✝² : Category C\ninst✝¹ : Preadditive C\nK K' : ChainComplex C ℕ\nf : K ⟶ K'\nΔ✝ Δ'✝ Δ'' : SimplexCategory\ninst✝ : HasFiniteCoproducts C\nΔ Δ' : SimplexCategoryᵒᵖ\nA : Splitting.IndexSet Δ\nθ : Δ ⟶ Δ'\n⊢ factorThruImage (θ.unop ≫ Splitting.IndexSet.e A) ≫ image.ι (... | [
280,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Std/Logic.lean | Decidable.imp_or | [
{
"state_after": "no goals",
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"tactic": "by_cases a <;> simp_all"
}
] | [
562,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
561,
1
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Mathlib/RingTheory/Polynomial/Basic.lean | Ideal.polynomial_not_isField | [
{
"state_after": "R : Type u\nS : Type ?u.190529\ninst✝ : Ring R\n✝ : Nontrivial R\n⊢ ¬IsField R[X]",
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"tactic": "nontriviality R"
},
{
"state_after": "R : Type u\nS : Type ?u.190529\ninst✝ : Ring R\n✝ : Nontrivial... | [
650,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Data/Real/GoldenRatio.lean | fib_isSol_fibRec | [
{
"state_after": "α : Type u_1\ninst✝ : CommSemiring α\n⊢ LinearRecurrence.IsSolution { order := 2, coeffs := ![1, 1] } fun x => ↑(Nat.fib x)",
"state_before": "α : Type u_1\ninst✝ : CommSemiring α\n⊢ LinearRecurrence.IsSolution fibRec fun x => ↑(Nat.fib x)",
"tactic": "rw [fibRec]"
},
{
"state_... | [
194,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/RingTheory/MvPolynomial/Homogeneous.lean | MvPolynomial.homogeneousComponent_zero | [
{
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"state_before": "σ : Type u_1\nτ : Type ?u.182889\nR : Type u_2\nS : Type ?u.1... | [
282,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Control/ULift.lean | PLift.bind_up | [] | [
59,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.add_mod_eq_ite | [
{
"state_after": "case zero\nm n l : ℕ\n⊢ (m + n) % zero = if zero ≤ m % zero + n % zero then m % zero + n % zero - zero else m % zero + n % zero\n\ncase succ\nm n l n✝ : ℕ\n⊢ (m + n) % succ n✝ =\n if succ n✝ ≤ m % succ n✝ + n % succ n✝ then m % succ n✝ + n % succ n✝ - succ n✝ else m % succ n✝ + n % succ n✝"... | [
514,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
505,
1
] |
Mathlib/Topology/Constructions.lean | DenseRange.quotient | [] | [
200,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Order/SymmDiff.lean | ofDual_bihimp | [] | [
114,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean | UniformFun.postcomp_uniformContinuous | [
{
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... | [
418,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
11
] |
Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean | Polynomial.IsWeaklyEisensteinAt.map | [
{
"state_after": "R : Type u\ninst✝¹ : CommSemiring R\n𝓟 : Ideal R\nf : R[X]\nhf : IsWeaklyEisensteinAt f 𝓟\nA : Type v\ninst✝ : CommRing A\nφ : R →+* A\nn✝ : ℕ\nhn : n✝ < natDegree (Polynomial.map φ f)\n⊢ coeff (Polynomial.map φ f) n✝ ∈ Ideal.map φ 𝓟",
"state_before": "R : Type u\ninst✝¹ : CommSemiring ... | [
72,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.square_to_iso_invert | [
{
"state_after": "no goals",
"state_before": "T : Type u\ninst✝ : Category T\ni : Arrow T\nX Y : T\np : X ≅ Y\nsq : i ⟶ mk p.hom\n⊢ i.hom ≫ sq.right ≫ p.inv = sq.left",
"tactic": "simpa only [Category.assoc] using (Iso.comp_inv_eq p).mpr (Arrow.w_mk_right sq).symm"
}
] | [
261,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.symm_trans_target_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.12276\nB : Type u_1\nF : Type u_2\nE : B → Type ?u.12287\nZ : Type u_3\ninst✝¹ : TopologicalSpace B\ninst✝ : TopologicalSpace F\nproj : Z → B\ne✝ : Pretrivialization F proj\nx : Z\ne e' : Pretrivialization F proj\n⊢ (LocalEquiv.trans (LocalEquiv.symm... | [
224,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.mem_support_bernoulli_iff | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.170166\nβ : Type ?u.170169\nγ : Type ?u.170172\np : ℝ≥0∞\nh : p ≤ 1\nb : Bool\n⊢ b ∈ support (bernoulli p h) ↔ bif b then p ≠ 0 else p ≠ 1",
"tactic": "simp"
}
] | [
324,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
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Mathlib/Data/Nat/Basic.lean | Nat.strongRecOn'_beta | [
{
"state_after": "m n✝ k : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → ((m : ℕ) → m < n → P m) → P n\nn : ℕ\n⊢ Nat.strongRec' h n = h n fun m x => Nat.strongRec' h m",
"state_before": "m n✝ k : ℕ\nP : ℕ → Sort u_1\nh : (n : ℕ) → ((m : ℕ) → m < n → P m) → P n\nn : ℕ\n⊢ strongRecOn' n h = h n fun m x => strongRecOn' m... | [
475,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Combinatorics/Quiver/SingleObj.lean | Quiver.SingleObj.pathToList_listToPath | [
{
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"state_before": "α : Type u_1\n... | [
148,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.ceil_add_le | [
{
"state_after": "F : Type ?u.92323\nα : Type u_1\nβ : Type ?u.92329\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na✝ : α\nn : ℕ\na b : α\n⊢ a + b ≤ ↑⌈a⌉₊ + ↑⌈b⌉₊",
"state_before": "F : Type ?u.92323\nα : Type u_1\nβ : Type ?u.92329\ninst✝¹ : LinearOrderedSemiring α\ninst✝ : FloorSemiring α\na... | [
488,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Order/Ideal.lean | Order.mem_idealOfCofinals | [] | [
596,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.map_inl_inr_codiag | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nX✝ Y✝ X Y : C\ninst✝¹ : HasBinaryCoproduct X Y\ninst✝ : HasBinaryCoproduct (X ⨿ Y) (X ⨿ Y)\n⊢ map inl inr ≫ codiag (X ⨿ Y) = 𝟙 (X ⨿ Y)",
"tactic": "simp"
}
] | [
943,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
941,
1
] |
Mathlib/CategoryTheory/Monad/Algebra.lean | CategoryTheory.Comonad.Coalgebra.id_eq_id | [] | [
406,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
405,
1
] |
Mathlib/Analysis/Calculus/IteratedDeriv.lean | iteratedDeriv_eq_iteratedFDeriv | [] | [
221,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Order/SymmDiff.lean | bihimp_eq | [] | [
717,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Data/PFun.lean | PFun.core_mono | [] | [
480,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | measurable_liminf | [] | [
1333,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1331,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.erase_size | [
{
"state_after": "α : Type u_1\nβ : Type u_2\ninst✝¹ : BEq α\ninst✝ : Hashable α\nm : Imp α β\nk : α\nh : m.size = Bucket.size m.buckets\n⊢ (match\n AssocList.contains k\n m.buckets.val[USize.toNat (mkIdx (_ : 0 < Array.size m.buckets.val) (UInt64.toUSize (hash k))).val] with\n | true =>\n ... | [
255,
12
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
241,
1
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