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/Finset/Basic.lean | Finset.disjiUnion_disjiUnion | [
{
"state_after": "case intro.intro\nα : Type ?u.491855\nβ : Type ?u.491858\nγ : Type ?u.491861\ns✝ s₁ s₂ : Finset α\nt t₁ t₂ : α → Finset β\ns : Finset α\nf : α → Finset β\ng : β → Finset γ\nh1 : Set.PairwiseDisjoint (↑s) f\nh2 : Set.PairwiseDisjoint (↑(disjiUnion s f h1)) g\na : { x // x ∈ s }\nx✝¹ : a ∈ ↑(att... | [
3494,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3478,
1
] |
Mathlib/Combinatorics/Additive/PluenneckeRuzsa.lean | Finset.card_pow_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : CommGroup α\ninst✝ : DecidableEq α\nA B✝ C : Finset α\nhA : Finset.Nonempty A\nB : Finset α\nn : ℕ\n⊢ ↑(card (B ^ n)) ≤ (↑(card (A * B)) / ↑(card A)) ^ n * ↑(card A)",
"tactic": "simpa only [_root_.pow_zero, div_one] using card_pow_div... | [
252,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Complex/ExponentialBounds.lean | Real.exp_one_lt_d9 | [
{
"state_after": "no goals",
"state_before": "⊢ 1 / 10 ^ 10 + 2244083 / 825552 < 2.7182818286",
"tactic": "norm_num"
}
] | [
44,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Order/Atoms.lean | Set.isSimpleOrder_Ici_iff_isCoatom | [] | [
691,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
686,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.ofConjAct_inv | [] | [
129,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Algebra/Hom/Group.lean | map_pow | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.50695\nβ : Type ?u.50698\nM : Type ?u.50701\nN : Type ?u.50704\nP : Type ?u.50707\nG : Type u_1\nH : Type u_2\nF : Type u_3\ninst✝⁴ : MulOneClass M\ninst✝³ : MulOneClass N\ninst✝² : Monoid G\ninst✝¹ : Monoid H\ninst✝ : MonoidHomClass F G H\nf : F\na ... | [
451,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/IsROrC/Basic.lean | IsROrC.mul_self_norm | [
{
"state_after": "no goals",
"state_before": "K : Type u_1\nE : Type ?u.6573042\ninst✝ : IsROrC K\nz : K\n⊢ ‖z‖ * ‖z‖ = ↑normSq z",
"tactic": "rw [normSq_eq_def', sq]"
}
] | [
705,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
705,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean | CategoryTheory.Limits.IsZero.hasZeroObject | [] | [
224,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.TransvectionStruct.reverse_inv_prod_mul_prod | [
{
"state_after": "case nil\nn : Type u_1\np : Type ?u.35992\nR : Type u₂\n𝕜 : Type ?u.35997\ninst✝⁴ : Field 𝕜\ninst✝³ : DecidableEq n\ninst✝² : DecidableEq p\ninst✝¹ : CommRing R\ni j : n\ninst✝ : Fintype n\n⊢ List.prod (List.map (toMatrix ∘ TransvectionStruct.inv) (List.reverse [])) ⬝ List.prod (List.map toM... | [
227,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.absolutelyContinuous_of_le | [] | [
2358,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2357,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_principal2 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.22457\nγ : Type ?u.22460\nι : Sort ?u.22463\nf✝ f₁ f₂ : Filter α\ng g₁ g₂ : Set α → Filter β\nf : Filter α\ns : Set α\nhs : s ∈ f\n⊢ f ≤ 𝓟 s",
"tactic": "simp only [hs, le_principal_iff]"
}
] | [
195,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/MeasureTheory/Function/L1Space.lean | MeasureTheory.integrable_withDensity_iff_integrable_coe_smul | [
{
"state_after": "case pos\nα : Type u_1\nβ : Type ?u.1006363\nγ : Type ?u.1006366\nδ : Type ?u.1006369\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁴ : MeasurableSpace δ\ninst✝³ : NormedAddCommGroup β\ninst✝² : NormedAddCommGroup γ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α →... | [
864,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
849,
1
] |
Mathlib/Analysis/LocallyConvex/Bounded.lean | Bornology.isVonNBounded_covers | [] | [
212,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.succ_eq_one_add | [
{
"state_after": "no goals",
"state_before": "n : Nat\n⊢ succ n = 1 + n",
"tactic": "rw [Nat.succ_eq_add_one, Nat.add_comm]"
}
] | [
311,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
310,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.gc_homogeneousIdeal | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\ninst✝³ : CommSemiring R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\n𝒜 : ℕ → Submodule R A\ninst✝ : GradedAlgebra 𝒜\nI : HomogeneousIdeal 𝒜\nt : (Set (ProjectiveSpectrum 𝒜))ᵒᵈ\n⊢ (fun I => zeroLocus 𝒜 ↑I) I ≤ t ↔ I ≤ (fun t => van... | [
153,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | PiToModule.fromMatrix_apply | [] | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Data/Pi/Algebra.lean | Pi.const_mul | [] | [
99,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.abs_exp | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ ↑abs (exp z) = Real.exp z.re",
"tactic": "rw [exp_eq_exp_re_mul_sin_add_cos, map_mul, abs_exp_ofReal, abs_cos_add_sin_mul_I, mul_one]"
}
] | [
2042,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2041,
1
] |
Mathlib/Data/Set/Countable.lean | Set.countable_iff_exists_surjective | [] | [
109,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
11
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic'_splits | [
{
"state_after": "K : Type u_1\ninst✝ : Field K\nn : ℕ\n⊢ ∀ (j : K), j ∈ primitiveRoots n K → Splits (RingHom.id K) (X - ↑C j)",
"state_before": "K : Type u_1\ninst✝ : Field K\nn : ℕ\n⊢ Splits (RingHom.id K) (cyclotomic' n K)",
"tactic": "apply splits_prod (RingHom.id K)"
},
{
"state_after": "K ... | [
159,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.one_sub_le_exp_minus_of_nonneg | [
{
"state_after": "case inl\nh : 0 ≤ 0\n⊢ 1 - 0 ≤ exp (-0)\n\ncase inr\ny : ℝ\nh✝ : 0 ≤ y\nh : 0 < y\n⊢ 1 - y ≤ exp (-y)",
"state_before": "y : ℝ\nh : 0 ≤ y\n⊢ 1 - y ≤ exp (-y)",
"tactic": "rcases eq_or_lt_of_le h with (rfl | h)"
},
{
"state_after": "no goals",
"state_before": "case inl\nh : ... | [
1973,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1970,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | Left.one_lt_inv_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ 1 < a⁻¹ ↔ a < 1",
"tactic": "rw [← mul_lt_mul_iff_left a, mul_inv_self, mul_one]"
}
] | [
162,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Nat/Choose/Basic.lean | Nat.choose_self | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ choose n n = 1",
"tactic": "induction n <;> simp [*, choose, choose_eq_zero_of_lt (lt_succ_self _)]"
}
] | [
82,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Data/List/Permutation.lean | List.length_permutationsAux2 | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nt : α\nts ys : List α\nf : List α → β\n⊢ length (permutationsAux2 t ts [] ys f).snd = length ys",
"tactic": "induction ys generalizing f <;> simp [*]"
}
] | [
172,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.zero_mul | [
{
"state_after": "no goals",
"state_before": "u : Lean.Level\nR : Type u_1\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝ : CommSemiring R\nb : R\n⊢ 0 * b = 0",
"tactic": "simp"
}
] | [
429,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_cons | [] | [
314,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/LinearAlgebra/Basic.lean | LinearEquiv.coe_ofEq_apply | [] | [
2032,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2031,
1
] |
Mathlib/Data/Sym/Basic.lean | Sym.filter_ne_fill | [
{
"state_after": "α : Type u_1\nβ : Type ?u.55875\nn n' m✝ : ℕ\ns : Sym α n\na✝ b : α\ninst✝ : DecidableEq α\na : α\nm : (i : Fin (n + 1)) × Sym α (n - ↑i)\nh : ¬a ∈ m.snd\n⊢ filter ((fun x x_1 => x ≠ x_1) a) (↑m.snd + ↑(replicate (↑m.fst) a)) = ↑m.snd",
"state_before": "α : Type u_1\nβ : Type ?u.55875\nn n... | [
586,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/Topology/Algebra/GroupWithZero.lean | Homeomorph.coe_mulLeft₀ | [] | [
259,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
] |
Mathlib/Algebra/BigOperators/Order.lean | Finset.single_lt_prod' | [] | [
503,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.isOpen_iff_mem_balls | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\n𝕜₂ : Type ?u.210790\n𝕝 : Type ?u.210793\n𝕝₂ : Type ?u.210796\nE : Type u_2\nF : Type ?u.210802\nG : Type ?u.210805\nι : Type u_3\nι' : Type ?u.210811\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\n... | [
333,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
331,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.mem_map_of_mem | [] | [
1326,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1325,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.MeasurePreserving.set_lintegral_comp_preimage_emb | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1687696\nδ : Type ?u.1687699\nm : MeasurableSpace α\nμ ν✝ : Measure α\nmb : MeasurableSpace β\nν : Measure β\ng : α → β\nhg : MeasurePreserving g\nhge : MeasurableEmbedding g\nf : β → ℝ≥0∞\ns : Set β\n⊢ (∫⁻ (a : α) in g ⁻¹... | [
1351,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1348,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.smulRight | [] | [
909,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Analysis/Normed/Group/AddTorsor.lean | nndist_vadd_left | [] | [
124,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean | CategoryTheory.Limits.IsInitial.isSplitEpi_to | [] | [
179,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.coe_toOrderHom | [] | [
112,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
9
] |
Mathlib/Algebra/CharZero/Lemmas.lean | RingHom.injective_nat | [] | [
202,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | InnerProductSpace.Core.inner_conj_symm | [] | [
209,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/CategoryTheory/IsConnected.lean | CategoryTheory.zigzag_isConnected | [
{
"state_after": "case h\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\ninst✝ : Nonempty J\nh : ∀ (j₁ j₂ : J), Zigzag j₁ j₂\n⊢ ∀ (p : Set J), ?j₀ ∈ p → (∀ {j₁ j₂ : J}, (j₁ ⟶ j₂) → (j₁ ∈ p ↔ j₂ ∈ p)) → ∀ (j : J), j ∈ p\n\ncase j₀\nJ : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Cate... | [
328,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.cof_univ | [
{
"state_after": "α : Type ?u.103379\nr : α → α → Prop\nc : Cardinal\nh : c < Cardinal.univ\n⊢ c < cof univ",
"state_before": "α : Type ?u.103379\nr : α → α → Prop\n⊢ Cardinal.univ ≤ cof univ",
"tactic": "refine' le_of_forall_lt fun c h => _"
},
{
"state_after": "case intro\nα : Type ?u.103379\n... | [
775,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
758,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | TendstoLocallyUniformly.tendstoLocallyUniformlyOn | [] | [
686,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
11
] |
Mathlib/RingTheory/Adjoin/Basic.lean | Algebra.adjoin_prod_le | [] | [
235,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | mul_inv_lt_inv_mul_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝³ : Group α\ninst✝² : LT α\ninst✝¹ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\ninst✝ : CovariantClass α α (swap fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c d : α\n⊢ a * b⁻¹ < d⁻¹ * c ↔ d * a < c * b",
"tactic": "r... | [
418,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/MeasureTheory/Constructions/Prod/Basic.lean | MeasureTheory.QuasiMeasurePreserving.prod_of_left | [
{
"state_after": "α✝ : Type ?u.4535638\nα' : Type ?u.4535641\nβ✝ : Type ?u.4535644\nβ' : Type ?u.4535647\nγ✝ : Type ?u.4535650\nE : Type ?u.4535653\ninst✝¹⁰ : MeasurableSpace α✝\ninst✝⁹ : MeasurableSpace α'\ninst✝⁸ : MeasurableSpace β✝\ninst✝⁷ : MeasurableSpace β'\ninst✝⁶ : MeasurableSpace γ✝\nμ✝ μ' : Measure α... | [
682,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.abs_exp_sub_one_le | [
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : ↑abs x ≤ 1\n⊢ ↑abs (exp x - 1) = ↑abs (exp x - ∑ m in range 1, x ^ m / ↑(Nat.factorial m))",
"tactic": "simp [sum_range_succ]"
},
{
"state_after": "no goals",
"state_before": "x : ℂ\nhx : ↑abs x ≤ 1\n⊢ 0 < 1",
"tactic": "decide"
... | [
1684,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1679,
1
] |
Std/Logic.lean | iff_self_and | [
{
"state_after": "no goals",
"state_before": "p q : Prop\n⊢ (p ↔ p ∧ q) ↔ p → q",
"tactic": "rw [@Iff.comm p, and_iff_left_iff_imp]"
}
] | [
215,
41
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
214,
9
] |
Mathlib/Data/Set/NAry.lean | Set.image2_union_inter_subset | [
{
"state_after": "α : Type u_1\nα' : Type ?u.51060\nβ : Type u_2\nβ' : Type ?u.51066\nγ : Type ?u.51069\nγ' : Type ?u.51072\nδ : Type ?u.51075\nδ' : Type ?u.51078\nε : Type ?u.51081\nε' : Type ?u.51084\nζ : Type ?u.51087\nζ' : Type ?u.51090\nν : Type ?u.51093\nf✝ f' : α → β → γ\ng g' : α → β → γ → δ\ns✝ s' : Se... | [
471,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
468,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_zero_set | [] | [
1681,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1680,
1
] |
Mathlib/Order/CompleteLattice.lean | iSup_sum | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_1\nβ₂ : Type ?u.168938\nγ : Type u_2\nι : Sort ?u.168944\nι' : Sort ?u.168947\nκ : ι → Sort ?u.168952\nκ' : ι' → Sort ?u.168957\ninst✝ : CompleteLattice α\nf✝ g s t : ι → α\na b : α\nf : β ⊕ γ → α\nc : α\n⊢ (⨆ (x : β ⊕ γ), f x) ≤ c ↔ ((⨆... | [
1568,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1567,
1
] |
Mathlib/Data/List/Basic.lean | List.nthLe_of_eq | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.87083\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ L L' : List α\nh : L = L'\ni : ℕ\nhi : i < length L\n⊢ nthLe L i hi = nthLe L' i (_ : i < length L')",
"tactic": "congr"
}
] | [
1316,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1315,
1
] |
Mathlib/GroupTheory/Transfer.lean | Subgroup.leftTransversals.diff_self | [] | [
72,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/Convex/Function.lean | StrictConcaveOn.translate_right | [] | [
947,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
945,
1
] |
Mathlib/CategoryTheory/StructuredArrow.lean | CategoryTheory.CostructuredArrow.map_id | [
{
"state_after": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nT T' T'' : D\nY Y' : C\nS : C ⥤ D\nf : CostructuredArrow S T\n⊢ (map (𝟙 T)).obj (mk f.hom) = mk f.hom",
"state_before": "C : Type u₁\ninst✝¹ : Category C\nD : Type u₂\ninst✝ : Category D\nT T' T'' : D\nY Y' : C\nS : C ⥤ D\... | [
435,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.mk.inj_iff | [] | [
211,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
11
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.lt_replicate_succ | [
{
"state_after": "α : Type u_1\nβ : Type ?u.93086\nγ : Type ?u.93089\nm : Multiset α\nx : α\nn : ℕ\n⊢ (∃ a, a ::ₘ m ≤ replicate (n + 1) x) ↔ m ≤ replicate n x",
"state_before": "α : Type u_1\nβ : Type ?u.93086\nγ : Type ?u.93089\nm : Multiset α\nx : α\nn : ℕ\n⊢ m < replicate (n + 1) x ↔ m ≤ replicate n x",
... | [
988,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Algebra/Order/Positive/Ring.lean | Positive.val_pow | [] | [
116,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Deriv.lean | Real.deriv_log | [
{
"state_after": "no goals",
"state_before": "x✝ x : ℝ\nhx : x = 0\n⊢ deriv log x = x⁻¹",
"tactic": "rw [deriv_zero_of_not_differentiableAt (differentiableAt_log_iff.not_left.2 hx), hx, inv_zero]"
}
] | [
73,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Analysis/Calculus/FDerivMeasurable.lean | RightDerivMeasurableAux.differentiable_set_subset_d | [
{
"state_after": "F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nx : ℝ\nhx : x ∈ {x | DifferentiableWithinAt ℝ f (Ici x) x ∧ derivWithin f (Ici x) x ∈ K}\n⊢ x ∈ D f K",
"state_before": "F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ →... | [
588,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
576,
1
] |
Mathlib/Data/Multiset/Sum.lean | Multiset.zero_disjSum | [] | [
38,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.mul_meas_ge_le_pow_snorm | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.4415601\nG : Type ?u.4415604\nm m0 : MeasurableSpace α\np : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → E\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ⊤\nhf : AEStronglyMeasura... | [
1150,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_const | [] | [
606,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_nat_mul_two_pi_add_pi | [
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ cos (↑n * (2 * π) + π) = -1",
"tactic": "simpa only [cos_zero] using (cos_periodic.nat_mul n).add_antiperiod_eq cos_antiperiodic"
}
] | [
386,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
385,
1
] |
Mathlib/Order/Disjoint.lean | codisjoint_inf_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DistribLattice α\ninst✝ : OrderTop α\na b c : α\n⊢ Codisjoint (a ⊓ b) c ↔ Codisjoint a c ∧ Codisjoint b c",
"tactic": "simp only [codisjoint_iff, sup_inf_right, inf_eq_top_iff]"
}
] | [
374,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
373,
1
] |
Mathlib/LinearAlgebra/Span.lean | Submodule.mem_iSup | [
{
"state_after": "R : Type u_2\nR₂ : Type ?u.237748\nK : Type ?u.237751\nM : Type u_3\nM₂ : Type ?u.237757\nV : Type ?u.237760\nS : Type ?u.237763\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nx : M\np✝ p' : Submodule R M\ninst✝² : Semiring R₂\nσ₁₂ : R →+* R₂\ninst✝¹ : AddCommMonoid M₂\ni... | [
731,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_le_sInf | [] | [
228,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/Data/Multiset/LocallyFinite.lean | Multiset.Ioc_eq_zero_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na b c : α\n⊢ Ioc a b = 0 ↔ ¬a < b",
"tactic": "rw [Ioc, Finset.val_eq_zero, Finset.Ioc_eq_empty_iff]"
}
] | [
59,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean | CategoryTheory.MonoidalOfChosenFiniteProducts.triangle | [
{
"state_after": "C : Type u\ninst✝ : Category C\nX✝ Y✝ : C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX Y : C\n⊢ (BinaryFan.associatorOfLimitCone ℬ X 𝒯.cone.pt Y).hom ≫\n IsLimit.lift (ℬ X Y).isLimit\n (BinaryFan.mk (BinaryFan.fst (ℬ X (ℬ 𝒯.cone.pt Y).cone.pt).cone ≫... | [
305,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
300,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.lift_cof | [
{
"state_after": "α : Type ?u.17400\nr : α → α → Prop\no : Ordinal\n⊢ ∀ (α : Type v) (r : α → α → Prop) [inst : IsWellOrder α r], Cardinal.lift (cof (type r)) = cof (lift (type r))",
"state_before": "α : Type ?u.17400\nr : α → α → Prop\no : Ordinal\n⊢ Cardinal.lift (cof o) = cof (lift o)",
"tactic": "re... | [
285,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_of_pos | [
{
"state_after": "x y : ℝ\nhx : 0 < x\n⊢ ↑(OrderIso.symm expOrderIso) { val := abs x, property := (_ : 0 < abs x) } =\n ↑(OrderIso.symm expOrderIso) { val := x, property := hx }",
"state_before": "x y : ℝ\nhx : 0 < x\n⊢ log x = ↑(OrderIso.symm expOrderIso) { val := x, property := hx }",
"tactic": "rw... | [
55,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.uniformContinuousOn | [] | [
507,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
11
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.mk_smul | [
{
"state_after": "case pos\nK : Type u\ninst✝⁴ : CommRing K\nR : Type u_1\ninst✝³ : IsDomain K\ninst✝² : Monoid R\ninst✝¹ : DistribMulAction R K[X]\ninst✝ : IsScalarTower R K[X] K[X]\nc : R\np q : K[X]\nhq : q = 0\n⊢ RatFunc.mk (c • p) q = c • RatFunc.mk p q\n\ncase neg\nK : Type u\ninst✝⁴ : CommRing K\nR : Typ... | [
479,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | LinearIsometry.coe_toAffineIsometry | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Logic/Basic.lean | ite_and | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort ?u.40023\nσ : α → Sort ?u.40019\nf : α → β\nP Q : Prop\ninst✝¹ : Decidable P\ninst✝ : Decidable Q\na b c : α\nA : P → α\nB : ¬P → α\n⊢ (if P ∧ Q then a else b) = if P then if Q then a else b else b",
"tactic": "by_cases hp : P <;> by_c... | [
1250,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1249,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | lt_mul_of_one_lt_right' | [] | [
441,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Topology/UniformSpace/UniformEmbedding.lean | uniformContinuous_uniformly_extend | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_3\nγ : Type u_1\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ne : β → α\nh_e : UniformInducing e\nh_dense : DenseRange e\nf : β → γ\nh_f : UniformContinuous f\ninst✝ : CompleteSpace γ\nd : Set (γ × γ)\nhd : ... | [
490,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
466,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasurableEquiv.map_map_symm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.2284080\nδ : Type ?u.2284083\nι : Type ?u.2284086\nR : Type ?u.2284089\nR' : Type ?u.2284092\ninst✝¹ : MeasurableSpace α\ninst✝ : MeasurableSpace β\nμ : MeasureTheory.Measure α\nν : MeasureTheory.Measure β\ne : α ≃ᵐ β\n⊢ M... | [
4303,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4302,
1
] |
Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.of_injective | [] | [
151,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Order/SymmDiff.lean | le_symmDiff_iff_left | [
{
"state_after": "ι : Type ?u.66703\nα : Type u_1\nβ : Type ?u.66709\nπ : ι → Type ?u.66714\ninst✝ : GeneralizedBooleanAlgebra α\na b c d : α\nh : a ≤ a ∆ b\n⊢ Disjoint a b",
"state_before": "ι : Type ?u.66703\nα : Type u_1\nβ : Type ?u.66709\nπ : ι → Type ?u.66714\ninst✝ : GeneralizedBooleanAlgebra α\na b ... | [
451,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | List.aestronglyMeasurable_prod | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.313618\nγ : Type ?u.313621\nι : Type ?u.313624\ninst✝⁵ : Countable ι\nm : MeasurableSpace α\nμ : Measure α\ninst✝⁴ : TopologicalSpace β\ninst✝³ : TopologicalSpace γ\nf g : α → β\nM : Type u_2\ninst✝² : Monoid M\ninst✝¹ : TopologicalSpac... | [
1389,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1386,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.BoundedFormula.realize_liftAt_one_self | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.123113\nP : Type ?u.123116\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn✝ l : ℕ\nφ✝ ψ : BoundedFormula L α l\nθ : BoundedFormula L α (Nat.succ l)\nv✝ : α → M\nxs✝ : Fin l → M\nn : ℕ\nφ : ... | [
450,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
446,
1
] |
Mathlib/MeasureTheory/Group/Integration.lean | MeasureTheory.integral_div_right_eq_self | [
{
"state_after": "𝕜 : Type ?u.43478\nM : Type ?u.43481\nα : Type ?u.43484\nG : Type u_1\nE : Type u_2\nF : Type ?u.43493\ninst✝⁷ : MeasurableSpace G\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\nμ : Measure G\nf✝ : G → E\ng✝ : G\ninst✝² : Gro... | [
123,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.nhdsWithin_basis_eball | [] | [
636,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.lt_bsup_of_ne_bsup | [] | [
1519,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1517,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degrees_prod | [
{
"state_after": "case refine'_1\nR : Type u\nS : Type v\nσ : Type u_2\nτ : Type ?u.39868\nr : R\ne : ℕ\nn m : σ\ns✝ : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\nι : Type u_1\ns : Finset ι\nf : ι → MvPolynomial σ R\n⊢ degrees (∏ i in ∅, f i) ≤ ∑ i in ∅, degrees (f i)\n\ncase refine'_2\nR : Type u\n... | [
179,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_ofPNatList | [
{
"state_after": "l : List ℕ+\nh : ∀ (p : ℕ+), p ∈ l → PNat.Prime p\nthis : prod (ofPNatMultiset (↑l) h) = Multiset.prod ↑l\n⊢ prod (ofPNatList l h) = List.prod l",
"state_before": "l : List ℕ+\nh : ∀ (p : ℕ+), p ∈ l → PNat.Prime p\n⊢ prod (ofPNatList l h) = List.prod l",
"tactic": "have := prod_ofPNatM... | [
213,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
210,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.prod_Ico_div_bot | [] | [
246,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.tendsto_translation_number' | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\n⊢ Tendsto (fun n => (↑(f ^ (n + 1)) x - x) / (↑n + 1)) atTop (𝓝 (τ f))",
"tactic": "exact_mod_cast (tendsto_add_atTop_iff_nat 1).2 (f.tendsto_translationNumber x)"
}
] | [
803,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/Order/SymmDiff.lean | symmDiff_hnot_self | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.56061\nα : Type u_1\nβ : Type ?u.56067\nπ : ι → Type ?u.56072\ninst✝ : CoheytingAlgebra α\na : α\n⊢ a ∆ (￢a) = ⊤",
"tactic": "rw [symmDiff_comm, hnot_symmDiff_self]"
}
] | [
355,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Valid'.node4L_lemma₁ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.278351\ninst✝ : Preorder α\na b c d : ℕ\nlr₂ : 3 * (b + c + 1 + d) ≤ 16 * a + 9\nmr₂ : b + c + 1 ≤ 3 * d\nmm₁ : b ≤ 3 * c\n⊢ b < 3 * a + 1",
"tactic": "linarith"
}
] | [
1143,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1142,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.real_le_real | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ ↑x ≤ ↑y ↔ x ≤ y",
"tactic": "simp [le_def, ofReal']"
}
] | [
1157,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1157,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.succ_pos' | [] | [
170,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.hasEqualizer_of_hasKernel | [] | [
355,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
352,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arcsin_projIcc | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arcsin ↑(projIcc (-1) 1 (_ : -1 ≤ 1) x) = arcsin x",
"tactic": "rw [arcsin, Function.comp_apply, IccExtend_val, Function.comp_apply, IccExtend,\n Function.comp_apply]"
}
] | [
61,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.le_mod_add_mod_of_dvd_add_of_not_dvd | [
{
"state_after": "m n a✝ b✝ c✝ d a b c : ℕ\nh : c ∣ a + b\nha : ¬c ∣ a\nhc : ¬c ≤ a % c + b % c\nthis : (a + b) % c = a % c + b % c\n⊢ False",
"state_before": "m n a✝ b✝ c✝ d a b c : ℕ\nh : c ∣ a + b\nha : ¬c ∣ a\nhc : ¬c ≤ a % c + b % c\n⊢ False",
"tactic": "have : (a + b) % c = a % c + b % c := add_mo... | [
493,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | mem_span_finset | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nM : Type u_1\nN : Type ?u.761155\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid N\ninst✝ : Module R N\ns : Finset M\nx : M\nhx : x ∈ span R ↑s\n⊢ x ∈ span R (_root_.id '' ↑s)",
"tactic": "rwa [Set.im... | [
1180,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
] |
Mathlib/Data/Complex/Exponential.lean | isCauSeq_of_decreasing_bounded | [
{
"state_after": "α : Type u_1\nβ : Type ?u.7193\ninst✝³ : Ring β\ninst✝² : LinearOrderedField α\ninst✝¹ : Archimedean α\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → α\na : α\nm : ℕ\nham : ∀ (n : ℕ), n ≥ m → abs' (f n) ≤ a\nhnm : ∀ (n : ℕ), n ≥ m → f (Nat.succ n) ≤ f n\nε : α\nε0 : ε > 0\nk : ℕ\nhk : a ≤ ... | [
71,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
] |
Std/Logic.lean | dite_not | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nP : Prop\ninst✝ : Decidable P\nx : ¬P → α\ny : ¬¬P → α\n⊢ dite (¬P) x y = dite P (fun h => y (_ : ¬¬P)) x",
"tactic": "by_cases h : P <;> simp [h]"
}
] | [
704,
30
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
702,
9
] |
Mathlib/Data/Int/Parity.lean | Int.even_xor'_odd' | [
{
"state_after": "case inl.intro\nm n k : ℤ\n⊢ Xor' (k + k = 2 * k) (k + k = 2 * k + 1)\n\ncase inr.intro\nm n k : ℤ\n⊢ Xor' (2 * k + 1 = 2 * k) (2 * k + 1 = 2 * k + 1)",
"state_before": "m n✝ n : ℤ\n⊢ ∃ k, Xor' (n = 2 * k) (n = 2 * k + 1)",
"tactic": "rcases even_or_odd n with (⟨k, rfl⟩ | ⟨k, rfl⟩) <;>... | [
86,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/SetTheory/Game/PGame.lean | PGame.Equiv.ge | [] | [
749,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
748,
1
] |
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