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/Pow/NNReal.lean | ENNReal.rpow_lt_rpow_iff | [] | [
578,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
577,
1
] |
Mathlib/LinearAlgebra/Pi.lean | LinearEquiv.piRing_symm_apply | [
{
"state_after": "no goals",
"state_before": "R : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nι' : Type x'\ninst✝¹³ : Semiring R\nφ : ι → Type ?u.240876\nψ : ι → Type ?u.240881\nχ : ι → Type ?u.240886\ninst✝¹² : (i : ι) → AddCo... | [
431,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isBigO_const_smul_left | [
{
"state_after": "α : Type u_2\nβ : Type ?u.546930\nE : Type ?u.546933\nF : Type u_4\nG : Type ?u.546939\nE' : Type u_3\nF' : Type ?u.546945\nG' : Type ?u.546948\nE'' : Type ?u.546951\nF'' : Type ?u.546954\nG'' : Type ?u.546957\nR : Type ?u.546960\nR' : Type ?u.546963\n𝕜 : Type u_1\n𝕜' : Type ?u.546969\ninst✝... | [
1717,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1713,
1
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Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_snorm | [
{
"state_after": "case pos\nα : Type ?u.20404\nβ : Type u_2\nι : Type ?u.20410\nE : Type u_1\nF : Type ?u.20416\n𝕜 : Type ?u.20419\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : MeasurableSpace E\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\nq : ℝ\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\n... | [
140,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
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Mathlib/Order/Heyting/Basic.lean | hnot_hnot_le | [] | [
1080,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1079,
1
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Mathlib/RingTheory/Localization/Integer.lean | IsLocalization.exist_integer_multiples_of_finset | [] | [
123,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/CategoryTheory/Preadditive/AdditiveFunctor.lean | CategoryTheory.AdditiveFunctor.ofLeftExact_obj_fst | [] | [
290,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
288,
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] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | lift.SubfieldWithHom.maximal_subfieldWithHom_chain_bounded | [
{
"state_after": "case pos\nk : Type u\ninst✝⁶ : Field k\nK : Type u\nL : Type v\nM : Type w\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : Field M\ninst✝¹ : Algebra K M\ninst✝ : IsAlgClosed M\nhL : Algebra.IsAlgebraic K L\nE₁ E₂ E₃ : SubfieldWithHom K L M\nc : Set (SubfieldWithHom K L M)\n... | [
273,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | div_le_comm | [] | [
840,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
839,
1
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Mathlib/GroupTheory/Coset.lean | leftCosetEquivalence_rel | [] | [
103,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
102,
1
] |
Mathlib/Data/Finset/Pointwise.lean | Finset.smul_def | [] | [
1269,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1268,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | MeasureTheory.FiniteMeasure.toMeasure_add | [] | [
224,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Nat.euler_four_squares | [
{
"state_after": "a b c d x y z w : ℕ\n⊢ ↑(Int.natAbs (↑a * ↑x - ↑b * ↑y - ↑c * ↑z - ↑d * ↑w) ^ 2 + Int.natAbs (↑a * ↑y + ↑b * ↑x + ↑c * ↑w - ↑d * ↑z) ^ 2 +\n Int.natAbs (↑a * ↑z - ↑b * ↑w + ↑c * ↑x + ↑d * ↑y) ^ 2 +\n Int.natAbs (↑a * ↑w + ↑b * ↑z - ↑c * ↑y + ↑d * ↑x) ^ 2) =\n ↑((a ^ 2 + b ^ ... | [
50,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/PNat/Prime.lean | PNat.Coprime.coprime_dvd_left | [
{
"state_after": "m k n : ℕ+\n⊢ ↑m ∣ ↑k → Coprime k n → Coprime m n",
"state_before": "m k n : ℕ+\n⊢ m ∣ k → Coprime k n → Coprime m n",
"tactic": "rw [dvd_iff]"
},
{
"state_after": "m k n : ℕ+\n⊢ ↑m ∣ ↑k → coprime ↑k ↑n → coprime ↑m ↑n",
"state_before": "m k n : ℕ+\n⊢ ↑m ∣ ↑k → Coprime k n ... | [
261,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
1
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Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.id_right | [] | [
341,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.rotateR_size | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Sized l\n⊢ size (Ordnode.rotateR l x r) = size l + size r + 1",
"tactic": "rw [← size_dual, dual_rotateR, hl.dual.rotateL_size, size_dual, size_dual, add_comm (size l)]"
}
] | [
431,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
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Mathlib/Data/Fintype/Fin.lean | Fin.Iio_castSucc | [
{
"state_after": "case a\nα : Type ?u.8321\nβ : Type ?u.8324\nn : ℕ\ni : Fin n\n⊢ map valEmbedding (Iio (↑castSucc i)) = map valEmbedding (map castSucc.toEmbedding (Iio i))",
"state_before": "α : Type ?u.8321\nβ : Type ?u.8324\nn : ℕ\ni : Fin n\n⊢ Iio (↑castSucc i) = map castSucc.toEmbedding (Iio i)",
"... | [
72,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/Order/Filter/Bases.lean | Filter.HasBasis.prod_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.81162\nγ : Type ?u.81165\nι : Sort u_2\nι' : Sort ?u.81171\nla : Filter α\npa : ι → Prop\nsa : ι → Set α\nlb : Filter β\npb : ι' → Prop\nsb : ι' → Set β\nf : α → β\nhl : HasBasis la pa sa\ni j : ι\nhi : pa i\nhj : pa j\n⊢ ∃ k, pa k ∧ sa... | [
939,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
935,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.mulVec_mulVec | [
{
"state_after": "case h\nl : Type ?u.885794\nm : Type u_3\nn : Type u_1\no : Type u_2\nm' : o → Type ?u.885808\nn' : o → Type ?u.885813\nR : Type ?u.885816\nS : Type ?u.885819\nα : Type v\nβ : Type w\nγ : Type ?u.885826\ninst✝² : NonUnitalSemiring α\ninst✝¹ : Fintype n\ninst✝ : Fintype o\nv : o → α\nM : Matrix... | [
1832,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1828,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyRel.trans_apply | [] | [
650,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
644,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Ideal.sup_mul | [] | [
782,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.blimsup_monotone_filter | [] | [
886,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
885,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.isRegular_succ | [
{
"state_after": "case intro\nα✝ : Type ?u.145277\nr : α✝ → α✝ → Prop\nc : Cardinal\nh : ℵ₀ ≤ c\nα : Type u\nαe : Quotient.mk isEquivalent α = succ c\n⊢ c < Ordinal.cof (ord (succ c))",
"state_before": "α : Type ?u.145277\nr : α → α → Prop\nc : Cardinal\nh : ℵ₀ ≤ c\n⊢ c < Ordinal.cof (ord (succ c))",
"t... | [
998,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.toLin_toMatrix | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type u_2\nκ : Type ?u.289930\nκ' : Type ?u.289933\nR : Type u_3\nM : Type u_4\ninst✝⁸ : CommSemiring R\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nR₂ : Type ?u.290126\nM₂ : Type ?u.290129\ninst✝⁵ : CommRing R₂\ninst✝⁴ : AddCommGroup M₂\nin... | [
134,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/Analysis/Complex/Basic.lean | Complex.continuous_normSq | [
{
"state_after": "no goals",
"state_before": "E : Type ?u.191731\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\n⊢ Continuous ↑normSq",
"tactic": "simpa [← normSq_eq_abs] using continuous_abs.pow 2"
}
] | [
181,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
180,
1
] |
Mathlib/Order/OrderIsoNat.lean | Nat.exists_subseq_of_forall_mem_union | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns✝ : Set ℕ\ninst✝ : Infinite ↑s✝\ns t : Set α\ne : ℕ → α\nhe : ∀ (n : ℕ), e n ∈ s ∪ t\n⊢ ∃ g, (∀ (n : ℕ), e (↑g n) ∈ s) ∨ ∀ (n : ℕ), e (↑g n) ∈ t",
"tactic": "classical\n have : Infinite (e ⁻¹' s) ∨ Infinite (e ⁻¹' t) := by\n simp only [Set... | [
164,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.SimpleFunc.norm_integral_le_integral_norm | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.205081\n𝕜 : Type ?u.205084\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : NormedSpace ℝ F\np : ℝ≥0∞\nG : Type ?u.205186\nF' : Type ?u.205189\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : NormedAddCommGroup F'\ninst✝⁴ : NormedSpace ℝ ... | [
448,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/NumberTheory/Fermat4.lean | Fermat42.exists_odd_minimal | [
{
"state_after": "case intro.intro.intro\na b c : ℤ\nh : Fermat42 a b c\na0 b0 c0 : ℤ\nhf : Minimal a0 b0 c0\n⊢ ∃ a0 b0 c0, Minimal a0 b0 c0 ∧ a0 % 2 = 1",
"state_before": "a b c : ℤ\nh : Fermat42 a b c\n⊢ ∃ a0 b0 c0, Minimal a0 b0 c0 ∧ a0 % 2 = 1",
"tactic": "obtain ⟨a0, b0, c0, hf⟩ := exists_minimal h... | [
140,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Deprecated/Ring.lean | IsRingHom.id | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝¹ : Ring α\ninst✝ : Ring β\nf : α → β\nhf : IsRingHom f\nx y : α\n⊢ IsRingHom _root_.id",
"tactic": "refine' { .. } <;> intros <;> rfl"
}
] | [
123,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
123,
1
] |
Mathlib/Data/Sigma/Order.lean | Sigma.mk_le_mk_iff | [] | [
73,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Order/UpperLower/Basic.lean | LowerSet.mem_sSup_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.75951\nγ : Type ?u.75954\nι : Sort ?u.75957\nκ : ι → Sort ?u.75962\ninst✝ : LE α\nS : Set (LowerSet α)\ns t : LowerSet α\na : α\n⊢ (∃ i j, a ∈ ↑i) ↔ ∃ s, s ∈ S ∧ a ∈ s",
"tactic": "simp only [exists_prop, SetLike.mem_coe]"
}
] | [
743,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
] |
Mathlib/GroupTheory/GroupAction/ConjAct.lean | ConjAct.stabilizer_eq_centralizer | [] | [
312,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Combinatorics/Young/YoungDiagram.lean | YoungDiagram.coe_inf | [] | [
150,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
149,
1
] |
Mathlib/Data/Nat/Parity.lean | Odd.mod_even | [] | [
358,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_of_mem | [] | [
898,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
896,
1
] |
Mathlib/Data/Nat/Bits.lean | Nat.bit1_eq_one | [
{
"state_after": "n : ℕ\n⊢ bit1 0 = 1",
"state_before": "n✝ n : ℕ\nh : n = 0\n⊢ bit1 n = 1",
"tactic": "subst h"
},
{
"state_after": "no goals",
"state_before": "n : ℕ\n⊢ bit1 0 = 1",
"tactic": "rfl"
}
] | [
84,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.div_lt_one_iff | [] | [
620,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
619,
1
] |
Mathlib/Analysis/Convex/Combination.lean | convexHull_add | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nE : Type u_1\nF : Type ?u.407254\nι : Type ?u.407257\nι' : Type ?u.407260\nα : Type ?u.407263\ninst✝⁷ : LinearOrderedField R\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : LinearOrderedAddCommGroup α\ninst✝³ : Module R E\ninst✝² : Modu... | [
431,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_of_mul_le_left | [] | [
236,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.traverse_eq_map_id | [
{
"state_after": "case mk\nF G : Type u → Type u\ninst✝³ : Applicative F\ninst✝² : Applicative G\ninst✝¹ : LawfulApplicative F\ninst✝ : LawfulApplicative G\nα✝ β✝ γ : Type u\nα β : Type u_1\nf : α → β\nx : List α\n⊢ Vector.traverse (pure ∘ f) { val := x, property := (_ : List.length x = List.length x) } =\n ... | [
692,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
11
] |
Mathlib/Data/List/Rdrop.lean | List.mem_rtakeWhile_imp | [
{
"state_after": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\nhx : x ∈ takeWhile p (reverse l)\n⊢ p x = true",
"state_before": "α : Type u_1\np : α → Bool\nl : List α\nn : ℕ\nx : α\nhx : x ∈ rtakeWhile p l\n⊢ p x = true",
"tactic": "rw [rtakeWhile, mem_reverse] at hx"
},
{
"state_after... | [
243,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.map_map | [] | [
1872,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1871,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.map_zero | [] | [
331,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
330,
11
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.aeval_eq_constantCoeff_of_vars | [] | [
838,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
Mathlib/Data/Set/Sigma.lean | Set.mk_preimage_sigma_fn_eq_if | [
{
"state_after": "no goals",
"state_before": "ι : Type u_2\nι' : Type ?u.13241\nα : ι → Type u_3\nβ✝ : ι → Type ?u.13251\ns s₁ s₂ : Set ι\nt t₁ t₂ : (i : ι) → Set (α i)\nu : Set ((i : ι) × α i)\nx : (i : ι) × α i\ni j : ι\na : α i\nβ : Type u_1\ninst✝ : DecidablePred fun x => x ∈ s\ng : β → α i\nx✝ : β\n⊢ x... | [
197,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.ext_nonempty | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.23881\nR : Type ?u.23884\nR' : Type ?u.23887\nms : Set (OuterMeasure α)\nm μ₁ μ₂ : OuterMeasure α\nh : ∀ (s : Set α), Set.Nonempty s → ↑μ₁ s = ↑μ₂ s\ns : Set α\nhe : s = ∅\n⊢ ↑μ₁ s = ↑μ₂ s",
"tactic": "rw [he, empty', empty']"
}
] | [
252,
88
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250,
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.comap_iSup | [
{
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558,
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Mathlib/RingTheory/MatrixAlgebra.lean | MatrixEquivTensor.left_inv | [
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigOWith.smul | [
{
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Mathlib/Logic/Equiv/Defs.lean | Equiv.conj_refl | [] | [
572,
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Mathlib/Order/GaloisConnection.lean | GaloisCoinsertion.u_biSup_l | [] | [
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Mathlib/CategoryTheory/Limits/Shapes/KernelPair.lean | CategoryTheory.IsKernelPair.comp_of_mono | [
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_one' | [
{
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Mathlib/Topology/Algebra/InfiniteSum/Order.lean | tsum_lt_tsum | [] | [
178,
37
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Mathlib/Algebra/BigOperators/Finprod.lean | finprod_true | [] | [
236,
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Mathlib/GroupTheory/FreeAbelianGroup.lean | FreeAbelianGroup.seq_neg | [] | [
314,
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Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.eq_one_of_pos_of_logb_eq_zero | [] | [
236,
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Mathlib/Topology/Order/Hom/Basic.lean | ContinuousOrderHom.cancel_left | [
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Mathlib/Geometry/Manifold/LocalInvariantProperties.lean | StructureGroupoid.LocalInvariantProp.congr_nhdsWithin' | [] | [
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Mathlib/Probability/ProbabilityMassFunction/Constructions.lean | Pmf.filter_apply_ne_zero_iff | [
{
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297,
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_eq_sub_fract_mul | [
{
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Mathlib/AlgebraicGeometry/StructureSheaf.lean | AlgebraicGeometry.StructureSheaf.localizationToStalk_mk' | [
{
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Mathlib/RingTheory/Nilpotent.lean | isNilpotent_iff_eq_zero | [] | [
90,
59
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Mathlib/LinearAlgebra/ProjectiveSpace/Subspace.lean | Projectivization.Subspace.span_univ | [
{
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160,
39
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157,
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Mathlib/Order/BoundedOrder.lean | Subtype.coe_bot | [] | [
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43
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771,
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Mathlib/Data/Matrix/Block.lean | Matrix.blockDiag'_diagonal | [
{
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Mathlib/Topology/MetricSpace/HausdorffDistance.lean | EMetric.hausdorffEdist_closure₁ | [
{
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401,
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Mathlib/FieldTheory/Subfield.lean | Subfield.multiset_prod_mem | [] | [
300,
22
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Mathlib/Data/List/Basic.lean | List.head!_cons | [] | [
886,
90
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Mathlib/Data/Set/Basic.lean | Set.inter_subset_right | [] | [
954,
75
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Mathlib/GroupTheory/GroupAction/SubMulAction/Pointwise.lean | SubMulAction.subset_coe_pow | [
{
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134,
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Mathlib/Data/Set/Basic.lean | Set.union_diff_cancel | [] | [
1830,
27
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1829,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mul_eq_left | [
{
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}
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652,
59
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651,
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src/lean/Init/Core.lean | cast_heq | [] | [
653,
25
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652,
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Mathlib/Data/Real/NNReal.lean | NNReal.div_le_div_left | [] | [
860,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
858,
8
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src/lean/Init/SimpLemmas.lean | eq_false_of_decide | [] | [
26,
34
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25,
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Mathlib/Order/WithBot.lean | WithBot.monotone_map_iff | [
{
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349,
43
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347,
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Mathlib/Data/Real/NNReal.lean | Real.lt_toNNReal_iff_coe_lt | [] | [
691,
48
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690,
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Mathlib/Algebra/Category/GroupCat/EpiMono.lean | GroupCat.SurjectiveOfEpiAuxs.τ_apply_infinity | [] | [
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29
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184,
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Mathlib/SetTheory/Ordinal/Arithmetic.lean | WellFounded.rank_strictAnti | [] | [
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50
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2579,
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Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₈'_nat_eq_if_mod_eight | [
{
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}
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209,
43
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Mathlib/Topology/Homeomorph.lean | Homeomorph.piCongrRight_symm | [] | [
549,
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Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.norm_sub_norm_compl_sub_single | [
{
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41
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Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.chromaticNumber_top | [
{
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376,
18
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369,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mk'_mul_coeIdeal_eq_coeIdeal | [
{
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Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.Equivalence.functor_asEquivalence | [
{
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588,
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586,
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Mathlib/Analysis/LocallyConvex/Basic.lean | Balanced.neg_mem_iff | [
{
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315,
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313,
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Mathlib/Data/Set/Basic.lean | Set.strictAntiOn_singleton | [] | [
2709,
40
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2708,
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Mathlib/Data/List/Sublists.lean | List.sublists_concat | [
{
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180,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Lattice.lean | List.inter_nil | [] | [
142,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
141,
1
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src/lean/Init/Data/List/Basic.lean | List.length_replicate | [
{
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}
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27
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767,
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Mathlib/Data/Seq/Seq.lean | Stream'.Seq.eq_of_bisim | [
{
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412,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Polynomial/Lifts.lean | Polynomial.lifts_iff_liftsRing | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝¹ : Ring R\nS : Type v\ninst✝ : Ring S\nf : R →+* S\np : S[X]\n⊢ p ∈ lifts f ↔ p ∈ liftsRing f",
"tactic": "simp only [lifts, liftsRing, RingHom.mem_range, RingHom.mem_rangeS]"
}
] | [
261,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
260,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | LinearIsometryEquiv.comp_hasFDerivAt_iff | [] | [
331,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
329,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.Ici_sSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.297530\nγ : Type ?u.297533\nι : Sort ?u.297536\nι' : Sort ?u.297539\nι₂ : Sort ?u.297542\nκ : ι → Sort ?u.297547\nκ₁ : ι → Sort ?u.297552\nκ₂ : ι → Sort ?u.297557\nκ' : ι' → Sort ?u.297562\ninst✝ : CompleteLattice α\ns : Set α\n⊢ Ici (s... | [
2142,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2142,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.disjoint_of_nodup_add | [] | [
123,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/MeasureTheory/Integral/VitaliCaratheodory.lean | MeasureTheory.exists_upperSemicontinuous_le_integral_le | [
{
"state_after": "case intro\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : WeaklyRegular μ\nf : α → ℝ≥0\nfint : Integrable fun x => ↑(f x)\nε : ℝ≥0\nεpos : 0 < ↑ε\n⊢ ∃ g,\n (∀ (x : α), g x ≤ f x) ∧\n UpperSemicontinuous g ∧ (Integra... | [
456,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
430,
1
] |
Mathlib/Algebra/Lie/Free.lean | FreeLieAlgebra.Rel.smulOfTower | [
{
"state_after": "R : Type u\nX : Type v\ninst✝³ : CommRing R\nS : Type u_1\ninst✝² : Monoid S\ninst✝¹ : DistribMulAction S R\ninst✝ : IsScalarTower S R R\nt : S\na b : lib R X\nh : Rel R X a b\n⊢ Rel R X ((t • 1) • a) ((t • 1) • b)",
"state_before": "R : Type u\nX : Type v\ninst✝³ : CommRing R\nS : Type u_... | [
114,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
1
] |
Mathlib/RingTheory/Subsemiring/Pointwise.lean | Subsemiring.coe_pointwise_smul | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiable_pi | [] | [
450,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
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