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/Algebra/Order/CompleteField.lean | LinearOrderedField.exists_mem_cutMap_mul_self_of_lt_inducedMap_mul_self | [
{
"state_after": "case inl\nF : Type ?u.29742\nα : Type u_1\nβ : Type u_2\nγ : Type ?u.29751\ninst✝³ : LinearOrderedField α\ninst✝² : ConditionallyCompleteLinearOrderedField β\ninst✝¹ : ConditionallyCompleteLinearOrderedField γ\ninst✝ : Archimedean α\na : α\nb✝ : β\nq : ℚ\nha : 0 < a\nb : β\nhba : b < inducedMa... | [
287,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.frequently_or_distrib_left | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type ?u.164287\nι : Sort x\nf : Filter α\ninst✝ : NeBot f\np : Prop\nq : α → Prop\n⊢ (∃ᶠ (x : α) in f, p ∨ q x) ↔ p ∨ ∃ᶠ (x : α) in f, q x",
"tactic": "simp"
}
] | [
1346,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1345,
1
] |
Mathlib/Analysis/Normed/Group/Basic.lean | NormedCommGroup.tendsto_nhds_nhds | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.108981\n𝕜 : Type ?u.108984\nα : Type ?u.108987\nι : Type ?u.108990\nκ : Type ?u.108993\nE : Type u_1\nF : Type u_2\nG : Type ?u.109002\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : ... | [
751,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.range_empty | [] | [
175,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.map_bit0 | [] | [
772,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
771,
11
] |
Mathlib/Data/Int/Bitwise.lean | Int.testBit_lor | [
{
"state_after": "no goals",
"state_before": "m n : ℤ\nk : ℕ\n⊢ testBit (lor m n) k = (testBit m k || testBit n k)",
"tactic": "rw [← bitwise_or, testBit_bitwise]"
}
] | [
346,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/NumberTheory/Padics/PadicIntegers.lean | PadicInt.coe_add | [] | [
125,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.iSup_lt_lift_of_isRegular | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.160553\nr : α → α → Prop\nι : Type u\nf : ι → Cardinal\nc : Cardinal\nhc : IsRegular c\nhι : lift (#ι) < c\n⊢ lift (#ι) < Ordinal.cof (ord c)",
"tactic": "rwa [hc.cof_eq]"
}
] | [
1105,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1103,
1
] |
Mathlib/Topology/MetricSpace/Isometry.lean | Isometry.ediam_image | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.44257\nα : Type u\nβ : Type v\nγ : Type w\ninst✝² : PseudoEMetricSpace α\ninst✝¹ : PseudoEMetricSpace β\ninst✝ : PseudoEMetricSpace γ\nf : α → β\nx y z : α\ns✝ : Set α\nhf : Isometry f\ns : Set α\nd : ℝ≥0∞\n⊢ EMetric.diam (f '' s) ≤ d ↔ EMetric.diam ... | [
157,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Submodule.torsionBy.mk_smul | [] | [
589,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
587,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.aeval_monomial | [] | [
1535,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1533,
1
] |
Mathlib/Data/List/Rotate.lean | List.mem_cyclicPermutations_iff | [
{
"state_after": "case mp\nα : Type u\nl✝ l'✝ l l' : List α\n⊢ l ∈ cyclicPermutations l' → l ~r l'\n\ncase mpr\nα : Type u\nl✝ l'✝ l l' : List α\n⊢ l ~r l' → l ∈ cyclicPermutations l'",
"state_before": "α : Type u\nl✝ l'✝ l l' : List α\n⊢ l ∈ cyclicPermutations l' ↔ l ~r l'",
"tactic": "constructor"
}... | [
640,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/Analysis/SpecialFunctions/Stirling.lean | Stirling.tendsto_stirlingSeq_sqrt_pi | [
{
"state_after": "case intro.intro\na : ℝ\nhapos : 0 < a\nhalimit : Tendsto stirlingSeq atTop (𝓝 a)\n⊢ Tendsto (fun n => stirlingSeq n) atTop (𝓝 (Real.sqrt π))",
"state_before": "⊢ Tendsto (fun n => stirlingSeq n) atTop (𝓝 (Real.sqrt π))",
"tactic": "obtain ⟨a, hapos, halimit⟩ := stirlingSeq_has_pos_... | [
271,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mul_power | [] | [
589,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.ListBlank.cons_head_tail | [
{
"state_after": "case h\nΓ : Type u_1\ninst✝ : Inhabited Γ\n⊢ ∀ (a : List Γ), cons (head (Quotient.mk'' a)) (tail (Quotient.mk'' a)) = Quotient.mk'' a",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\n⊢ ∀ (l : ListBlank Γ), cons (head l) (tail l) = l",
"tactic": "apply Quotient.ind'"
},
{
"... | [
273,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.IsPushout.of_is_coproduct' | [] | [
394,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
392,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.piecewise_apply' | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nι : Type ?u.1459789\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ η : { x // x ∈ kernel α β }\ns : Set α\nhs : MeasurableSet s\ninst✝ : DecidablePred fun x => x ∈ s\na : α\nt : Set β\n⊢ ↑↑(if a ∈ s then ↑κ a else ↑η a) t = if a ∈ s then ↑↑(↑κ a) t else ↑↑(↑η a)... | [
623,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
621,
1
] |
Mathlib/Topology/ContinuousOn.lean | Set.MapsTo.closure_of_continuousWithinAt | [] | [
739,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Algebra/Periodic.lean | Function.Periodic.int_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.105416\nf g : α → β\nc c₁ c₂ x : α\ninst✝ : Ring α\nh : Periodic f c\nn : ℤ\n⊢ Periodic f (↑n * c)",
"tactic": "simpa only [zsmul_eq_mul] using h.zsmul n"
}
] | [
241,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
240,
11
] |
Mathlib/Data/Fin/Basic.lean | Fin.succAbove_predAbove | [
{
"state_after": "n m : ℕ\np : Fin n\ni : Fin (n + 1)\nh : i ≠ ↑castSucc p\n⊢ (if ↑castSucc (if h : ↑castSucc p < i then pred i (_ : i ≠ 0) else castLT i (_ : ↑i < n)) < ↑castSucc p then\n ↑castSucc (if h : ↑castSucc p < i then pred i (_ : i ≠ 0) else castLT i (_ : ↑i < n))\n else succ (if h : ↑castSucc... | [
2384,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2367,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum_pos' | [
{
"state_after": "case zero\nα : Type u\nβ : Type ?u.241921\nx : α\ninst✝ : LinearOrderedRing α\nhx : 0 < x + 1\nhn : Nat.zero ≠ 0\n⊢ 0 < ∑ i in range Nat.zero, x ^ i\n\ncase succ.zero\nα : Type u\nβ : Type ?u.241921\nx : α\ninst✝ : LinearOrderedRing α\nhx : 0 < x + 1\nhn : Nat.succ Nat.zero ≠ 0\n⊢ 0 < ∑ i in r... | [
516,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Analysis/InnerProductSpace/Calculus.lean | DifferentiableWithinAt.inner | [] | [
130,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
127,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_tsum | [
{
"state_after": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.1015473\nδ : Type ?u.1015476\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : Countable β\nf : β → α → ℝ≥0∞\nhf : ∀ (i : β), AEMeasurable (f i)\n⊢ (∫⁻ (a : α), ⨆ (s : Finset β), ∑ i in s, f i a ∂μ) = ⨆ (s : Finset β), ∑ i in s, ∫⁻ (a : α), f i a ∂μ",
... | [
1179,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1168,
1
] |
Std/Data/PairingHeap.lean | Std.PairingHeapImp.Heap.size_merge | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nle : α → α → Bool\ns₁ s₂ : Heap α\nh₁ : NoSibling s₁\nh₂ : NoSibling s₂\n⊢ size (merge le s₁ s₂) = size s₁ + size s₂",
"tactic": "match h₁, h₂ with\n| .nil, .nil | .nil, .node _ _ | .node _ _, .nil => simp [size]\n| .node _ _, .node _ _ => unfo... | [
128,
77
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
124,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sinh_add_cosh | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sinh x + cosh x = exp x",
"tactic": "rw [add_comm, cosh_add_sinh]"
}
] | [
1407,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1407,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.Bijective.of_comp_iff | [] | [
267,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | MultilinearMap.mkContinuousLinear_norm_le | [] | [
1092,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1090,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.mem_divisorsAntidiagonal | [
{
"state_after": "n : ℕ\nx : ℕ × ℕ\n⊢ ((1 ≤ x.fst ∧ x.fst < n + 1) ∧ 1 ≤ x.snd ∧ x.snd < n + 1) ∧ x.fst * x.snd = n ↔ x.fst * x.snd = n ∧ ¬n = 0",
"state_before": "n : ℕ\nx : ℕ × ℕ\n⊢ x ∈ divisorsAntidiagonal n ↔ x.fst * x.snd = n ∧ n ≠ 0",
"tactic": "simp only [divisorsAntidiagonal, Finset.mem_Ico, Ne.... | [
132,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/RingTheory/Polynomial/Cyclotomic/Basic.lean | Polynomial.cyclotomic_one | [
{
"state_after": "R : Type u_1\ninst✝ : Ring R\nhspec : map (Int.castRingHom ℂ) (X - 1) = cyclotomic' 1 ℂ\n⊢ cyclotomic 1 R = X - 1",
"state_before": "R : Type u_1\ninst✝ : Ring R\n⊢ cyclotomic 1 R = X - 1",
"tactic": "have hspec : map (Int.castRingHom ℂ) (X - 1) = cyclotomic' 1 ℂ := by\n simp only [cy... | [
318,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
313,
1
] |
Mathlib/Order/Chain.lean | Flag.le_or_le | [] | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
11
] |
Mathlib/Analysis/SpecialFunctions/Log/Base.lean | Real.logb_le_iff_le_rpow | [
{
"state_after": "no goals",
"state_before": "b x y : ℝ\nhb : 1 < b\nhx : 0 < x\n⊢ logb b x ≤ y ↔ x ≤ b ^ y",
"tactic": "rw [← rpow_le_rpow_left_iff hb, rpow_logb (b_pos hb) (b_ne_one' hb) hx]"
}
] | [
164,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.isCobounded_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.20125\nγ : Type ?u.20128\nι : Type ?u.20131\nr : α → α → Prop\nf g : Filter α\n⊢ IsCobounded r ⊤ ↔ Nonempty α",
"tactic": "simp (config := { contextual := true }) [IsCobounded, eq_univ_iff_forall,\n exists_true_iff_nonempty]"
}
] | [
221,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Limits.lean | CategoryTheory.preserves_desc_mapCocone | [
{
"state_after": "no goals",
"state_before": "C : Type u₁\ninst✝³ : Category C\nD : Type u₂\ninst✝² : Category D\nG : C ⥤ D\nJ : Type w\ninst✝¹ : Category J\nF : J ⥤ C\ninst✝ : PreservesColimit F G\nc₁ c₂ : Cocone F\nt : IsColimit c₁\n⊢ ∀ (j : J), (G.mapCocone c₁).ι.app j ≫ G.map (IsColimit.desc t c₂) = (G.... | [
107,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Basic.lean | Set.setOf_and | [] | [
302,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/BigOperators/Multiset/Basic.lean | Multiset.pow_count | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.36621\nα : Type u_1\nβ : Type ?u.36627\nγ : Type ?u.36630\ninst✝¹ : CommMonoid α\ns t : Multiset α\na✝ : α\nm : Multiset ι\nf g : ι → α\ninst✝ : DecidableEq α\na : α\n⊢ a ^ count a s = prod (filter (Eq a) s)",
"tactic": "rw [filter_eq, prod_repli... | [
154,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Init/Function.lean | Function.RightInverse.id | [] | [
153,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
11
] |
Mathlib/Analysis/Normed/Group/Basic.lean | lipschitzOnWith_iff_norm_div_le | [
{
"state_after": "no goals",
"state_before": "𝓕 : Type ?u.185016\n𝕜 : Type ?u.185019\nα : Type ?u.185022\nι : Type ?u.185025\nκ : Type ?u.185028\nE : Type u_1\nF : Type u_2\nG : Type ?u.185037\ninst✝² : SeminormedGroup E\ninst✝¹ : SeminormedGroup F\ninst✝ : SeminormedGroup G\ns : Set E\na a₁ a₂ b b₁ b₂ : ... | [
803,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/RingTheory/Bezout.lean | IsBezout.dvd_gcd | [
{
"state_after": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsBezout R\nx y z : R\nhx : Ideal.span {x} ≤ Ideal.span {z}\nhy : Ideal.span {y} ≤ Ideal.span {z}\n⊢ Ideal.span {gcd x y} ≤ Ideal.span {z}",
"state_before": "R : Type u\ninst✝¹ : CommRing R\ninst✝ : IsBezout R\nx y z : R\nhx : z ∣ x\nhy : z ∣ y\n⊢ z... | [
82,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.sInter_lift'_sets | [] | [
274,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
273,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.comap_preimage | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.252454\nγ : Type ?u.252457\nδ : Type ?u.252460\nι : Type ?u.252463\nR : Type ?u.252466\nR' : Type ?u.252469\nm0 : MeasurableSpace α\ninst✝² : MeasurableSpace β✝\ninst✝¹ : MeasurableSpace γ\nμ✝ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns✝ s' t :... | [
1381,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1377,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.restrOpen_toLocalEquiv | [] | [
687,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.closedBall_subset_closedBall | [] | [
580,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
579,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_zero | [] | [
77,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Order/Hom/Order.lean | OrderHom.iInf_apply | [] | [
96,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Logic/Nonempty.lean | nonempty_sigma | [] | [
50,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Algebra/Hom/Iterate.lean | MonoidHom.iterate_map_zpow | [] | [
84,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Prod.lean | differentiableWithinAt_pi | [] | [
435,
86
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432,
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Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.inv | [] | [
230,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.edgeSet_fromEdgeSet | [
{
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625,
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Mathlib/RingTheory/Derivation/Basic.lean | Derivation.coe_add_linearMap | [] | [
214,
6
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213,
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Mathlib/RingTheory/Finiteness.lean | Submodule.fg_of_fg_map_of_fg_inf_ker | [
{
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335,
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264,
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Mathlib/LinearAlgebra/Matrix/Transvection.lean | Matrix.Pivot.exists_list_transvec_mul_mul_list_transvec_eq_diagonal_induction | [
{
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622,
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598,
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Mathlib/Algebra/Algebra/Unitization.lean | Unitization.inr_mul_inl | [
{
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428,
64
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424,
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Mathlib/Analysis/Convex/Side.lean | AffineSubspace.SSameSide.trans_wSameSide | [] | [
559,
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557,
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Mathlib/Order/CompleteLattice.lean | iInf_option | [] | [
1580,
25
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1579,
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Mathlib/Data/Real/CauSeqCompletion.lean | CauSeq.Completion.cau_seq_zero_ne_one | [
{
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248,
47
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245,
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Mathlib/Logic/Lemmas.lean | dite_dite_distrib_right | [
{
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43,
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Mathlib/Data/Finsupp/Multiset.lean | Finsupp.toMultiset_sum_single | [
{
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] | [
81,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
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Mathlib/Data/Matrix/Basic.lean | Matrix.row_vecMul | [
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2705,
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.opow_le_of_limit | [
{
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] | [
71,
77
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70,
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Mathlib/Order/Filter/Basic.lean | Filter.tendsto_principal | [
{
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3042,
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3040,
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_smul | [] | [
190,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
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Mathlib/Analysis/Calculus/Darboux.lean | exists_hasDerivWithinAt_eq_of_gt_of_lt | [
{
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67,
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_one_le_add_one_iff_of_lt_aleph_0 | [] | [
895,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
894,
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Mathlib/RingTheory/Bezout.lean | IsBezout.span_gcd | [] | [
68,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/Data/Real/ENNReal.lean | ENNReal.div_lt_of_lt_mul | [
{
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] | [
1620,
55
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1619,
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Mathlib/Data/Setoid/Basic.lean | Setoid.ext' | [] | [
61,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | LocalHomeomorph.continuousOn_extend_symm | [] | [
867,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
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Mathlib/Algebra/DirectLimit.lean | AddCommGroup.DirectLimit.of.zero_exact | [] | [
323,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
321,
1
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Mathlib/Topology/Order/Basic.lean | nhds_top_order | [
{
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] | [
1131,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
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Mathlib/Data/Set/Function.lean | Function.insert_injOn | [] | [
1691,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1690,
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Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.closed_range | [] | [
302,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
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Mathlib/Data/Countable/Defs.lean | countable_iff_exists_surjective | [] | [
68,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
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Mathlib/CategoryTheory/Limits/Shapes/FiniteLimits.lean | CategoryTheory.Limits.hasFiniteWidePullbacks_of_hasFiniteLimits | [] | [
260,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
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] |
Mathlib/Data/List/Rotate.lean | List.rotate_zero | [
{
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}
] | [
46,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
46,
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Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.not_mem | [] | [
62,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
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Mathlib/Algebra/Hom/Ring.lean | AddMonoidHom.coe_fn_mkRingHomOfMulSelfOfTwoNeZero | [] | [
796,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
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Mathlib/Data/List/Basic.lean | List.nil_zipWith | [
{
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}
] | [
1897,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1897,
1
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Mathlib/Data/Stream/Init.lean | Stream'.mem_interleave_left | [
{
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}
] | [
453,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
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Mathlib/Order/Max.lean | isMin_ofDual_iff | [] | [
263,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_disjUnion | [
{
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1001,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1000,
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Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.one_le_div | [
{
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875,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
871,
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Mathlib/Algebra/Lie/Basic.lean | LieModuleEquiv.toEquiv_injective | [
{
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1031,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1026,
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Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.natCast_injective | [] | [
1372,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1371,
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Mathlib/RingTheory/Nilpotent.lean | Commute.isNilpotent_add | [
{
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"state_before": "R S : Type u\nx y : R\ninst✝ : Semiring R\nh_comm : Commute x y\nhx : IsNilpotent x\nhy : IsNilpotent y\n⊢ IsNilpotent (x + y)",
... | [
155,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.neg_coeff' | [] | [
454,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
453,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_smul | [] | [
410,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
409,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_lt_iff_unbounded_le | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝¹ : Preorder α\ninst✝ : NoMaxOrder α\n⊢ Unbounded (fun x x_1 => x < x_1) s ↔ Unbounded (fun x x_1 => x ≤ x_1) s",
"tactic": "simp_rw [← not_bounded_iff, bounded_le_iff_bounded_lt]"
}
] | [
120,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Std/Data/String/Lemmas.lean | Substring.Valid.prev | [
{
"state_after": "m₁ : List Char\nc : Char\nm₂ : List Char\nx✝ : Substring\nh✝ : Valid x✝\ne : (toString x✝).data = m₁ ++ c :: m₂\nl m r : List Char\nh : ValidFor l m r x✝\n⊢ Substring.prev x✝ { byteIdx := utf8Len m₁ + csize c } = { byteIdx := utf8Len m₁ }",
"state_before": "m₁ : List Char\nc : Char\nm₂ : L... | [
999,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
995,
1
] |
Mathlib/Topology/Basic.lean | continuousAt_iff_ultrafilter | [] | [
1728,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1726,
1
] |
Mathlib/Order/Hom/CompleteLattice.lean | sSupHom.cancel_right | [] | [
345,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/CategoryTheory/Idempotents/Karoubi.lean | CategoryTheory.Idempotents.Karoubi.hom_ext | [
{
"state_after": "no goals",
"state_before": "C : Type u_1\ninst✝ : Category C\nP Q : Karoubi C\nf g : P ⟶ Q\nh : f.f = g.f\n⊢ f = g",
"tactic": "simpa [hom_ext_iff] using h"
}
] | [
121,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.card_le_diff_of_interleaved | [] | [
1616,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1609,
1
] |
Mathlib/Topology/ContinuousOn.lean | IsOpenMap.continuousOn_range_of_leftInverse | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.329904\nδ : Type ?u.329907\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\nhf : IsOpenMap f\nfinv : β → α\nhleft : LeftInverse finv f\n⊢ ContinuousOn finv (f '' univ)",
"s... | [
819,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
816,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | Collinear.collinear_insert_iff_of_ne | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nι : Type ?u.318365\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\nh : Collinear k s\np₁ p₂ p₃ : P\nhp₂ : p₂ ∈ s\nhp₃ : p₃ ∈ s\nhp₂p₃ : p₂ ≠ p₃\nhv : vectorSpan k (insert p₁ s) = vectorSpan k ... | [
546,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
538,
1
] |
Mathlib/Topology/Order/LowerTopology.lean | WithLowerTopology.ofLower_toLower | [] | [
92,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
91,
1
] |
Mathlib/RingTheory/OreLocalization/Basic.lean | OreLocalization.eq_of_num_factor_eq | [
{
"state_after": "case mk.mk\nR : Type u_1\ninst✝¹ : Monoid R\nS : Submonoid R\ninst✝ : OreSet S\nr r' r₁ r₂ : R\ns t : { x // x ∈ S }\nh : r * ↑t = r' * ↑t\nr₂' : R\nt' : { x // x ∈ S }\nhr₂ : r₂ * ↑t' = ↑t * r₂'\n⊢ r₁ * r * r₂ /ₒ s = r₁ * r' * r₂ /ₒ s",
"state_before": "R : Type u_1\ninst✝¹ : Monoid R\nS ... | [
145,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
11
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | Embedding.comp_stronglyMeasurable_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nι : Type ?u.139878\ninst✝⁴ : Countable ι\nf✝ g✝ : α → β\nm : MeasurableSpace α\ninst✝³ : TopologicalSpace β\ninst✝² : PseudoMetrizableSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : PseudoMetrizableSpace γ\ng : β → γ\nf : α → β\nhg : _root_.Embedding g\n... | [
712,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
691,
1
] |
Mathlib/MeasureTheory/Measure/Lebesgue/Basic.lean | Real.volume_pi_Ioo | [] | [
228,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_biUnion_partition | [] | [
786,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
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