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/Computability/TuringMachine.lean | Turing.TM2to1.addBottom_nth_snd | [
{
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"tactic": "c... | [
2391,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2389,
1
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Mathlib/Algebra/Order/Floor.lean | Nat.floor_lt_ceil_of_lt_of_pos | [
{
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358,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
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Mathlib/LinearAlgebra/Determinant.lean | Basis.det_ne_zero | [
{
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548,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
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Mathlib/Data/Nat/Factorial/Basic.lean | Nat.one_lt_factorial | [] | [
121,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
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Mathlib/Init/Logic.lean | and_self_iff | [] | [
152,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
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Mathlib/Data/Complex/Basic.lean | Complex.ofReal_mul' | [] | [
288,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
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Mathlib/Order/CompleteLattice.lean | le_iSup₂ | [] | [
799,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.withDensity_absolutelyContinuous | [
{
"state_after": "α : Type u_1\nβ : Type ?u.1763263\nγ : Type ?u.1763266\nδ : Type ?u.1763269\nm✝ : MeasurableSpace α\nμ✝ ν : Measure α\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\ns : Set α\nhs₁ : MeasurableSet s\nhs₂ : ↑↑μ s = 0\n⊢ ↑↑(withDensity μ f) s = 0",
"state_before": "α : Type u_1\nβ : Typ... | [
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43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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1
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Mathlib/Topology/Constructions.lean | ContinuousAt.restrictPreimage | [] | [
1104,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
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Mathlib/Data/Dfinsupp/Interval.lean | Dfinsupp.card_Icc | [] | [
182,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nonempty.some_mem | [] | [
474,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
11
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Mathlib/CategoryTheory/Generator.lean | CategoryTheory.groupoid_of_isCodetecting_empty | [] | [
250,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
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Mathlib/Computability/TuringMachine.lean | Turing.TM1to1.tr_respects | [
{
"state_after": "case intro.intro\nΓ : Type u_1\ninst✝² : Inhabited Γ\nΛ : Type u_3\ninst✝¹ : Inhabited Λ\nσ : Type u_2\ninst✝ : Inhabited σ\nn : ℕ\nenc : Γ → Vector Bool n\ndec : Vector Bool n → Γ\nenc0 : enc default = Vector.replicate n false\nM : Λ → Stmt₁\nencdec : ∀ (a : Γ), dec (enc a) = a\nenc₀ : enc de... | [
1891,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/ZMod/Basic.lean | ZMod.int_cast_rightInverse | [] | [
219,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
218,
1
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Mathlib/Order/Chain.lean | IsMaxChain.top_mem | [] | [
154,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
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Mathlib/Data/PNat/Factors.lean | PrimeMultiset.prod_dvd_iff' | [
{
"state_after": "u : PrimeMultiset\nn : ℕ+\nh : prod u ∣ prod (PNat.factorMultiset n) ↔ u ≤ PNat.factorMultiset n := prod_dvd_iff\n⊢ prod u ∣ n ↔ u ≤ PNat.factorMultiset n",
"state_before": "u : PrimeMultiset\nn : ℕ+\n⊢ prod u ∣ n ↔ u ≤ PNat.factorMultiset n",
"tactic": "let h := @prod_dvd_iff u n.fact... | [
360,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Connected.lean | irreducibleComponent_subset_connectedComponent | [] | [
722,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Polynomial/Basic.lean | Polynomial.ext_iff | [
{
"state_after": "case ofFinsupp\nR : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q✝ q : R[X]\ntoFinsupp✝ : AddMonoidAlgebra R ℕ\n⊢ { toFinsupp := toFinsupp✝ } = q ↔ ∀ (n : ℕ), coeff { toFinsupp := toFinsupp✝ } n = coeff q n",
"state_before": "R : Type u\na b : R\nm n : ℕ\ninst✝ : Semiring R\np✝ q✝ p q ... | [
790,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
785,
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Mathlib/CategoryTheory/Monad/Basic.lean | CategoryTheory.ComonadHom.id_toNatTrans | [] | [
257,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
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] |
Mathlib/Data/Set/Basic.lean | Set.sep_subset | [] | [
1429,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1429,
1
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Mathlib/Analysis/NormedSpace/WeakDual.lean | NormedSpace.Dual.isClosed_image_polar_of_mem_nhds | [] | [
242,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Probability/Independence/Basic.lean | ProbabilityTheory.indepSet_iff_indepSets_singleton | [
{
"state_after": "no goals",
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605,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
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] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.fst_comp_prod | [] | [
571,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.continuous_log | [] | [
312,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
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] |
Mathlib/LinearAlgebra/AdicCompletion.lean | isPrecomplete_iff | [] | [
80,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.erase_injOn' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.220219\nγ : Type ?u.220222\ninst✝ : DecidableEq α\ns✝ t✝ u v : Finset α\na✝ b a : α\ns : Finset α\nhs : s ∈ {s | a ∈ s}\nt : Finset α\nht : t ∈ {s | a ∈ s}\nh : erase s a = (fun s => erase s a) t\n⊢ s = t",
"tactic": "rw [← insert_e... | [
2020,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2019,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Complex.sin_two_pi | [
{
"state_after": "no goals",
"state_before": "⊢ sin (2 * ↑π) = 0",
"tactic": "simp [two_mul, sin_add]"
}
] | [
1130,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1130,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Real.lean | Real.rpow_sub_one | [
{
"state_after": "no goals",
"state_before": "x✝ y✝ z x : ℝ\nhx : x ≠ 0\ny : ℝ\n⊢ x ^ (y - 1) = x ^ y / x",
"tactic": "simpa using rpow_sub_nat hx y 1"
}
] | [
350,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.bind_map_comm | [
{
"state_after": "no goals",
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"tactic": "simp"... | [
184,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.empty_of_word_prod_eq_one | [
{
"state_after": "ι : Type u_1\nM : ι → Type ?u.898798\ninst✝⁴ : (i : ι) → Monoid (M i)\nN : Type ?u.898809\ninst✝³ : Monoid N\nhnontriv : Nontrivial ι\nG : Type u_3\ninst✝² : Group G\nH : ι → Type u_2\ninst✝¹ : (i : ι) → Group (H i)\nf : (i : ι) → H i →* G\nhcard : 3 ≤ (#ι) ∨ ∃ i, 3 ≤ (#H i)\nα : Type ?u.89959... | [
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83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
806,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_ofAdd | [] | [
1197,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1196,
1
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Mathlib/Algebra/Parity.lean | IsSquare.map | [
{
"state_after": "case intro\nF : Type u_3\nα : Type u_1\nβ : Type u_2\nR : Type ?u.2218\ninst✝² : MulOneClass α\ninst✝¹ : MulOneClass β\ninst✝ : MonoidHomClass F α β\nf : F\nm : α\n⊢ IsSquare (↑f (m * m))",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\nR : Type ?u.2218\ninst✝² : MulOneClass α\... | [
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23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
1
] |
Mathlib/Data/Fintype/Card.lean | Finset.card_lt_iff_ne_univ | [] | [
277,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
275,
1
] |
src/lean/Init/Control/Lawful.lean | seq_eq_bind | [
{
"state_after": "no goals",
"state_before": "m : Type u → Type u_1\nα β : Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nmf : m (α → β)\nx : m α\n⊢ (Seq.seq mf fun x_1 => x) = do\n let f ← mf\n f <$> x",
"tactic": "rw [bind_map]"
}
] | [
78,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
77,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsLittleO.triangle | [] | [
1172,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1170,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | one_div_lt_one_div_of_neg | [] | [
891,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
890,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.colimitEquivQuot_symm_apply | [] | [
297,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
295,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.eq_re_ofReal_le | [
{
"state_after": "case a\nr : ℝ\nz : ℂ\nhz : ↑r ≤ z\n⊢ z.re = (↑z.re).re\n\ncase a\nr : ℝ\nz : ℂ\nhz : ↑r ≤ z\n⊢ z.im = (↑z.re).im",
"state_before": "r : ℝ\nz : ℂ\nhz : ↑r ≤ z\n⊢ z = ↑z.re",
"tactic": "ext"
},
{
"state_after": "case a\nr : ℝ\nz : ℂ\nhz : ↑r ≤ z\n⊢ z.im = (↑z.re).im",
"state_... | [
1194,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1191,
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.degree_map_le | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm✝ n : ℕ\ninst✝¹ : Semiring R\np✝ q r : R[X]\ninst✝ : Semiring S\nf : R →+* S\np : R[X]\nm : ℕ\nhm : degree p < ↑m\n⊢ coeff (map f p) m = 0",
"state_before": "R : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ :... | [
840,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
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Mathlib/LinearAlgebra/Matrix/ToLin.lean | Matrix.toLin_eq_toLin' | [] | [
550,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Order/Disjoint.lean | IsCompl.of_le | [] | [
490,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.ConnectedComponent.sound | [] | [
2000,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1998,
11
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Mathlib/Topology/Maps.lean | openEmbedding_of_continuous_injective_open | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.257906\nδ : Type ?u.257909\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : TopologicalSpace γ\nf : α → β\nh₁ : Continuous f\nh₂ : Injective f\nh₃ : IsOpenMap f\n⊢ ∀ (a : α), 𝓝 a = comap f (𝓝 (f a))",
"state_before": "α : Type u_1... | [
600,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.I_mul | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ (I * z).re = { re := -z.im, im := z.re }.re ∧ (I * z).im = { re := -z.im, im := z.re }.im",
"tactic": "simp"
}
] | [
319,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Analysis/Calculus/Monotone.lean | Monotone.ae_differentiableAt | [
{
"state_after": "no goals",
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"tactic": "filter_upwards [hf.ae_hasDerivAt] with x hx using hx.differentiableAt"
}
] | [
223,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/List/OfFn.lean | List.ofFn_mul | [
{
"state_after": "case zero\nα : Type u\nm n : ℕ\nf✝ : Fin (m * n) → α\nf : Fin (zero * n) → α\n⊢ ofFn f = join (ofFn fun i => ofFn fun j => f { val := ↑i * n + ↑j, isLt := (_ : ↑i * n + ↑j < zero * n) })\n\ncase succ\nα : Type u\nm✝ n : ℕ\nf✝ : Fin (m✝ * n) → α\nm : ℕ\nIH :\n ∀ (f : Fin (m * n) → α),\n ofF... | [
175,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Algebra/Algebra/Equiv.lean | AlgEquiv.symm_toRingEquiv | [] | [
384,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
383,
1
] |
Mathlib/Data/Set/Function.lean | Set.EqOn.mapsTo_iff | [] | [
420,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
419,
1
] |
Mathlib/Algebra/Module/LinearMap.lean | LinearMap.mul_eq_comp | [] | [
1026,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
1
] |
Mathlib/Data/Set/Intervals/Disjoint.lean | Set.iUnion_Iic | [] | [
68,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Data/List/Range.lean | List.chain_range_succ | [
{
"state_after": "α : Type u\nr : ℕ → ℕ → Prop\nn a : ℕ\n⊢ r a 0 → (Chain r 0 (map succ (range n)) ↔ Chain' (fun m => r m) (0 :: map succ (range n)))",
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"tactic": "rw [range_su... | [
110,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
src/lean/Init/Core.lean | heq_of_eqRec_eq | [
{
"state_after": "α : Sort u\na b : α\nh₂ : Eq.rec a (_ : α = α) = b\n⊢ HEq a b",
"state_before": "α β : Sort u\na : α\nb : β\nh₁ : α = β\nh₂ : Eq.rec a h₁ = b\n⊢ HEq a b",
"tactic": "subst h₁"
},
{
"state_after": "case h\nα : Sort u\na b : α\nh₂ : Eq.rec a (_ : α = α) = b\n⊢ a = b",
"state_... | [
650,
11
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
647,
1
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Mathlib/Order/Filter/Basic.lean | Filter.comap_coe_neBot_of_le_principal | [] | [
2432,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2430,
1
] |
Mathlib/SetTheory/Cardinal/Finite.lean | Nat.card_eq_two_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9840\n⊢ (#α) = ↑2 ↔ (#α) = 2",
"tactic": "rw [Nat.cast_two]"
}
] | [
91,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.one_le_iff_ne_zero | [] | [
87,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Analysis/Calculus/DiffContOnCl.lean | DiffContOnCl.smul | [] | [
129,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
126,
1
] |
Mathlib/Topology/Sets/Compacts.lean | TopologicalSpace.CompactOpens.isOpen | [] | [
477,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
11
] |
Mathlib/Deprecated/Submonoid.lean | powers.mul_mem | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninst✝¹ : Monoid M\ns : Set M\nA : Type ?u.21578\ninst✝ : AddMonoid A\nt : Set A\nx y z : M\nx✝¹ : y ∈ powers x\nx✝ : z ∈ powers x\nn₁ : ℕ\nh₁ : x ^ n₁ = y\nn₂ : ℕ\nh₂ : x ^ n₂ = z\n⊢ x ^ (n₁ + n₂) = y * z",
"tactic": "simp only [pow_add, *]"
... | [
155,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.not_one_mem_ker | [
{
"state_after": "R : Type u\nS : Type v\nT : Type w\nF : Type u_1\nG : Type ?u.1722384\ninst✝³ : Semiring R\ninst✝² : Semiring S\ninst✝¹ : Semiring T\nrcf : RingHomClass F R S\nrcg : RingHomClass G T S\nf✝ : F\ng : G\ninst✝ : Nontrivial S\nf : F\n⊢ ¬1 = 0",
"state_before": "R : Type u\nS : Type v\nT : Type... | [
2019,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2017,
1
] |
Mathlib/SetTheory/Cardinal/SchroederBernstein.lean | Function.Embedding.min_injective | [
{
"state_after": "no goals",
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134,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | ChainComplex.mk'_d_1_0 | [
{
"state_after": "ι : Type ?u.191407\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nX₀ X₁ X₂ : V\nd₀ : X₁ ⟶ X₀\nd₁ : X₂ ⟶ X₁\ns : d₁ ≫ d₀ = 0\nsucc :\n (t : (X₀ : V) ×' (X₁ : V) ×' (X₂ : V) ×' (d₀ : X₁ ⟶ X₀) ×' (d₁ : X₂ ⟶ X₁) ×' d₁ ≫ d₀ = 0) →\n (X₃ : V) ×' (d₂ : X₃ ⟶ t.snd.snd.fst) ×' d₂ ≫ t... | [
779,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
777,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineMap.lean | AffineMap.lineMap_vsub_right | [
{
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646,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
645,
1
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Mathlib/Data/Set/Sups.lean | Set.singleton_sups_singleton | [] | [
157,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Cardinal.derivBFamily_lt_ord_lift | [
{
"state_after": "no goals",
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1192,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1188,
1
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Mathlib/Algebra/MonoidAlgebra/Support.lean | AddMonoidAlgebra.mem_span_support' | [
{
"state_after": "k : Type u₁\nG : Type u₂\ninst✝ : Semiring k\nf : AddMonoidAlgebra k G\n⊢ f ∈ Submodule.span k ((fun a => single a 1) '' ↑f.support)",
"state_before": "k : Type u₁\nG : Type u₂\ninst✝ : Semiring k\nf : AddMonoidAlgebra k G\n⊢ f ∈ Submodule.span k (of' k G '' ↑f.support)",
"tactic": "de... | [
153,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/List/Card.lean | List.card_insert_of_mem | [
{
"state_after": "no goals",
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"tactic": "simp [h]"
}
] | [
93,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
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] |
Mathlib/Algebra/Order/Monoid/WithTop.lean | WithTop.add_lt_add_right | [
{
"state_after": "case intro\nα : Type u\nβ : Type v\ninst✝² : Add α\nb c d : WithTop α\nx y : α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (swap fun x x_1 => x + x_1) fun x x_1 => x < x_1\nh : b < c\na : α\n⊢ b + ↑a < c + ↑a",
"state_before": "α : Type u\nβ : Type v\ninst✝² : Add α\na b c d : WithTop α\nx ... | [
257,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
11
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Mathlib/Analysis/Calculus/ContDiffDef.lean | contDiffWithinAt_insert | [
{
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521,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
516,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval_C_mul | [
{
"state_after": "no goals",
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"tactic": "induction p using Polynomial.induction_on' with\n| h_add p q ph qh =>\n simp only [mul_add, eval_add, ... | [
410,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSubOfPoint_eq_of_weights_eq | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_1\ns : Finset ι\nι₂ : Type ?u.26193\ns₂ : Finset ι₂\np : ι → P\nj : ι\nw₁ w₂ : ι → k\nhw : ∀ (i : ι), i ≠ j → w₁ i = w₂ i\n⊢ ∑ i in s, w₁ i • (p i -ᵥ p j) = ∑... | [
113,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Analysis/NormedSpace/Ray.lean | SameRay.eq_of_norm_eq | [] | [
115,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.pow_right | [] | [
171,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.smul_comap_le_comap_smul | [
{
"state_after": "R : Type u\nM : Type v\nF : Type ?u.162652\nG : Type ?u.162655\ninst✝⁴ : CommSemiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\nI✝ J : Ideal R\nN P : Submodule R M\nS✝ : Set R\nT : Set M\nM' : Type w\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'\nf : M →ₗ[R] M'\nS : Submodule R M'\nI... | [
348,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Topology/SubsetProperties.lean | CompactExhaustion.exists_mem | [] | [
1472,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1471,
1
] |
Mathlib/Logic/Equiv/Set.lean | Equiv.subset_image | [
{
"state_after": "no goals",
"state_before": "α✝ : Sort u\nβ✝ : Sort v\nγ : Sort w\nα : Type u_1\nβ : Type u_2\ne : α ≃ β\ns : Set α\nt : Set β\n⊢ ↑e.symm '' t ⊆ s ↔ t ⊆ ↑e '' s",
"tactic": "rw [image_subset_iff, e.image_eq_preimage]"
}
] | [
66,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
11
] |
Mathlib/Analysis/MeanInequalitiesPow.lean | ENNReal.add_rpow_le_rpow_add | [
{
"state_after": "ι : Type u\ns : Finset ι\np : ℝ\na b : ℝ≥0∞\nhp1 : 1 ≤ p\nhp_pos : 0 < p\n⊢ a ^ p + b ^ p ≤ (a + b) ^ p",
"state_before": "ι : Type u\ns : Finset ι\np : ℝ\na b : ℝ≥0∞\nhp1 : 1 ≤ p\n⊢ a ^ p + b ^ p ≤ (a + b) ^ p",
"tactic": "have hp_pos : 0 < p := by positivity"
},
{
"state_afte... | [
318,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Order/Disjoint.lean | Codisjoint.eq_top_of_ge | [] | [
283,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.bounded_of_finite | [] | [
2408,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2407,
1
] |
Mathlib/RingTheory/PrincipalIdealDomain.lean | Submodule.IsPrincipal.principal | [] | [
61,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.biprod.lift_eq | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\ninst✝² : Preadditive C\nJ : Type\ninst✝¹ : Fintype J\nX Y : C\ninst✝ : HasBinaryBiproduct X Y\nT : C\nf : T ⟶ X\ng : T ⟶ Y\n⊢ lift f g = f ≫ inl + g ≫ inr",
"tactic": "ext <;> simp [add_comp]"
}
] | [
455,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Algebra/IndicatorFunction.lean | Set.mulIndicator_mul_eq_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.65680\nι : Type ?u.65683\nM : Type u_2\nN : Type ?u.65689\ninst✝ : MulOneClass M\ns t : Set α\nf✝ g✝ : α → M\na : α\nf g : α → M\nh : Disjoint (mulSupport f) (mulSupport g)\nx : α\nhx : x ∈ mulSupport f\n⊢ (f * g) x = f x",
"state_before": "α : Type u_1\nβ : Type ... | [
449,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
445,
1
] |
Mathlib/Order/Lattice.lean | SemilatticeSup.ext_sup | [
{
"state_after": "α✝ : Type u\nβ : Type v\ninst✝ : SemilatticeSup α✝\na b c✝ d : α✝\nα : Type u_1\nA B : SemilatticeSup α\nH : ∀ (x y : α), x ≤ y ↔ x ≤ y\nx y c : α\n⊢ x ⊔ y ≤ c ↔ x ≤ c ∧ y ≤ c",
"state_before": "α✝ : Type u\nβ : Type v\ninst✝ : SemilatticeSup α✝\na b c✝ d : α✝\nα : Type u_1\nA B : Semilatt... | [
326,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_iff_rank_le_one | [] | [
324,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
323,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.norm_equiv_symm_single | [] | [
853,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
852,
1
] |
Mathlib/Topology/MetricSpace/Equicontinuity.lean | Metric.uniformEquicontinuous_iff | [] | [
87,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.ofFinsupp_sum | [] | [
377,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Algebra/Order/Sub/Canonical.lean | lt_tsub_iff_left_of_le | [] | [
264,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
263,
1
] |
Mathlib/Analysis/Seminorm.lean | Seminorm.sup_apply | [] | [
248,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
247,
1
] |
Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Functor.eqToHom_proj | [
{
"state_after": "I : Type w₀\nJ : Type w₁\nC : I → Type u₁\ninst✝² : (i : I) → Category (C i)\nD : I → Type u₁\ninst✝¹ : (i : I) → Category (D i)\nA : Type u₁\ninst✝ : Category A\nx : (i : I) → C i\ni : I\n⊢ eqToHom (_ : x = x) i = eqToHom (_ : x i = x i)",
"state_before": "I : Type w₀\nJ : Type w₁\nC : I ... | [
247,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/FieldTheory/IsAlgClosed/Basic.lean | isAlgClosure_iff | [] | [
184,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/CategoryTheory/Bicategory/Basic.lean | CategoryTheory.Bicategory.associator_naturality_left | [
{
"state_after": "no goals",
"state_before": "B : Type u\ninst✝ : Bicategory B\na b c d e : B\nf f' : a ⟶ b\nη : f ⟶ f'\ng : b ⟶ c\nh : c ⟶ d\n⊢ η ▷ g ▷ h ≫ (α_ f' g h).hom = (α_ f g h).hom ≫ η ▷ (g ≫ h)",
"tactic": "simp"
}
] | [
345,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
1
] |
Mathlib/Data/Bool/AllAny.lean | List.any_of_mem | [] | [
55,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Order/Heyting/Basic.lean | le_himp_iff | [] | [
318,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
317,
1
] |
src/lean/Init/Core.lean | Subtype.eq | [] | [
961,
31
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
960,
11
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_sup_homogeneousIdeal | [] | [
241,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Topology/Homotopy/Equiv.lean | ContinuousMap.HomotopyEquiv.toFun_eq_coe | [] | [
67,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.hausdorffDist_le_of_infDist | [
{
"state_after": "case pos\nι : Sort ?u.75570\nα : Type u\nβ : Type v\ninst✝¹ : PseudoMetricSpace α\ninst✝ : PseudoMetricSpace β\ns t u : Set α\nx y : α\nΦ : α → β\nr : ℝ\nhr : 0 ≤ r\nH1 : ∀ (x : α), x ∈ s → infDist x t ≤ r\nH2 : ∀ (x : α), x ∈ t → infDist x s ≤ r\nh1 : hausdorffEdist s t = ⊤\n⊢ hausdorffDist s... | [
764,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
745,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | HasDerivWithinAt.arsinh | [] | [
311,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/MeasureTheory/Measure/Doubling.lean | IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul | [
{
"state_after": "α : Type u_1\ninst✝² : MetricSpace α\ninst✝¹ : MeasurableSpace α\nμ : MeasureTheory.Measure α\ninst✝ : IsUnifLocDoublingMeasure μ\nK : ℝ\nh :\n ∀ᶠ (ε : ℝ) in 𝓝[Ioi 0] 0,\n ∀ (x : α) (t : ℝ),\n t ≤ K →\n ↑↑μ (closedBall x (t * ε)) ≤\n ↑(Classical.choose\n ... | [
135,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Rel.lean | Rel.image_univ | [
{
"state_after": "case h\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.16693\nr : Rel α β\ny : β\n⊢ y ∈ image r Set.univ ↔ y ∈ codom r",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type ?u.16693\nr : Rel α β\n⊢ image r Set.univ = codom r",
"tactic": "ext y"
},
{
"state_after": "no goals",
"s... | [
171,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
169,
1
] |
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