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/NumberTheory/Padics/PadicVal.lean | padicValRat.le_padicValRat_add_of_le | [
{
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"state_before": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhqr : q + r ≠ 0\nh : padicValRat p q ≤ padicValRat p r\nhq : q = 0\n⊢ padicValRat p q ≤ padicValRat p (q + r)",
"tactic": "simpa [hq] using h"
},
{
"state_after": "no goals",
"state_before": "p : ℕ\nhp : F... | [
372,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
343,
1
] |
Mathlib/Topology/PathConnected.lean | Path.continuous | [] | [
119,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
11
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | HasFDerivAtFilter.add_const | [] | [
184,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
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Mathlib/MeasureTheory/Measure/Regular.lean | MeasureTheory.Measure.InnerRegular.trans | [
{
"state_after": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\np q : Set α → Prop\nU✝ : Set α\nε : ℝ≥0∞\nq' : Set α → Prop\nH : InnerRegular μ p q\nH' : InnerRegular μ q q'\nU : Set α\nhU : q' U\nr : ℝ≥0∞\nhr : r < ↑↑μ U\n⊢ ∃ K, K ⊆ U ∧ p K ∧ r < ↑↑μ K",
"state_before": "α : Type u_1\nm : MeasurableS... | [
194,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
190,
1
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Mathlib/Data/Option/NAry.lean | Option.map_uncurry | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ : Type u_1\nγ : Type u_3\nf✝ : α → β → γ\na : Option α\nb : Option β\nc : Option γ\nf : α → β → γ\nx : Option (α × β)\n⊢ Option.map (uncurry f) x = map₂ f (Option.map Prod.fst x) (Option.map Prod.snd x)",
"tactic": "cases x <;> rfl"
}
] | [
112,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
111,
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Mathlib/GroupTheory/FreeProduct.lean | FreeProduct.Word.prod_empty | [] | [
282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
281,
1
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Mathlib/Order/InitialSeg.lean | PrincipalSeg.trans_top | [] | [
327,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
326,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Monovary.dual_right | [] | [
216,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
1
] |
Std/Data/List/Lemmas.lean | List.get?_concat_length | [
{
"state_after": "α : Type u_1\nb : α\nl : List α\na : α\n⊢ get? (b :: (l ++ [a])) (succ (length l)) = some a",
"state_before": "α : Type u_1\nb : α\nl : List α\na : α\n⊢ get? (b :: l ++ [a]) (length (b :: l)) = some a",
"tactic": "rw [cons_append, length_cons]"
},
{
"state_after": "no goals",
... | [
637,
88
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
635,
9
] |
src/lean/Init/Data/List/Basic.lean | List.length_append | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas bs : List α\n⊢ length (as ++ bs) = length as + length bs",
"tactic": "induction as with\n| nil => simp\n| cons _ as ih => simp [ih, Nat.succ_add]"
},
{
"state_after": "no goals",
"state_before": "case nil\nα... | [
793,
44
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
790,
9
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Mathlib/Deprecated/Subring.lean | Ring.closure_subset | [] | [
196,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Topology/Homotopy/Basic.lean | ContinuousMap.HomotopyWith.continuous | [] | [
450,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
11
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.symm_apply_rel | [
{
"state_after": "no goals",
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"tactic": "rw [← e.map_rel_iff, e.apply_symm_apply]"... | [
799,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
798,
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] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.congr_mk' | [] | [
317,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Init/Data/Bool/Lemmas.lean | Bool.xor_true | [
{
"state_after": "no goals",
"state_before": "b : Bool\n⊢ xor b true = !b",
"tactic": "cases b <;> simp"
}
] | [
53,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
53,
1
] |
Mathlib/Topology/Instances/Rat.lean | Rat.continuous_mul | [] | [
119,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
119,
11
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.map_pow | [] | [
1296,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1295,
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] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.addSalemSpencer_image_sphere | [
{
"state_after": "α : Type ?u.461418\nβ : Type ?u.461421\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ AddSalemSpencer (↑(map (2 * d - 1)) '' ↑(sphere n d k))",
"state_before": "α : Type ?u.461418\nβ : Type ?u.461421\nn d k N : ℕ\nx : Fin n → ℕ\n⊢ AddSalemSpencer ↑(image (↑(map (2 * d - 1))) (sphere n d k))",
"tactic"... | [
196,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/PFunctor/Multivariate/Basic.lean | MvPFunctor.liftR_iff | [
{
"state_after": "case mp\nn m : ℕ\nP : MvPFunctor n\nQ : Fin2 n → MvPFunctor m\nα✝ β : TypeVec m\nα : TypeVec n\nr : ⦃i : Fin2 n⦄ → α i → α i → Prop\nx y : Obj P α\n⊢ LiftR r x y →\n ∃ a f₀ f₁,\n x = { fst := a, snd := f₀ } ∧ y = { fst := a, snd := f₁ } ∧ ∀ (i : Fin2 n) (j : B P a i), r (f₀ i j) (f₁ i ... | [
200,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_to_countable' | [] | [
410,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiff.fderiv_right | [] | [
1066,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
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Mathlib/NumberTheory/LSeries.lean | Nat.ArithmeticFunction.LSeriesSummable_iff_of_re_eq_re | [
{
"state_after": "f : ArithmeticFunction ℂ\nw z : ℂ\nh✝ : w.re = z.re\nh : ∀ (n : ℕ), ↑Complex.abs (↑f n) / ↑Complex.abs (↑n ^ w) = ↑Complex.abs (↑f n) / ↑Complex.abs (↑n ^ z)\n⊢ LSeriesSummable f w ↔ LSeriesSummable f z\n\ncase h\nf : ArithmeticFunction ℂ\nw z : ℂ\nh : w.re = z.re\n⊢ ∀ (n : ℕ), ↑Complex.abs (↑... | [
98,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/RingTheory/WittVector/Teichmuller.lean | WittVector.ghostComponent_teichmuller | [] | [
138,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
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Mathlib/Order/Hom/Lattice.lean | LatticeHom.cancel_left | [
{
"state_after": "no goals",
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1162,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1159,
1
] |
src/lean/Init/Data/Nat/Linear.lean | Nat.Linear.Poly.denote_eq_cancel_eq | [] | [
425,
86
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
424,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_mem_uniformity | [] | [
268,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Algebra/Order/Floor.lean | abs_sub_round | [
{
"state_after": "F : Type ?u.283221\nα : Type u_1\nβ : Type ?u.283227\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α\nx : α\n⊢ x - ↑⌊x + 1 / 2⌋ ≤ 1 / 2 ∧ ↑⌊x + 1 / 2⌋ - x ≤ 1 / 2",
"state_before": "F : Type ?u.283221\nα : Type u_1\nβ : Type ?u.283227\ninst✝¹ : LinearOrderedField α\ninst✝ : FloorRing α... | [
1472,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1468,
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] |
Mathlib/Analysis/SpecialFunctions/ExpDeriv.lean | Complex.contDiff_exp | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : NormedAlgebra 𝕜 ℂ\nn : ℕ\n⊢ ContDiff 𝕜 (↑n) exp",
"state_before": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : NormedAlgebra 𝕜 ℂ\n⊢ ∀ {n : ℕ∞}, ContDiff 𝕜 n exp",
"tactic": "refine' @(contDiff_all_iff_nat.2... | [
72,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.max_eq_sup_withBot | [] | [
1161,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1160,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.add_nat_eq | [] | [
812,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
1
] |
Mathlib/Topology/Constructions.lean | continuous_toMul | [] | [
97,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Algebra/Order/Ring/Defs.lean | pow_pos | [
{
"state_after": "α : Type u\nβ : Type ?u.57127\ninst✝¹ : StrictOrderedSemiring α\na b c d : α\nH : 0 < a\ninst✝ : Nontrivial α\n⊢ 0 < a ^ 0",
"state_before": "α : Type u\nβ : Type ?u.57127\ninst✝ : StrictOrderedSemiring α\na b c d : α\nH : 0 < a\n⊢ 0 < a ^ 0",
"tactic": "nontriviality"
},
{
"st... | [
537,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.mem_val | [] | [
187,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_sigma' | [] | [
670,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
668,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.one_comp | [] | [
1412,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1411,
1
] |
Mathlib/Algebra/Module/Torsion.lean | Module.isTorsionBySet_annihilator_top | [] | [
676,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | mul_lt_mul_right | [] | [
208,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
206,
1
] |
Mathlib/Algebra/Ring/Equiv.lean | RingEquiv.ofBijective_apply | [] | [
452,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Data/Nat/Cast/Basic.lean | Nat.commute_cast | [] | [
82,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
81,
1
] |
Mathlib/Analysis/Convex/Normed.lean | dist_add_dist_of_mem_segment | [
{
"state_after": "ι : Type ?u.46254\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns t : Set E\nx y z : E\nh : SameRay ℝ (y - x) (z - y)\n⊢ ‖x - y‖ + ‖y - z‖ = ‖x - z‖",
"state_before": "ι : Type ?u.46254\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\n... | [
138,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/GroupTheory/Submonoid/Basic.lean | MonoidHom.eqOn_closureM | [] | [
603,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
602,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.monomial_eq_zero | [] | [
355,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
354,
1
] |
Mathlib/Analysis/Normed/Group/Seminorm.lean | GroupNorm.lt_def | [] | [
790,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
789,
1
] |
Mathlib/MeasureTheory/Integral/Average.lean | MeasureTheory.average_mem_openSegment_compl_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type ?u.228473\nm0 : MeasurableSpace α\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : CompleteSpace E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : CompleteSpace F\nμ : Measure α\ns✝ : Set ... | [
192,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
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] |
Mathlib/Data/Real/EReal.lean | EReal.coe_one | [] | [
137,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/BigOperators/Intervals.lean | Finset.sum_range_reflect | [] | [
183,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | MonotoneOn.map_csInf | [] | [
992,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
990,
1
] |
Mathlib/LinearAlgebra/Matrix/ToLin.lean | LinearMap.toMatrix_apply' | [] | [
594,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
592,
1
] |
Mathlib/Data/Part.lean | Part.eta | [] | [
88,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_zpow | [
{
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"state_before": "a b : ℝ\nn✝ : ℕ\nn : ℤ\nh : 0 ≤... | [
377,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
374,
1
] |
Mathlib/Algebra/Group/Basic.lean | div_eq_of_eq_mul' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.65284\nβ : Type ?u.65287\nG : Type u_1\ninst✝ : CommGroup G\na✝ b✝ c✝ d a b c : G\nh : a = b * c\n⊢ a / b = c",
"tactic": "rw [h, div_eq_mul_inv, mul_comm, inv_mul_cancel_left]"
}
] | [
903,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
902,
1
] |
Mathlib/Algebra/Polynomial/GroupRingAction.lean | Polynomial.smul_X | [] | [
62,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Topology/Algebra/Monoid.lean | continuous_mul | [] | [
72,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/NumberTheory/Padics/RingHoms.lean | PadicInt.norm_sub_modPart_aux | [
{
"state_after": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ ↑(r.num - r.num * gcdA r.den p % ↑p * ↑r.den) = 0",
"state_before": "p : ℕ\nhp_prime : Fact (Nat.Prime p)\nr✝ r : ℚ\nh : ‖↑r‖ ≤ 1\n⊢ ↑p ∣ r.num - r.num * gcdA r.den p % ↑p * ↑r.den",
"tactic": "rw [← ZMod.int_cast_zmod_eq_... | [
123,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/RightAngle.lean | EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two | [
{
"state_after": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\np₁ p₂ p₃ : P\nh : inner (p₂ -ᵥ p₃) (p₁ -ᵥ p₂) = 0\nh0 : p₁ = p₂ ∨ p₃ ≠ p₂\n⊢ dist p₃ p₂ / Real.cos (∠ p₂ p₃ p₁) = dist p₁ p₃",
"state_before": "V ... | [
500,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
1
] |
Mathlib/Data/Real/Pi/Wallis.lean | Real.Wallis.le_W | [
{
"state_after": "k : ℕ\n⊢ (2 * ↑k + 1) / (2 * ↑k + 2) ≤ (π / 2)⁻¹ * W k",
"state_before": "k : ℕ\n⊢ (2 * ↑k + 1) / (2 * ↑k + 2) * (π / 2) ≤ W k",
"tactic": "rw [← le_div_iff pi_div_two_pos, div_eq_inv_mul (W k) _]"
},
{
"state_after": "k : ℕ\n⊢ ((2 * ↑k + 1) / (2 * ↑k + 2) * ∫ (x : ℝ) in 0 ..π,... | [
103,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
96,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Type.lean | Equiv.Perm.cycleType_of_card_le_mem_cycleType_add_two | [
{
"state_after": "case intro.intro.intro.intro.intro\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nc g' : Perm α\nhd : Disjoint c g'\nhc : IsCycle c\nhn2 : Fintype.card α < Finset.card (support c) + 2\nhng : Finset.card (support c) ∈ cycleType (c * g')\n⊢ cycleType (c * g') = {Finset.card (support c... | [
320,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
312,
1
] |
Mathlib/RingTheory/WittVector/StructurePolynomial.lean | wittStructureRat_prop | [
{
"state_after": "p : ℕ\nR : Type ?u.65060\nidx : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ ↑(bind₁ (wittStructureRat p Φ)) (W_ ℚ n) =\n ↑(bind₁ fun i => ↑(bind₁ fun k => ↑(bind₁ fun i => ↑(rename (Prod.mk i)) (W_ ℚ k)) Φ) (xInTermsOfW p ℚ i)) (W_ ℚ n)",
"sta... | [
151,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Analysis/BoxIntegral/Partition/Tagged.lean | BoxIntegral.TaggedPrepartition.IsSubordinate.mono' | [] | [
278,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
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Mathlib/ModelTheory/Syntax.lean | FirstOrder.Language.BoundedFormula.IsQF.relabel | [] | [
729,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
727,
1
] |
Mathlib/Analysis/BoxIntegral/Integrability.lean | BoxIntegral.hasIntegralIndicatorConst | [
{
"state_after": "ι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nl : IntegrationParams\nhl : l.bRiemann = false\ns : Set (ι → ℝ)\nhs : MeasurableSet s\nI : Box ι\ny : E\nμ : MeasureTheory.Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nε : ℝ\nε0 : 0 < ε\n... | [
101,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
40,
1
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Mathlib/CategoryTheory/Limits/Constructions/Filtered.lean | CategoryTheory.Limits.hasCoproducts_of_finite_and_filtered | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝² : Category C\nα✝ : Type w\ninst✝¹ : HasFiniteCoproducts C\ninst✝ : HasFilteredColimitsOfSize C\nα : Type w\n⊢ HasColimitsOfShape (Discrete α) C",
"tactic": "classical exact ⟨fun F => HasColimit.mk (liftToFinsetColimitCocone F)⟩"
},
{
... | [
84,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.map_eq | [] | [
1141,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1140,
1
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Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.adjMatrix_pow_apply_eq_card_walk | [
{
"state_after": "V : Type u_1\nα : Type u_2\nβ : Type ?u.68771\nG : SimpleGraph V\ninst✝³ : DecidableRel G.Adj\ninst✝² : Fintype V\ninst✝¹ : DecidableEq V\ninst✝ : Semiring α\nn : ℕ\nu v : V\n⊢ (adjMatrix α G ^ n) u v = ↑(card (finsetWalkLength G n u v))",
"state_before": "V : Type u_1\nα : Type u_2\nβ : T... | [
282,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
264,
1
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src/lean/Init/Control/Lawful.lean | StateT.run_seq | [
{
"state_after": "m : Type u → Type u_1\nα β σ : Type u\ninst✝¹ : Monad m\ninst✝ : LawfulMonad m\nf : StateT σ m (α → β)\nx : StateT σ m α\ns : σ\n⊢ run\n (do\n let g ← f\n g <$> x)\n s =\n do\n let fs ← run f s\n (fun p => (Prod.fst fs p.fst, p.snd)) <$> run x fs.snd",
"sta... | [
278,
7
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
276,
9
] |
Mathlib/Algebra/Group/Basic.lean | div_mul_cancel' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.56920\nβ : Type ?u.56923\nG : Type u_1\ninst✝ : Group G\na✝ b✝ c d a b : G\n⊢ a / b * b = a",
"tactic": "rw [div_eq_mul_inv, inv_mul_cancel_right a b]"
}
] | [
743,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
742,
1
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Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.induction_on'' | [] | [
442,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
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Mathlib/Analysis/SpecialFunctions/Integrals.lean | intervalIntegral.intervalIntegrable_inv_one_add_sq | [
{
"state_after": "a b : ℝ\nn : ℕ\nf : ℝ → ℝ\nμ ν : MeasureTheory.Measure ℝ\ninst✝ : IsLocallyFiniteMeasure μ\nc d : ℝ\n⊢ IntervalIntegrable (fun x => 1 / (1 + x ^ 2)) μ a b",
"state_before": "a b : ℝ\nn : ℕ\nf : ℝ → ℝ\nμ ν : MeasureTheory.Measure ℝ\ninst✝ : IsLocallyFiniteMeasure μ\nc d : ℝ\n⊢ IntervalInteg... | [
243,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Deprecated/Subgroup.lean | Multiplicative.isSubgroup | [] | [
76,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
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Mathlib/Data/Nat/Log.lean | Nat.log_of_lt | [] | [
49,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
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Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.isLittleO_refl_left | [] | [
1216,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.map_subtype_le_map_subtype | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nG'✝ : Type ?u.596430\ninst✝³ : Group G\ninst✝² : Group G'✝\nA : Type ?u.596439\ninst✝¹ : AddGroup A\nN : Type ?u.596445\ninst✝ : Group N\nf : G →* N\nG' : Subgroup G\nH K : Subgroup { x // x ∈ G' }\n⊢ Injective ↑(Subgroup.subtype G')",
"tactic"... | [
3109,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3107,
1
] |
Mathlib/NumberTheory/ClassNumber/AdmissibleAbs.lean | AbsoluteValue.exists_partition_int | [
{
"state_after": "n : ℕ\nε : ℝ\nhε : 0 < ε\nb : ℤ\nhb : b ≠ 0\nA : Fin n → ℤ\nhb' : 0 < ↑(abs b)\n⊢ ∃ t, ∀ (i₀ i₁ : Fin n), t i₀ = t i₁ → ↑(abs (A i₁ % b - A i₀ % b)) < abs b • ε",
"state_before": "n : ℕ\nε : ℝ\nhε : 0 < ε\nb : ℤ\nhb : b ≠ 0\nA : Fin n → ℤ\n⊢ ∃ t, ∀ (i₀ i₁ : Fin n), t i₀ = t i₁ → ↑(abs (A i... | [
54,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
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] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero | [
{
"state_after": "x z✝ z : ℂ\nhre : z.re < 0\nhim : z.im = 0\nH : Tendsto (fun x => arcsin ((-x).im / ↑abs x) - π) (𝓝[{z | z.im < 0}] z) (𝓝 (-π))\n⊢ Tendsto arg (𝓝[{z | z.im < 0}] z) (𝓝 (-π))\n\ncase H\nx z✝ z : ℂ\nhre : z.re < 0\nhim : z.im = 0\n⊢ Tendsto (fun x => arcsin ((-x).im / ↑abs x) - π) (𝓝[{z | z... | [
577,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
559,
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] |
Mathlib/Logic/Equiv/Fin.lean | finSuccEquiv'_succAbove | [] | [
148,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
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Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.restrict_nondegenerate_of_isCompl_orthogonal | [
{
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1450,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1436,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.reachable_iff_exists_finsetWalkLength_nonempty | [
{
"state_after": "case mp\nV : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\ninst✝² : DecidableEq V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nu v : V\n⊢ Reachable G u v → ∃ n, Finset.Nonempty (finsetWalkLength G (↑n) u v)\n\ncase mpr\nV : Type u\nV' : T... | [
2414,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2406,
1
] |
Mathlib/Data/List/Basic.lean | List.tail_append_singleton_of_ne_nil | [
{
"state_after": "case nil\nι : Type ?u.43325\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nh : [] ≠ []\n⊢ tail ([] ++ [a]) = tail [] ++ [a]\n\ncase cons\nι : Type ?u.43325\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na head✝ : α\ntail✝ : List α\ntail_ih✝ : tail✝ ≠ ... | [
908,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
906,
1
] |
Mathlib/Combinatorics/Additive/Behrend.lean | Behrend.bound_aux | [
{
"state_after": "case h.e'_3\nα : Type ?u.578354\nβ : Type ?u.578357\nn d k N : ℕ\nx : Fin n → ℕ\nhd : d ≠ 0\nhn : 2 ≤ n\n⊢ ↑d ^ (↑n - 2) / ↑n = ↑d ^ ↑n / ↑(n * d ^ 2)",
"state_before": "α : Type ?u.578354\nβ : Type ?u.578357\nn d k N : ℕ\nx : Fin n → ℕ\nhd : d ≠ 0\nhn : 2 ≤ n\n⊢ ↑d ^ (↑n - 2) / ↑n ≤ ↑(↑ro... | [
283,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Multiequalizer.lean | CategoryTheory.Limits.Multiequalizer.condition | [] | [
786,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.cast_zero' | [] | [
1042,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1041,
1
] |
Mathlib/ModelTheory/Basic.lean | FirstOrder.Language.Embedding.map_rel | [] | [
633,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | Real.exp_eq_exp_ℝ | [
{
"state_after": "case h\nx : ℝ\n⊢ exp x = _root_.exp ℝ x",
"state_before": "⊢ exp = _root_.exp ℝ",
"tactic": "ext x"
},
{
"state_after": "no goals",
"state_before": "case h\nx : ℝ\n⊢ exp x = _root_.exp ℝ x",
"tactic": "exact_mod_cast congr_fun Complex.exp_eq_exp_ℂ x"
}
] | [
230,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
1
] |
Mathlib/Order/Filter/Lift.lean | Filter.lift_comm | [] | [
143,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | swap_dist | [
{
"state_after": "case h.h\nα : Type u\nβ : Type v\nX : Type ?u.14808\nι : Type ?u.14811\ninst✝ : PseudoMetricSpace α\nx y : α\n⊢ Function.swap dist x y = dist x y",
"state_before": "α : Type u\nβ : Type v\nX : Type ?u.14808\nι : Type ?u.14811\ninst✝ : PseudoMetricSpace α\n⊢ Function.swap dist = dist",
... | [
265,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/Data/Seq/Seq.lean | Stream'.Seq.tail_nil | [] | [
267,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.mul_le_mul_right | [] | [
243,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
242,
1
] |
Mathlib/Analysis/NormedSpace/ContinuousLinearMap.lean | LinearMap.mkContinuousOfExistsBound_coe | [] | [
115,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left' | [
{
"state_after": "α : Type u_1\nE : Type u_2\nF : Type ?u.251923\nF' : Type u_3\nG : Type ?u.251929\n𝕜 : Type ?u.251932\np : ℝ≥0∞\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\ninst✝² : NormedAddCommGroup F'\ninst✝¹ : NormedSpace ℝ F'\ninst✝ :... | [
449,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.SummableFamily.coe_powers | [] | [
1790,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1789,
1
] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.proj_symm_apply' | [] | [
400,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
398,
1
] |
Mathlib/Order/Heyting/Basic.lean | hnot_le_iff_codisjoint_right | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.172893\nα : Type u_1\nβ : Type ?u.172899\ninst✝ : CoheytingAlgebra α\na b c : α\n⊢ ￢a ≤ b ↔ Codisjoint a b",
"tactic": "rw [← top_sdiff', sdiff_le_iff, codisjoint_iff_le_sup]"
}
] | [
1019,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Std/Data/List/Lemmas.lean | List.replaceF_cons_of_some | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\na' a : α\nl : List α\np : α → Option α\nh : p a = some a'\n⊢ replaceF p (a :: l) = a' :: l",
"tactic": "simp [replaceF_cons, h]"
}
] | [
1311,
26
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1309,
1
] |
Mathlib/FieldTheory/IntermediateField.lean | AlgHom.coe_fieldRange | [] | [
473,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | tendsto_exp_div_rpow_atTop | [
{
"state_after": "case intro\ns : ℝ\nn : ℕ\nhn : s < ↑n\n⊢ Tendsto (fun x => exp x / x ^ s) atTop atTop",
"state_before": "s : ℝ\n⊢ Tendsto (fun x => exp x / x ^ s) atTop atTop",
"tactic": "cases' archimedean_iff_nat_lt.1 Real.instArchimedean s with n hn"
},
{
"state_after": "case intro\ns : ℝ\n... | [
98,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Data/List/Perm.lean | List.Perm.swap' | [] | [
72,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Topology/Separation.lean | separatedNhds_iff_disjoint | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : TopologicalSpace α\ns t : Set α\n⊢ SeparatedNhds s t ↔ Disjoint (𝓝ˢ s) (𝓝ˢ t)",
"tactic": "simp only [(hasBasis_nhdsSet s).disjoint_iff (hasBasis_nhdsSet t), SeparatedNhds, exists_prop, ←\n exists_and_left, and_assoc, and_c... | [
112,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.comp_sub | [
{
"state_after": "case h.e'_6.h.e'_1\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type ?u.408332\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf... | [
445,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
] |
Mathlib/Data/Part.lean | Part.toOption_eq_some_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7998\nγ : Type ?u.8001\no : Part α\ninst✝ : Decidable o.Dom\na : α\n⊢ toOption o = Option.some a ↔ a ∈ o",
"tactic": "rw [← Option.mem_def, mem_toOption]"
}
] | [
303,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.abs_intervalIntegral_eq | [] | [
499,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
1
] |
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