file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/PNat/Prime.lean | PNat.Coprime.gcd_mul_right_cancel_right | [
{
"state_after": "m n k : ℕ+\n⊢ Coprime k m → gcd m (k * n) = gcd m n",
"state_before": "m n k : ℕ+\n⊢ Coprime k m → gcd m (n * k) = gcd m n",
"tactic": "rw [mul_comm]"
},
{
"state_after": "no goals",
"state_before": "m n k : ℕ+\n⊢ Coprime k m → gcd m (k * n) = gcd m n",
"tactic": "apply... | [
226,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Std/Data/List/Lemmas.lean | List.disjoint_of_disjoint_append_left_left | [] | [
1396,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1395,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.stabilizer_eq_normalizer | [
{
"state_after": "case h\np : ℕ\nG : Type u_1\ninst✝ : Group G\nP : Sylow p G\nx✝ : G\n⊢ x✝ ∈ stabilizer G P ↔ x✝ ∈ normalizer ↑P",
"state_before": "p : ℕ\nG : Type u_1\ninst✝ : Group G\nP : Sylow p G\n⊢ stabilizer G P = normalizer ↑P",
"tactic": "ext"
},
{
"state_after": "no goals",
"state_... | [
372,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
370,
1
] |
Mathlib/LinearAlgebra/QuotientPi.lean | Submodule.piQuotientLift_single | [
{
"state_after": "ι : Type u_1\nR : Type u_2\ninst✝⁸ : CommRing R\nMs : ι → Type u_3\ninst✝⁷ : (i : ι) → AddCommGroup (Ms i)\ninst✝⁶ : (i : ι) → Module R (Ms i)\nN : Type u_4\ninst✝⁵ : AddCommGroup N\ninst✝⁴ : Module R N\nNs : ι → Type ?u.40793\ninst✝³ : (i : ι) → AddCommGroup (Ns i)\ninst✝² : (i : ι) → Module ... | [
66,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.coe_one | [] | [
245,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.sqLe_smul | [
{
"state_after": "no goals",
"state_before": "d✝ : ℤ\nc d x y n : ℕ\nxy : SqLe x c y d\n⊢ SqLe (n * x) c (n * y) d",
"tactic": "simpa [SqLe, mul_left_comm, mul_assoc] using Nat.mul_le_mul_left (n * n) xy"
}
] | [
464,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
463,
1
] |
Mathlib/GroupTheory/NoncommPiCoprod.lean | Subgroup.commute_subtype_of_commute | [
{
"state_after": "case mk.mk\nG : Type u_2\ninst✝ : Group G\nι : Type u_1\nhdec : DecidableEq ι\nhfin : Fintype ι\nH : ι → Subgroup G\nf g : (i : ι) → { x // x ∈ H i }\nhcomm : ∀ (i j : ι), i ≠ j → ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\ni j : ι\nhne : i ≠ j\nx : G\nhx : x ∈ H i\ny : G\nhy : y ∈ H j\n⊢ Co... | [
301,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.eq_adjoint_iff_basis_right | [
{
"state_after": "𝕜 : Type u_2\nE : Type u_4\nF : Type u_3\nG : Type ?u.2052027\ninst✝⁹ : IsROrC 𝕜\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : NormedAddCommGroup G\ninst✝⁵ : InnerProductSpace 𝕜 E\ninst✝⁴ : InnerProductSpace 𝕜 F\ninst✝³ : InnerProductSpace 𝕜 G\ninst✝² : FiniteDim... | [
452,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | hasFDerivAt_id | [] | [
1003,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Topology/MetricSpace/IsometricSMul.lean | EMetric.preimage_mul_left_closedBall | [] | [
320,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
318,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.zero_div_subset | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.142624\nα : Type u_1\nβ : Type ?u.142630\nγ : Type ?u.142633\ninst✝ : GroupWithZero α\ns✝ t s : Set α\n⊢ 0 / s ⊆ 0",
"tactic": "simp [subset_def, mem_div]"
}
] | [
1277,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1277,
1
] |
Mathlib/Data/List/Cycle.lean | Cycle.chain_range_succ | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.317005\nr : ℕ → ℕ → Prop\nn : ℕ\n⊢ Chain r ↑(range (Nat.succ n)) ↔ r n 0 ∧ ∀ (m : ℕ), m < n → r m (Nat.succ m)",
"tactic": "rw [range_succ, ← coe_cons_eq_coe_append, chain_coe_cons, ← range_succ, chain_range_succ]"
}
] | [
969,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
8
] |
Mathlib/Analysis/Calculus/Deriv/Add.lean | HasDerivWithinAt.sub | [] | [
301,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
8
] |
Mathlib/Algebra/Order/Ring/Defs.lean | Monotone.mul_const | [] | [
278,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Dynamics/Circle/RotationNumber/TranslationNumber.lean | CircleDeg1Lift.iterate_pos_lt_iff | [
{
"state_after": "no goals",
"state_before": "f g : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (↑f^[n]) x < x + ↑n * ↑m ↔ ↑f x < x + ↑m",
"tactic": "simpa only [nsmul_eq_mul, add_right_iterate] using\n (f.commute_add_int m).iterate_pos_lt_iff_map_lt f.monotone (strictMono_id.add_const (m : ℝ)) ... | [
597,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
594,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.convex_strict_hypograph | [] | [
586,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/SetTheory/Ordinal/Topology.lean | Ordinal.mem_closed_iff_sup | [
{
"state_after": "no goals",
"state_before": "s : Set Ordinal\na : Ordinal\nhs : IsClosed s\n⊢ a ∈ s ↔ ∃ ι _hι f, (∀ (i : ι), f i ∈ s) ∧ sup f = a",
"tactic": "rw [← mem_closure_iff_sup, hs.closure_eq]"
}
] | [
138,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Order/Circular.lean | SBtw.sbtw.trans_left | [] | [
240,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
239,
1
] |
Mathlib/Order/Bounded.lean | Set.bounded_lt_inter_le | [
{
"state_after": "case h.e'_1.h.e'_3.h.e'_4.h.e'_2.h.a\nα : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\na x✝ : α\n⊢ a ≤ x✝ ↔ ¬x✝ < a",
"state_before": "α : Type u_1\nr : α → α → Prop\ns t : Set α\ninst✝ : LinearOrder α\na : α\n⊢ Bounded (fun x x_1 => x < x_1) (s ∩ {b | a ≤ b}) ↔ Bounded ... | [
371,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.gcd_mul_right_add_left | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ gcd (k * n + m) n = gcd m n",
"tactic": "rw [gcd_comm, gcd_mul_right_add_right, gcd_comm]"
}
] | [
66,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/Data/Finmap.lean | Finmap.lookup_insert_of_ne | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na a' : α\nb : β a\ns✝ : Finmap β\nh : a' ≠ a\ns : AList β\n⊢ lookup a' (insert a b ⟦s⟧) = lookup a' ⟦s⟧",
"tactic": "simp only [insert_toFinmap, lookup_toFinmap, lookup_insert_ne h]"
}
] | [
508,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.cmpLT.trans_l | [] | [
34,
84
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
33,
1
] |
Std/Data/List/Lemmas.lean | List.isSuffix.filter | [
{
"state_after": "case intro\nα : Type u_1\np : α → Bool\nl₁ xs : List α\n⊢ List.filter p l₁ <:+ List.filter p (xs ++ l₁)",
"state_before": "α : Type u_1\np : α → Bool\nl₁ l₂ : List α\nh : l₁ <:+ l₂\n⊢ List.filter p l₁ <:+ List.filter p l₂",
"tactic": "obtain ⟨xs, rfl⟩ := h"
},
{
"state_after": ... | [
1744,
42
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1741,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.succ_le_iff_isMax | [] | [
234,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Topology/Order/Basic.lean | interior_Iic' | [] | [
2282,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2281,
1
] |
Mathlib/Data/List/Rotate.lean | List.cyclicPermutations_of_ne_nil | [
{
"state_after": "case intro.intro\nα : Type u\nl l' : List α\nhd : α\ntl : List α\nh : hd :: tl ≠ []\n⊢ cyclicPermutations (hd :: tl) = dropLast (zipWith (fun x x_1 => x ++ x_1) (tails (hd :: tl)) (inits (hd :: tl)))",
"state_before": "α : Type u\nl✝ l' l : List α\nh : l ≠ []\n⊢ cyclicPermutations l = drop... | [
587,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
584,
1
] |
Mathlib/Data/Sign.lean | exists_signed_sum_aux | [
{
"state_after": "case refine'_1\nα✝ : Type ?u.131858\nα : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nf : α → ℤ\n⊢ card (Finset.sigma univ fun a => range (Int.natAbs (f ↑a))) = ∑ a in s, Int.natAbs (f a)\n\ncase refine'_2\nα✝ : Type ?u.131858\nα : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\nf : α → ℤ\n⊢ ... | [
508,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
497,
9
] |
Mathlib/Analysis/SpecialFunctions/Pow/Asymptotics.lean | Complex.isTheta_cpow_rpow | [
{
"state_after": "α : Type u_1\nl : Filter α\nf g : α → ℂ\nhl_im : IsBoundedUnder (fun x x_1 => x ≤ x_1) l fun x => Abs.abs (g x).im\nhl : ∀ᶠ (x : α) in l, f x = 0 → (g x).re = 0 → g x = 0\n⊢ (fun x => ↑abs (f x) ^ (g x).re) =ᶠ[l] fun x => ↑abs (f x) ^ (g x).re",
"state_before": "α : Type u_1\nl : Filter α\... | [
194,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Algebra/Algebra/Basic.lean | Module.End_isUnit_iff | [] | [
661,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | Real.hasStrictDerivAt_arsinh | [
{
"state_after": "case h.e'_7.h.e'_3\nx✝ y x : ℝ\n⊢ sqrt (1 + x ^ 2) = cosh (↑(LocalHomeomorph.symm (Homeomorph.toLocalHomeomorph sinhHomeomorph)) x)",
"state_before": "x✝ y x : ℝ\n⊢ HasStrictDerivAt arsinh (sqrt (1 + x ^ 2))⁻¹ x",
"tactic": "convert sinhHomeomorph.toLocalHomeomorph.hasStrictDerivAt_sym... | [
185,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/CategoryTheory/Preadditive/Biproducts.lean | CategoryTheory.Limits.hasBinaryBiproduct_of_total | [] | [
336,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
332,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_strict_mono | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.799785\nβ : Type ?u.799788\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nhb : b ≠ ⊤\nh : a < b\n⊢ ENNReal.toNNReal a < ENNReal.toNNReal b",
"tactic": "simpa [← ENNReal.coe_lt_coe, hb, h.ne_top]"
}
] | [
2038,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2037,
1
] |
src/lean/Init/Control/Lawful.lean | StateT.run_monadMap | [] | [
274,
74
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
273,
9
] |
Mathlib/Data/Nat/Factorization/PrimePow.lean | Nat.mul_divisors_filter_prime_pow | [
{
"state_after": "case inl\nR : Type ?u.20477\ninst✝ : CommMonoidWithZero R\nn p : R\nk b : ℕ\nhab : coprime 0 b\n⊢ Finset.filter IsPrimePow (divisors (0 * b)) = Finset.filter IsPrimePow (divisors 0 ∪ divisors b)\n\ncase inr\nR : Type ?u.20477\ninst✝ : CommMonoidWithZero R\nn p : R\nk a b : ℕ\nhab : coprime a b... | [
158,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/MeasureTheory/Group/Prod.lean | MeasureTheory.measure_mul_right_ne_zero | [] | [
225,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Order/RelClasses.lean | antisymm_iff | [
{
"state_after": "α : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsRefl α r\ninst✝ : IsAntisymm α r\na : α\n⊢ r a a ∧ r a a",
"state_before": "α : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsRefl α r\ninst✝ : IsAntisymm α r\na b : α\n⊢ a = b → r a b ∧ r b a",
... | [
45,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_X_pow | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\nn : ℕ\n⊢ ↑toLaurent (X ^ n) = T ↑n",
"tactic": "simp only [map_pow, Polynomial.toLaurent_X, T_pow, mul_one]"
}
] | [
247,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
] |
Mathlib/Analysis/NormedSpace/Star/Multiplier.lean | DoubleCentralizer.nnnorm_fst | [] | [
653,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/StrongEpi.lean | CategoryTheory.StrongMono.of_arrow_iso | [
{
"state_after": "C : Type u\ninst✝ : Category C\nP Q R : C\nf✝ : P ⟶ Q\ng✝ : Q ⟶ R\nA B A' B' : C\nf : A ⟶ B\ng : A' ⟶ B'\ne : Arrow.mk f ≅ Arrow.mk g\nh : StrongMono f\n⊢ Mono (e.inv.left ≫ f ≫ e.hom.right)",
"state_before": "C : Type u\ninst✝ : Category C\nP Q R : C\nf✝ : P ⟶ Q\ng✝ : Q ⟶ R\nA B A' B' : C... | [
173,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/RingTheory/Multiplicity.lean | multiplicity.mul' | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : DecidableRel fun x x_1 => x ∣ x_1\np a b : α\nhp : Prime p\nh : (multiplicity p (a * b)).Dom\nhdiva : p ^ Part.get (multiplicity p a) (_ : Finite p a) ∣ a\n⊢ Part.get (multiplicity p (a * b)) h =\n Part.get (multiplicity p a) (_ : F... | [
571,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
11
] |
Mathlib/Data/Finset/Basic.lean | Finset.coe_mem | [] | [
222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiCountable.dist_summable | [
{
"state_after": "E : ℕ → Type ?u.303411\nι : Type u_1\ninst✝¹ : Encodable ι\nF : ι → Type u_2\ninst✝ : (i : ι) → MetricSpace (F i)\nx y : (i : ι) → F i\ni : ι\n⊢ 0 ≤ min ((1 / 2) ^ encode i) (dist (x i) (y i))",
"state_before": "E : ℕ → Type ?u.303411\nι : Type u_1\ninst✝¹ : Encodable ι\nF : ι → Type u_2\n... | [
840,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
836,
1
] |
src/lean/Init/Data/String/Basic.lean | String.mapAux_lemma | [
{
"state_after": "s : String\ni : Pos\nc : Char\nh : ¬atEnd s i = true\nthis : (endPos (set s i c)).byteIdx - (next (set s i c) i).byteIdx = (endPos s).byteIdx - (next s i).byteIdx\n⊢ (endPos s).byteIdx - (next s i).byteIdx < (endPos s).byteIdx - i.byteIdx",
"state_before": "s : String\ni : Pos\nc : Char\nh... | [
457,
64
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
444,
1
] |
Mathlib/Data/Rat/Floor.lean | Rat.floor_def | [] | [
56,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
11
] |
Mathlib/Data/PNat/Defs.lean | PNat.mk_coe | [] | [
57,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
56,
1
] |
Mathlib/Order/Bounds/Basic.lean | IsLeast.isLeast_iff_eq | [] | [
1077,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1076,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_castAdd_right | [
{
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"tactic": "ext"
},
{
"state_after": "no goals",
... | [
1179,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1176,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | AddMonoidAlgebra.ringHom_ext | [] | [
1820,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1817,
1
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Mathlib/Topology/MetricSpace/EMetricSpace.lean | EMetric.cauchySeq_iff | [] | [
743,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
741,
1
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Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.mk'_mul | [
{
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714,
13
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708,
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Mathlib/Data/Matrix/Basic.lean | Matrix.map_smul | [] | [
365,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
363,
1
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Mathlib/Analysis/Convex/Integral.lean | ae_eq_const_or_exists_average_ne_compl | [
{
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251,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
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Mathlib/Algebra/Order/Floor.lean | Int.floor_add_nat | [
{
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"tactic": "rw [← Int.cast_ofNat, floor_add_int]"
}
] | [
752,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
752,
1
] |
Mathlib/Topology/Order.lean | continuous_sSup_rng | [] | [
759,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
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Std/Data/Nat/Gcd.lean | Nat.exists_coprime | [] | [
285,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
281,
1
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Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.isCaratheodory_inter | [
{
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"ta... | [
992,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
1
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Mathlib/Topology/Sheaves/Presheaf.lean | TopCat.Presheaf.pushforwardEq_eq | [] | [
196,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
194,
1
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Mathlib/Data/Setoid/Partition.lean | Setoid.finite_classes_ker | [] | [
89,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/Data/Real/NNReal.lean | NNReal.iSup_of_not_bddAbove | [] | [
938,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
937,
1
] |
Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgHom.coe_mk | [] | [
409,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Algebra/Group/Prod.lean | MonoidHom.coe_prod | [] | [
559,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
] |
Mathlib/Data/Multiset/Bind.lean | Multiset.count_bind | [] | [
209,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nndist_eq_sum | [
{
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506,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
500,
1
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Mathlib/LinearAlgebra/Matrix/SesquilinearForm.lean | LinearMap.mul_toMatrix₂_mul | [
{
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493,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
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Mathlib/Order/Hom/CompleteLattice.lean | FrameHom.toFun_eq_coe | [] | [
559,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
558,
1
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src/lean/Init/Data/List/Basic.lean | List.reverseAux_reverseAux | [
{
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"state_before": "α : Type u\nβ : Type v\nγ : Type w\nas bs cs : List α\n⊢ reverseAux (reverseAux as bs) cs = reverseAux bs (reverseAux (reverseAux as nil) cs)",
"tactic": "induction as generalizing bs cs with\n| nil => rfl\n| cons a as ih => simp [reverseAux, ih (a::bs), ih ... | [
65,
58
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
62,
1
] |
Mathlib/Data/MvPolynomial/Monad.lean | MvPolynomial.bind₁_comp_bind₁ | [
{
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235,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Seq/Parallel.lean | Computation.parallel_promises | [] | [
363,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/RingTheory/Ideal/Prod.lean | Ideal.isPrime_of_isPrime_prod_top' | [
{
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129,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Std/Logic.lean | not_iff_false_intro | [] | [
75,
86
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
75,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.toLinearMap_injective | [] | [
140,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
139,
1
] |
Std/Data/Int/DivMod.lean | Int.mul_mod_left | [
{
"state_after": "no goals",
"state_before": "a b : Int\nh : b = 0\n⊢ mod (a * b) b = 0",
"tactic": "simp [h, Int.mul_zero]"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh : ¬b = 0\n⊢ mod (a * b) b = 0",
"tactic": "rw [Int.mod_def, Int.mul_div_cancel _ h, Int.mul_comm, Int... | [
455,
73
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
453,
9
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.bot_div | [] | [
453,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Data/Set/Image.lean | Set.image_id' | [
{
"state_after": "case h\nα : Type u_1\nβ : Type ?u.39227\nγ : Type ?u.39230\nι : Sort ?u.39233\nι' : Sort ?u.39236\nf : α → β\ns✝ t s : Set α\nx✝ : α\n⊢ x✝ ∈ (fun x => x) '' s ↔ x✝ ∈ s",
"state_before": "α : Type u_1\nβ : Type ?u.39227\nγ : Type ?u.39230\nι : Sort ?u.39233\nι' : Sort ?u.39236\nf : α → β\ns... | [
377,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Inverse.lean | Real.arccos_eq_pi | [
{
"state_after": "no goals",
"state_before": "x : ℝ\n⊢ arccos x = π ↔ x ≤ -1",
"tactic": "rw [arccos, sub_eq_iff_eq_add, ← sub_eq_iff_eq_add', div_two_sub_self, neg_pi_div_two_eq_arcsin]"
}
] | [
404,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/Topology/SubsetProperties.lean | isCompact_iff_finite_subcover | [] | [
356,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Analysis/Convex/Complex.lean | convex_halfspace_im_le | [] | [
43,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime.dvd_mul_left | [] | [
129,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Data/Sum/Basic.lean | Sum.elim_update_left | [
{
"state_after": "case h\nα : Type u\nα' : Type w\nβ : Type v\nβ' : Type x\nγ : Type u_1\nδ : Type ?u.36815\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq β\nf : α → γ\ng : β → γ\ni : α\nc : γ\nx : α ⊕ β\n⊢ Sum.elim (update f i c) g x = update (Sum.elim f g) (inl i) c x",
"state_before": "α : Type u\nα' : Typ... | [
643,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
635,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasurableEmbedding.set_integral_map | [
{
"state_after": "no goals",
"state_before": "α : Type u_2\nβ✝ : Type ?u.136486\nE : Type u_3\nF : Type ?u.136492\ninst✝³ : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nf✝ g✝ : α → E\ns✝ t : Set α\nμ ν : Measure α\nl l' : Filter α\ninst✝¹ : CompleteSpace E\ninst✝ : NormedSpace ℝ E\nβ : Type u_1\nx✝ : M... | [
494,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
491,
1
] |
Mathlib/Algebra/GroupWithZero/Basic.lean | inv_eq_zero | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.28276\nM₀ : Type ?u.28279\nG₀ : Type u_1\nM₀' : Type ?u.28285\nG₀' : Type ?u.28288\nF : Type ?u.28291\nF' : Type ?u.28294\ninst✝ : GroupWithZero G₀\na✝ b c a : G₀\n⊢ a⁻¹ = 0 ↔ a = 0",
"tactic": "rw [inv_eq_iff_eq_inv, inv_zero]"
}
] | [
399,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
399,
1
] |
Mathlib/Algebra/Order/Hom/Ring.lean | OrderRingHom.toRingHom_eq_coe | [] | [
206,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_left_strictMono | [] | [
121,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Set/Image.lean | Set.subset_image_compl | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.46973\nι : Sort ?u.46976\nι' : Sort ?u.46979\nf✝ : α → β\ns✝ t : Set α\nf : α → β\ns : Set α\nH : Surjective f\n⊢ f '' (s ∪ sᶜ) = univ",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.46973\nι : Sort ?u.46976\nι' : Sort ?u.46979\nf✝ : α → β... | [
424,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
421,
1
] |
Mathlib/Analysis/Complex/PhragmenLindelof.lean | PhragmenLindelof.quadrant_III | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b C : ℝ\nf g : ℂ → E\nz : ℂ\nhd : DiffContOnCl ℂ f (Iio 0 ×ℂ Iio 0)\nhB : ∃ c, c < 2 ∧ ∃ B, f =O[comap (↑Complex.abs) atTop ⊓ 𝓟 (Iio 0 ×ℂ Iio 0)] fun z => expR (B * ↑Complex.abs z ^ c)\nhre : ∀ (x : ℝ), x ≤ 0 → ‖f ↑x‖ ≤ C... | [
561,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
540,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.iInf_adj_of_nonempty | [
{
"state_after": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGraph V\nG₁ G₂ : Subgraph G\na b : V\ninst✝ : Nonempty ι\nf : ι → Subgraph G\n⊢ (∀ (G' : Subgraph G), (G' ∈ Set.range fun i => f i) → Adj G' a b) ↔ ∀ (i : ι), Adj (f i) a b",
"state_before": "ι : Sort u_1\nV : Type u\nW : Type v\nG : SimpleGr... | [
419,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Analysis/Calculus/BumpFunctionInner.lean | Real.smoothTransition.nonneg | [] | [
220,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
219,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.sdiff_val | [] | [
2038,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2037,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.insert_self_properDivisors | [
{
"state_after": "no goals",
"state_before": "n : ℕ\nh : n ≠ 0\n⊢ insert n (properDivisors n) = divisors n",
"tactic": "rw [divisors, properDivisors, Ico_succ_right_eq_insert_Ico (one_le_iff_ne_zero.2 h),\n Finset.filter_insert, if_pos (dvd_refl n)]"
}
] | [
88,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Analysis/SpecialFunctions/Arsinh.lean | ContinuousWithinAt.arsinh | [] | [
225,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
8
] |
Mathlib/Analysis/Convex/Quasiconvex.lean | QuasiconvexOn.sup | [
{
"state_after": "𝕜 : Type u_1\nE : Type u_2\nF : Type ?u.4373\nβ : Type u_3\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : LinearOrderedAddCommMonoid β\ninst✝ : SMul 𝕜 E\ns : Set E\nf g : E → β\nhf : QuasiconvexOn 𝕜 s f\nhg : QuasiconvexOn 𝕜 s g\nr : β\n⊢ Convex ... | [
117,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
113,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.eq_iff | [] | [
144,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Data/Fintype/Units.lean | UnitsInt.univ | [] | [
27,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
27,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atBot_add_right_of_ge | [] | [
806,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.comp | [] | [
825,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
824,
1
] |
Mathlib/Topology/UniformSpace/Separation.lean | eq_of_clusterPt_uniformity | [] | [
166,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Order/Filter/SmallSets.lean | Filter.smallSets_eq_generate | [
{
"state_after": "α : Type u_1\nβ : Type ?u.169\nι : Sort ?u.172\nl l' la : Filter α\nlb : Filter β\nf : Filter α\n⊢ Filter.lift' f powerset = ⨅ (b : Set α) (_ : b ∈ f.sets), 𝓟 (𝒫 b)",
"state_before": "α : Type u_1\nβ : Type ?u.169\nι : Sort ?u.172\nl l' la : Filter α\nlb : Filter β\nf : Filter α\n⊢ small... | [
45,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | LinearMap.coe_isometryOfOrthonormal | [] | [
1354,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1352,
1
] |
Mathlib/Logic/Function/Basic.lean | Function.invFun_eq | [
{
"state_after": "no goals",
"state_before": "α : Sort u_1\nβ : Sort u_2\ninst✝ : Nonempty α\nf : α → β\na : α\nb : β\nh : ∃ a, f a = b\n⊢ f (invFun f b) = b",
"tactic": "simp only [invFun, dif_pos h, h.choose_spec]"
}
] | [
438,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_eq_one | [] | [
427,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
11
] |
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