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/SetTheory/Ordinal/Exponential.lean | Ordinal.div_opow_log_lt | [
{
"state_after": "b o : Ordinal\nhb : 1 < b\n⊢ o < b ^ succ (log b o)",
"state_before": "b o : Ordinal\nhb : 1 < b\n⊢ o / b ^ log b o < b",
"tactic": "rw [div_lt (opow_pos _ (zero_lt_one.trans hb)).ne', ← opow_succ]"
},
{
"state_after": "no goals",
"state_before": "b o : Ordinal\nhb : 1 < b\... | [
440,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_subtype_mono | [] | [
2122,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2120,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.iterate_comp_eval₂ | [
{
"state_after": "case zero\nR : Type u\nS : Type v\nT : Type w\nι : Type y\na b : R\nm n : ℕ\ninst✝¹ : Semiring R\np q : R[X]\nx : R\ninst✝ : CommSemiring S\nf : R →+* S\nt : S\n⊢ eval₂ f t ((comp p^[Nat.zero]) q) = ((fun x => eval₂ f x p)^[Nat.zero]) (eval₂ f t q)\n\ncase succ\nR : Type u\nS : Type v\nT : Typ... | [
1042,
84
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/Data/Real/NNReal.lean | Real.coe_toNNReal' | [] | [
604,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.exists_next_left | [] | [
1576,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1574,
1
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.mul_add_subset | [] | [
816,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/Data/Polynomial/AlgebraMap.lean | Polynomial.aevalTower_C | [] | [
404,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/RingTheory/Algebraic.lean | isAlgebraic_of_pow | [
{
"state_after": "case intro.intro\nR : Type u\nS : Type ?u.226844\nA : Type v\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing S\ninst✝⁴ : Ring A\ninst✝³ : Algebra R A\ninst✝² : Algebra R S\ninst✝¹ : Algebra S A\ninst✝ : IsScalarTower R S A\nr : A\nn : ℕ\nhn : 0 < n\np : R[X]\np_nonzero : p ≠ 0\nhp : ↑(aeval (r ^ n)) p... | [
177,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
172,
1
] |
Mathlib/Algebra/GroupPower/Lemmas.lean | zmultiplesHom_symm_apply | [] | [
888,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
887,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_eq_of_subset_of_ae_diff_eq_zero_aux | [
{
"state_after": "α : Type u_1\nβ : Type ?u.88408\nE : Type u_2\nF : Type ?u.88414\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\nhts : s ⊆ t\nh't : ∀ᵐ (x : α) ∂μ, x ∈ t \\ s → f x = 0\nha... | [
358,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
334,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.row_apply | [] | [
213,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
212,
1
] |
Mathlib/Topology/ContinuousOn.lean | ite_inter_closure_compl_eq_of_inter_frontier_eq | [
{
"state_after": "α : Type u_1\nβ : Type ?u.398706\nγ : Type ?u.398709\nδ : Type ?u.398712\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\ns s' t : Set α\nht : s ∩ frontier t = s' ∩ frontier t\n⊢ s' ∩ frontier (tᶜ) = s ∩ frontier (tᶜ)",
"st... | [
1237,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1234,
1
] |
Mathlib/MeasureTheory/Constructions/Pi.lean | MeasureTheory.piPremeasure_pi_eval | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.1733303\nα : ι → Type u_2\ninst✝ : Fintype ι\nm : (i : ι) → OuterMeasure (α i)\ns : Set ((i : ι) → α i)\n⊢ ∏ i : ι, ↑(m i) ((fun a => a i) '' s) = piPremeasure m s",
"state_before": "ι : Type u_1\nι' : Type ?u.1733303\nα : ι → Type u_2\ninst✝ : Fintype ι\nm : (i ... | [
188,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_pow | [
{
"state_after": "no goals",
"state_before": "a b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in a..b, x ^ n) = (b ^ (n + 1) - a ^ (n + 1)) / (↑n + 1)",
"tactic": "simpa only [← Int.ofNat_succ, zpow_ofNat] using integral_zpow (Or.inl (Int.coe_nat_nonneg n))"
}
] | [
382,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
Mathlib/Order/Disjoint.lean | codisjoint_ofDual_iff | [] | [
435,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.ofFractionRing_inv | [
{
"state_after": "no goals",
"state_before": "K : Type u\ninst✝¹ : CommRing K\ninst✝ : IsDomain K\np : FractionRing K[X]\n⊢ { toFractionRing := p⁻¹ } = { toFractionRing := p }⁻¹",
"tactic": "simp only [Inv.inv, RatFunc.inv]"
}
] | [
417,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.mk_compl_of_infinite | [
{
"state_after": "α : Type u_1\ninst✝ : Infinite α\ns : Set α\nh2 : (#↑s) < (#α)\n⊢ (#↑s) + (#↑(sᶜ)) = (#α)",
"state_before": "α : Type u_1\ninst✝ : Infinite α\ns : Set α\nh2 : (#↑s) < (#α)\n⊢ (#↑(sᶜ)) = (#α)",
"tactic": "refine' eq_of_add_eq_of_aleph0_le _ h2 (aleph0_le_mk α)"
},
{
"state_after... | [
1152,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1149,
1
] |
Mathlib/MeasureTheory/Function/AEEqOfIntegral.lean | MeasureTheory.ae_eq_zero_of_forall_inner | [
{
"state_after": "α : Type u_3\nE : Type u_1\n𝕜 : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝³ : IsROrC 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : SecondCountableTopology E\nf : α → E\nhf : ∀ (c : E), (fun x => inner c (f x)) =ᵐ[μ] 0\ns : ℕ → E := denseSeq E\n⊢ f =ᵐ[μ... | [
70,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Data/Polynomial/Module.lean | PolynomialModule.induction_linear | [] | [
110,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/Data/PNat/Basic.lean | Nat.succPNat_le_succPNat | [] | [
95,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | IsIntegral.algebraMap | [
{
"state_after": "case intro.intro\nR : Type u_3\nA : Type u_1\nB : Type u_2\nS : Type ?u.210572\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing B\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R A\ninst✝² : Algebra R B\nf✝ : R →+* S\ninst✝¹ : Algebra A B\ninst✝ : IsScalarTower R A B\nx : A\nf : R[X]\nhf :... | [
181,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Analysis/Convex/Between.lean | wbtw_iff_right_eq_or_left_mem_image_Ici | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nV : Type u_2\nV' : Type ?u.504435\nP : Type u_3\nP' : Type ?u.504441\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nx y z : P\n⊢ Wbtw R x y z ↔ z = y ∨ x ∈ ↑(lineMap z y) '' Set.Ici 1",
"tac... | [
739,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
737,
1
] |
Mathlib/Probability/Kernel/Basic.lean | ProbabilityTheory.kernel.ext_iff' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nι : Type ?u.361579\nmα : MeasurableSpace α\nmβ : MeasurableSpace β\nκ η : { x // x ∈ kernel α β }\n⊢ κ = η ↔ ∀ (a : α) (s : Set β), MeasurableSet s → ↑↑(↑κ a) s = ↑↑(↑η a) s",
"tactic": "simp_rw [ext_iff, Measure.ext_iff]"
}
] | [
191,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/NumberTheory/PythagoreanTriples.lean | PythagoreanTriple.even_odd_of_coprime | [
{
"state_after": "case inl.inl\nx y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhx : x % 2 = 0\nhy : y % 2 = 0\n⊢ x % 2 = 0 ∧ y % 2 = 1 ∨ x % 2 = 1 ∧ y % 2 = 0\n\ncase inl.inr\nx y z : ℤ\nh : PythagoreanTriple x y z\nhc : Int.gcd x y = 1\nhx : x % 2 = 0\nhy : y % 2 = 1\n⊢ x % 2 = 0 ∧ y % 2 = 1 ∨ x... | [
161,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Analysis/Convex/Between.lean | Sbtw.not_swap_right | [] | [
408,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/Fin/VecNotation.lean | Matrix.smul_cons | [
{
"state_after": "case h\nα : Type u\nm n o : ℕ\nm' : Type ?u.54537\nn' : Type ?u.54540\no' : Type ?u.54543\nM : Type u_1\ninst✝ : SMul M α\nx : M\ny : α\nv : Fin n → α\ni : Fin (Nat.succ n)\n⊢ (x • vecCons y v) i = vecCons (x • y) (x • v) i",
"state_before": "α : Type u\nm n o : ℕ\nm' : Type ?u.54537\nn' :... | [
442,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Types.lean | CategoryTheory.Limits.Types.coproductIso_ι_comp_hom | [] | [
370,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.map_ceil | [
{
"state_after": "no goals",
"state_before": "F : Type u_3\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrderedRing α\ninst✝³ : LinearOrderedRing β\ninst✝² : FloorRing α\ninst✝¹ : FloorRing β\ninst✝ : RingHomClass F α β\na✝ : α\nb : β\nf : F\nhf : StrictMono ↑f\na : α\nn : ℤ\n⊢ ↑f a ≤ ↑n ↔ a ≤ ↑n",
"tact... | [
1539,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1538,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Iio_subset_Iio_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.73808\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\nh : Iio a ⊆ Iio b\n⊢ a ≤ b",
"state_before": "α : Type u_1\nβ : Type ?u.73808\ninst✝ : LinearOrder α\na a₁ a₂ b b₁ b₂ c d : α\n⊢ Iio a ⊆ Iio b ↔ a ≤ b",
"tactic": "refine' ⟨fun h => _, fun h => Iio_subset_... | [
1188,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_mul_I | [
{
"state_after": "x y : ℂ\n⊢ cosh (x * I * I) = cosh x",
"state_before": "x y : ℂ\n⊢ cos (x * I) = cosh x",
"tactic": "rw [← cosh_mul_I]"
},
{
"state_after": "x y : ℂ\n⊢ cosh (x * I ^ 2) = cosh x",
"state_before": "x y : ℂ\n⊢ cosh (x * I * I) = cosh x",
"tactic": "ring_nf"
},
{
"... | [
828,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/Topology/Homeomorph.lean | Homeomorph.preimage_symm | [] | [
214,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Midpoint.lean | vsub_midpoint | [
{
"state_after": "no goals",
"state_before": "R : Type u_3\nV : Type u_1\nV' : Type ?u.65321\nP : Type u_2\nP' : Type ?u.65327\ninst✝⁷ : Ring R\ninst✝⁶ : Invertible 2\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddTorsor V P\ninst✝² : AddCommGroup V'\ninst✝¹ : Module R V'\ninst✝ : AddTorsor V' P... | [
137,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.coe_fn_toEquiv | [] | [
685,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.append_assoc | [] | [
795,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
794,
1
] |
Mathlib/Data/Finsupp/Order.lean | Finsupp.le_iff' | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nα : Type u_2\ninst✝ : CanonicallyOrderedAddMonoid α\nf g : ι →₀ α\ns✝ : Finset ι\nhf : f.support ⊆ s✝\nh : ∀ (i : ι), i ∈ s✝ → ↑f i ≤ ↑g i\ns : ι\n⊢ ↑f s ≤ ↑g s",
"tactic": "classical exact\n if H : s ∈ f.support then h s (hf H) else (not_me... | [
160,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
157,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.piecewise_mem_Icc_of_mem_of_mem | [] | [
2580,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2577,
1
] |
Mathlib/Data/Real/Basic.lean | Real.ofCauchy_ratCast | [] | [
189,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
1
] |
Mathlib/Order/Minimal.lean | minimals_swap | [] | [
81,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Combinatorics/SetFamily/Compression/Down.lean | Finset.nonMemberSubfamily_inter | [] | [
74,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.isNormal_iff_lt_succ_and_blsub_eq | [
{
"state_after": "α : Type ?u.366887\nβ : Type ?u.366890\nγ : Type ?u.366893\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nf : Ordinal → Ordinal\n⊢ (∀ (a : Ordinal), f a < f (succ a)) →\n ((∀ (o : Ordinal), IsLimit o → (bsup o fun x x_1 => f x) = f o) ↔\n ∀ (o : Ordinal), IsLimit o → (blsub o f... | [
1987,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1981,
1
] |
Mathlib/Order/Heyting/Basic.lean | sup_himp_distrib | [
{
"state_after": "ι : Type ?u.71182\nα : Type u_1\nβ : Type ?u.71188\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c✝ d✝ a b c d : α\n⊢ a ≤ d ⇨ c ∧ b ≤ d ⇨ c ↔ d ≤ a ⇨ c ∧ d ≤ b ⇨ c",
"state_before": "ι : Type ?u.71182\nα : Type u_1\nβ : Type ?u.71188\ninst✝ : GeneralizedHeytingAlgebra α\na✝ b✝ c✝ d✝ a b c d ... | [
411,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/EuclideanDomain/Defs.lean | EuclideanDomain.mod_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\ninst✝ : EuclideanDomain R\na : R\n⊢ a % 0 = a",
"tactic": "simpa only [zero_mul, zero_add] using div_add_mod a 0"
}
] | [
158,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Data/UnionFind.lean | UFModel.Agrees.empty | [] | [
90,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Logic/Hydra.lean | Relation.cutExpand_singleton_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nr : α → α → Prop\nx' x : α\nh✝ : r x' x\na : α\nh : a ∈ {x'}\n⊢ r a x",
"tactic": "rwa [mem_singleton.1 h]"
}
] | [
85,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Data/Rat/Defs.lean | Rat.num_zero | [] | [
408,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_Ici | [] | [
89,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/CategoryTheory/Sums/Basic.lean | CategoryTheory.NatTrans.sum_app_inr | [] | [
243,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/FieldTheory/Finite/Basic.lean | ZMod.frobenius_zmod | [
{
"state_after": "case a\nK : Type ?u.1003397\nR : Type ?u.1003400\np : ℕ\ninst✝ : Fact (Nat.Prime p)\na : ZMod p\n⊢ ↑(frobenius (ZMod p) p) a = ↑(RingHom.id (ZMod p)) a",
"state_before": "K : Type ?u.1003397\nR : Type ?u.1003400\np : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ frobenius (ZMod p) p = RingHom.id (ZMod ... | [
419,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
417,
1
] |
Mathlib/NumberTheory/PellMatiyasevic.lean | Pell.isPell_nat | [
{
"state_after": "a : ℕ\na1 : 1 < a\nx y : ℕ\nh : IsPell { re := ↑x, im := ↑y }\n⊢ ↑(x * x) - ↑(Pell.d a1 * y * y) = ↑1",
"state_before": "a : ℕ\na1 : 1 < a\nx y : ℕ\nh : IsPell { re := ↑x, im := ↑y }\n⊢ ↑(x * x - Pell.d a1 * y * y) = ↑1",
"tactic": "rw [Int.ofNat_sub (Int.le_of_ofNat_le_ofNat <| Int.le... | [
219,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Order/Lattice.lean | Prod.swap_inf | [] | [
1294,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1293,
1
] |
Mathlib/Algebra/Order/Field/Basic.lean | abs_div | [] | [
1005,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1004,
1
] |
Mathlib/Algebra/Group/OrderSynonym.lean | pow_ofDual | [] | [
162,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
162,
1
] |
Mathlib/Analysis/Analytic/Basic.lean | HasFPowerSeriesOnBall.analyticOn | [] | [
1369,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1367,
1
] |
Mathlib/GroupTheory/PGroup.lean | IsPGroup.commutative_of_card_eq_prime_sq | [] | [
409,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Analysis/SpecificLimits/Normed.lean | norm_sub_le_of_geometric_bound_of_hasSum | [
{
"state_after": "α : Type u_1\nβ : Type ?u.749948\nι : Type ?u.749951\ninst✝ : SeminormedAddCommGroup α\nr C : ℝ\nf : ℕ → α\nhr : r < 1\nhf : ∀ (n : ℕ), ‖f n‖ ≤ C * r ^ n\na : α\nha : HasSum f a\nn : ℕ\n⊢ dist (∑ x in Finset.range n, f x) a ≤ C * r ^ n / (1 - r)",
"state_before": "α : Type u_1\nβ : Type ?u... | [
405,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Order/CompactlyGenerated.lean | inf_sSup_eq_iSup_inf_sup_finset | [
{
"state_after": "ι : Sort ?u.103797\nα : Type u_1\ninst✝² : CompleteLattice α\nf : ι → α\ninst✝¹ : CompleteLattice α\ninst✝ : IsCompactlyGenerated α\na b : α\ns : Set α\n⊢ ∀ (c : α),\n CompleteLattice.IsCompactElement c → c ≤ a ⊓ sSup s → c ≤ ⨆ (t : Finset α) (_ : ↑t ⊆ s), a ⊓ Finset.sup t id",
"state_b... | [
424,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
413,
1
] |
Mathlib/MeasureTheory/Measure/FiniteMeasure.lean | BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub | [
{
"state_after": "Ω : Type u_1\ninst✝³ : MeasurableSpace Ω\ninst✝² : TopologicalSpace Ω\ninst✝¹ : OpensMeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\nf : Ω →ᵇ ℝ\n⊢ ((∫ (a : Ω), (NNReal.toReal ∘ ↑(nnrealPart f)) a ∂μ) - ∫ (a : Ω), (NNReal.toReal ∘ ↑(nnrealPart (-f))) a ∂μ) =\n (∫ (ω : Ω), ↑(↑(nn... | [
690,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.relindex_mul_index | [] | [
102,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/Invertible.lean | inv_mul_cancel_of_invertible | [] | [
389,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
388,
1
] |
Mathlib/Algebra/Algebra/Hom.lean | AlgHom.ofLinearMap_id | [] | [
418,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
416,
1
] |
Mathlib/Order/Circular.lean | btw_refl_left | [] | [
303,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Analysis/LocallyConvex/WithSeminorms.lean | WithSeminorms.hasBasis | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type ?u.182411\n𝕝 : Type ?u.182414\n𝕝₂ : Type ?u.182417\nE : Type u_2\nF : Type ?u.182423\nG : Type ?u.182426\nι : Type u_3\nι' : Type ?u.182432\ninst✝⁴ : NormedField 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : Nonempty ι\ninst✝ : TopologicalSpace E\np : ... | [
294,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
291,
1
] |
Mathlib/Analysis/InnerProductSpace/Adjoint.lean | LinearMap.star_eq_adjoint | [] | [
472,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
471,
1
] |
Mathlib/MeasureTheory/Measure/Haar/InnerProductSpace.lean | Orientation.measure_orthonormalBasis | [
{
"state_after": "ι : Type u_2\nF : Type u_1\ninst✝⁵ : Fintype ι\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace ℝ F\ninst✝² : FiniteDimensional ℝ F\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\nm n : ℕ\n_i : Fact (finrank ℝ F = n)\no : Orientation ℝ F (Fin n)\nb : OrthonormalBasis ι ℝ F\ne : ι ... | [
48,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
39,
1
] |
Mathlib/Analysis/Convex/Between.lean | Wbtw.trans_left_right | [
{
"state_after": "case intro.intro\nR : Type u_1\nV : Type u_2\nV' : Type ?u.567237\nP : Type u_3\nP' : Type ?u.567243\ninst✝³ : LinearOrderedField R\ninst✝² : AddCommGroup V\ninst✝¹ : Module R V\ninst✝ : AddTorsor V P\nw x z : P\nt₁ : R\nht₁ : t₁ ∈ Set.Icc 0 1\nh₂ : Wbtw R w x (↑(lineMap w z) t₁)\n⊢ Wbtw R x (... | [
830,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
808,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffWithinAt.congr_nhds | [] | [
498,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
496,
1
] |
Mathlib/RingTheory/RootsOfUnity/Basic.lean | IsPrimitiveRoot.iff | [
{
"state_after": "M : Type u_1\nN : Type ?u.2067990\nG : Type ?u.2067993\nR : Type ?u.2067996\nS : Type ?u.2067999\nF : Type ?u.2068002\ninst✝² : CommMonoid M\ninst✝¹ : CommMonoid N\ninst✝ : DivisionCommMonoid G\nk l✝ : ℕ\nζ : M\nf : F\nh✝ : IsPrimitiveRoot ζ k\nhk : 0 < k\nh : IsPrimitiveRoot ζ k\nl : ℕ\nhl' :... | [
472,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
11
] |
Mathlib/Logic/Equiv/Defs.lean | Equiv.equivCongr_symm | [
{
"state_after": "case H.H\nα : Sort u\nβ : Sort v\nγ : Sort w\nδ : Sort u_1\nab : α ≃ β\ncd : γ ≃ δ\nx✝¹ : β ≃ δ\nx✝ : α\n⊢ ↑(↑(equivCongr ab cd).symm x✝¹) x✝ = ↑(↑(equivCongr ab.symm cd.symm) x✝¹) x✝",
"state_before": "α : Sort u\nβ : Sort v\nγ : Sort w\nδ : Sort u_1\nab : α ≃ β\ncd : γ ≃ δ\n⊢ (equivCongr... | [
404,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
9
] |
Mathlib/Order/RelIso/Basic.lean | RelIso.default_def | [] | [
740,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
739,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | HasStrictFDerivAt.sinh | [] | [
1125,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1123,
1
] |
Mathlib/LinearAlgebra/TensorProduct.lean | LinearMap.lTensor_mul | [] | [
1085,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1084,
1
] |
Mathlib/RingTheory/DedekindDomain/Ideal.lean | FractionalIdeal.right_inverse_eq | [
{
"state_after": "R : Type ?u.24145\nA : Type ?u.24148\nK : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : Field K\ninst✝⁴ : IsDomain A\nR₁ : Type u_1\ninst✝³ : CommRing R₁\ninst✝² : IsDomain R₁\ninst✝¹ : Algebra R₁ K\ninst✝ : IsFractionRing R₁ K\nI✝ J✝ I J : FractionalIdeal R₁⁰ K\nh : I * J = 1\n... | [
131,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_eq_inr_of_epi_eq | [] | [
1967,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1965,
1
] |
Mathlib/Data/Set/Function.lean | Set.SurjOn.mapsTo_invFunOn | [] | [
1272,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1271,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.sub_self | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.131882\nβ : Type ?u.131885\nγ : Type ?u.131888\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\na : Ordinal\n⊢ a - a = 0",
"tactic": "simpa only [add_zero] using add_sub_cancel a 0"
}
] | [
595,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Algebra/Order/Ring/Lemmas.lean | lt_mul_of_le_of_one_lt' | [] | [
803,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
801,
1
] |
Mathlib/LinearAlgebra/Matrix/Determinant.lean | Matrix.det_mul_comm | [
{
"state_after": "no goals",
"state_before": "m : Type u_1\nn : Type ?u.897636\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\nR : Type v\ninst✝ : CommRing R\nM N : Matrix m m R\n⊢ det (M ⬝ N) = det (N ⬝ M)",
"tactic": "rw [det_mul, det_mul, mul_comm]"
}
] | [
206,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ioi_pred_eq_insert | [] | [
851,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
850,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_re | [
{
"state_after": "no goals",
"state_before": "d n : ℤ\n⊢ (↑n).re = n",
"tactic": "cases n <;> rfl"
}
] | [
299,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Data/Polynomial/Degree/Lemmas.lean | Polynomial.natDegree_le_iff_coeff_eq_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nι : Type w\na b : R\nm n : ℕ\ninst✝ : Semiring R\np q r : R[X]\n⊢ natDegree p ≤ n ↔ ∀ (N : ℕ), n < N → coeff p N = 0",
"tactic": "simp_rw [natDegree_le_iff_degree_le, degree_le_iff_coeff_zero, Nat.cast_withBot,\n WithBot.coe_lt_coe]"... | [
76,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.univ_id | [] | [
1252,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1251,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.coe_currySumEquiv_symm | [] | [
1520,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1519,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac | [
{
"state_after": "no goals",
"state_before": "G : Type u_1\nH : Type ?u.157160\nα : Type u_2\nβ : Type ?u.157166\nE : Type ?u.157169\ninst✝¹⁰ : Group G\ninst✝⁹ : Group H\ninst✝⁸ : MulAction G α\ninst✝⁷ : MeasurableSpace α\ninst✝⁶ : MulAction H β\ninst✝⁵ : MeasurableSpace β\ninst✝⁴ : NormedAddCommGroup E\ns ... | [
224,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
220,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_iff | [] | [
360,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
357,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | HasFTaylorSeriesUpToOn.add | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁹ : NormedAddCommGroup D\ninst✝⁸ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜... | [
1187,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1184,
1
] |
Mathlib/ModelTheory/Semantics.lean | FirstOrder.Language.Formula.realize_rel₁ | [
{
"state_after": "L : Language\nL' : Language\nM : Type w\nN : Type ?u.236870\nP : Type ?u.236873\ninst✝² : Structure L M\ninst✝¹ : Structure L N\ninst✝ : Structure L P\nα : Type u'\nβ : Type v'\nn : ℕ\nφ ψ : Formula L α\nv : α → M\nR : Relations L 1\nt : Term L α\n⊢ (RelMap R fun i => Term.realize v (Matrix.ve... | [
651,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
647,
1
] |
Mathlib/Data/Finset/Card.lean | Finset.card_le_card_sdiff_add_card | [] | [
449,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
448,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.degree_C_lt | [] | [
262,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
261,
1
] |
Mathlib/Data/QPF/Multivariate/Constructions/Fix.lean | MvQPF.wEquiv.symm | [
{
"state_after": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nx y : MvPFunctor.W (P F) α\nh : WEquiv x y\n⊢ WEquiv y x",
"state_before": "n : ℕ\nF : TypeVec (n + 1) → Type u\ninst✝ : MvFunctor F\nq : MvQPF F\nα : TypeVec n\nx y : MvPFunctor.W (P F) α\n⊢ WEquiv x y →... | [
132,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Topology/UniformSpace/CompactConvergence.lean | ContinuousMap.tendstoLocallyUniformly_of_tendsto | [
{
"state_after": "α : Type u₁\nβ : Type u₂\ninst✝¹ : TopologicalSpace α\ninst✝ : UniformSpace β\nK : Set α\nV : Set (β × β)\nf : C(α, β)\nι : Type u₃\np : Filter ι\nF : ι → C(α, β)\nhα : ∀ (x : α), ∃ n, IsCompact n ∧ n ∈ 𝓝 x\nh : ∀ (K : Set α), IsCompact K → TendstoUniformlyOn (fun i a => ↑(F i) a) (↑f) p K\n⊢... | [
409,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
404,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_pushoutAssoc_inv | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁵ : Category C\nD : Type u₂\ninst✝⁴ : Category D\nW X Y Z X₁ X₂ X₃ Z₁ Z₂ : C\ng₁ : Z₁ ⟶ X₁\ng₂ : Z₁ ⟶ X₂\ng₃ : Z₂ ⟶ X₂\ng₄ : Z₂ ⟶ X₃\ninst✝³ : HasPushout g₁ g₂\ninst✝² : HasPushout g₃ g₄\ninst✝¹ : HasPushout (g₃ ≫ pushout.inr) g₄\ninst✝ : HasPus... | [
2637,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2634,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Ordered.lean | midpoint_le_left | [] | [
151,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.IsFundamentalDomain.essSup_measure_restrict | [
{
"state_after": "G : Type u_1\nH : Type ?u.448297\nα : Type u_2\nβ : Type ?u.448303\nE : Type ?u.448306\ninst✝¹² : Group G\ninst✝¹¹ : Group H\ninst✝¹⁰ : MulAction G α\ninst✝⁹ : MeasurableSpace α\ninst✝⁸ : MulAction H β\ninst✝⁷ : MeasurableSpace β\ninst✝⁶ : NormedAddCommGroup E\ns t : Set α\nμ : Measure α\ninst... | [
523,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
512,
1
] |
Mathlib/Combinatorics/Composition.lean | List.length_splitWrtComposition | [] | [
689,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
687,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_lt_of_lt_div' | [] | [
1616,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1615,
1
] |
Mathlib/Data/Nat/ModEq.lean | Nat.chineseRemainder'_lt_lcm | [
{
"state_after": "m n a b c d : ℕ\nh : a ≡ b [MOD gcd n m]\nhn : n ≠ 0\nhm : m ≠ 0\n⊢ ↑(if hn : n = 0 then { val := a, property := (_ : a ≡ a [MOD n] ∧ a ≡ b [MOD m]) }\n else\n if hm : m = 0 then { val := b, property := (_ : b ≡ a [MOD n] ∧ b ≡ b [MOD m]) }\n else\n { val := Int.toN... | [
373,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/Set/Finite.lean | Set.finite_le_nat | [] | [
904,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
1
] |
Mathlib/Algebra/Order/Chebyshev.lean | sq_sum_le_card_mul_sum_sq | [
{
"state_after": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.19415\ninst✝ : LinearOrderedRing α\ns : Finset ι\nσ : Perm ι\nf g : ι → α\n⊢ (∑ i in s, f i) * ∑ i in s, f i ≤ ↑(card s) * ∑ x in s, f x * f x",
"state_before": "ι : Type u_2\nα : Type u_1\nβ : Type ?u.19415\ninst✝ : LinearOrderedRing α\ns : Finset ι... | [
131,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
129,
1
] |
Mathlib/Combinatorics/Colex.lean | Colex.hom_fin_lt_iff | [
{
"state_after": "α : Type ?u.6170\nn : ℕ\nA B : Finset (Fin n)\n⊢ StrictMono fun i => ↑i",
"state_before": "α : Type ?u.6170\nn : ℕ\nA B : Finset (Fin n)\n⊢ toColex (image (fun i => ↑i) A) < toColex (image (fun i => ↑i) B) ↔ toColex A < toColex B",
"tactic": "refine' Colex.hom_lt_iff _ _ _"
},
{
... | [
144,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
140,
1
] |
Mathlib/Data/Int/Interval.lean | Int.image_Ico_emod | [
{
"state_after": "case inl\na b n : ℤ\nh : 0 ≤ 0\n⊢ image (fun x => x % 0) (Ico n (n + 0)) = Ico 0 0\n\ncase inr\na✝ b n a : ℤ\nh : 0 ≤ a\nha : 0 < a\n⊢ image (fun x => x % a) (Ico n (n + a)) = Ico 0 a",
"state_before": "a✝ b n a : ℤ\nh : 0 ≤ a\n⊢ image (fun x => x % a) (Ico n (n + a)) = Ico 0 a",
"tact... | [
206,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.