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/Set/Ncard.lean | Set.ncard_insert_of_not_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.9534\ns t : Set α\na b x y : α\nf : α → β\nh : ¬a ∈ s\nhs : autoParam (Set.Finite s) _auto✝\n⊢ ncard (insert a s) = ncard s + 1",
"tactic": "classical\nhave hft := hs.fintype\nrw [ncard_eq_toFinset_card _, ncard_eq_toFinset_card _, ... | [
152,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
9
] |
Mathlib/Data/Nat/GCD/Basic.lean | Nat.coprime_add_mul_left_right | [
{
"state_after": "no goals",
"state_before": "m n k : ℕ\n⊢ coprime m (n + m * k) ↔ coprime m n",
"tactic": "rw [coprime, coprime, gcd_add_mul_left_right]"
}
] | [
159,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
] |
Mathlib/Order/Disjointed.lean | disjointedRec_zero | [] | [
105,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.card_nsmul | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.55179\nγ : Type ?u.55182\ns : Multiset α\nn : ℕ\n⊢ ↑card (n • s) = n * ↑card s",
"tactic": "rw [card.map_nsmul s n, Nat.nsmul_eq_mul]"
}
] | [
739,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Order/Monotone/Monovary.lean | antivary_comm | [] | [
409,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Std/Data/Int/DivMod.lean | Int.dvd_sub_of_emod_eq | [
{
"state_after": "a b c : Int\nh : a % b = c\nhx : a % b % b = c % b\n⊢ b ∣ a - c",
"state_before": "a b c : Int\nh : a % b = c\n⊢ b ∣ a - c",
"tactic": "have hx : (a % b) % b = c % b := by\n rw [h]"
},
{
"state_after": "a b c : Int\nh : a % b = c\nhx : (a - c) % b = 0\n⊢ b ∣ a - c",
"state... | [
698,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
694,
1
] |
Mathlib/Topology/MetricSpace/EMetricSpace.lean | edist_le_range_sum_edist | [] | [
144,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Data/Stream/Init.lean | Stream'.nats_eq | [
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\n⊢ ∀ (n : ℕ), nth nats n = nth (0 :: map succ nats) n",
"state_before": "α : Type u\nβ : Type v\nδ : Type w\n⊢ nats = 0 :: map succ nats",
"tactic": "apply Stream'.ext"
},
{
"state_after": "case a\nα : Type u\nβ : Type v\nδ : Type w\nn... | [
765,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
763,
1
] |
Mathlib/MeasureTheory/Integral/Lebesgue.lean | MeasureTheory.lintegral_add_left | [
{
"state_after": "α : Type u_1\nβ : Type ?u.898603\nγ : Type ?u.898606\nδ : Type ?u.898609\nm : MeasurableSpace α\nμ ν : Measure α\nf : α → ℝ≥0∞\nhf : Measurable f\ng : α → ℝ≥0∞\n⊢ (∫⁻ (a : α), f a + g a ∂μ) ≤ (∫⁻ (a : α), f a ∂μ) + ∫⁻ (a : α), g a ∂μ",
"state_before": "α : Type u_1\nβ : Type ?u.898603\nγ :... | [
579,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.le_half_of_half_lt_sub | [
{
"state_after": "m n k l a b : ℕ\nh : a / 2 < a - b\n⊢ b * 2 ≤ a",
"state_before": "m n k l a b : ℕ\nh : a / 2 < a - b\n⊢ b ≤ a / 2",
"tactic": "rw [Nat.le_div_iff_mul_le two_pos]"
},
{
"state_after": "m n k l a b : ℕ\nh✝ : a < a * 2 - b * 2\nh : a + b * 2 < a + a\n⊢ b * 2 ≤ a",
"state_befo... | [
440,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.preimage_coe_Iio_top | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some ⁻¹' Iio ⊤ = univ",
"tactic": "rw [← range_coe, preimage_range]"
}
] | [
77,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Algebra/Order/Interval.lean | NonemptyInterval.length_nonneg | [] | [
642,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
641,
1
] |
Mathlib/Algebra/Group/Commute.lean | Commute.left_comm | [
{
"state_after": "no goals",
"state_before": "G : Type ?u.2631\nS : Type u_1\ninst✝ : Semigroup S\na b c✝ : S\nh : Commute a b\nc : S\n⊢ a * (b * c) = b * (a * c)",
"tactic": "simp only [← mul_assoc, h.eq]"
}
] | [
125,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
124,
11
] |
Mathlib/Order/Heyting/Basic.lean | himp_top | [] | [
373,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.setToFun_add | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nE : Type u_2\nF : Type u_3\nF' : Type ?u.1404218\nG : Type ?u.1404221\n𝕜 : Type ?u.1404224\np : ℝ≥0∞\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace ℝ F\ninst✝³ : NormedAddCommGroup F'\... | [
1374,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1371,
1
] |
Mathlib/Algebra/Star/Subalgebra.lean | StarSubalgebra.coe_map | [] | [
234,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Algebra/Hom/Group.lean | OneHom.coe_mk | [] | [
586,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Algebra/Opposites.lean | MulOpposite.unop_injective | [] | [
165,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
164,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.irrefl | [] | [
189,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
188,
11
] |
Mathlib/CategoryTheory/Adhesive.lean | CategoryTheory.IsPushout.IsVanKampen.mono_of_mono_left | [
{
"state_after": "no goals",
"state_before": "J : Type v'\ninst✝² : Category J\nC : Type u\ninst✝¹ : Category C\nW X Y Z : C\nf : W ⟶ X\ng : W ⟶ Y\nh : X ⟶ Z\ni : Y ⟶ Z\ninst✝ : Mono f\nH : IsPushout f g h i\nH' : IsVanKampen H\n⊢ g ≫ 𝟙 Y = 𝟙 W ≫ g",
"tactic": "simp"
},
{
"state_after": "no go... | [
213,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Analysis/Convex/Basic.lean | stdSimplex_eq_inter | [
{
"state_after": "case h\n𝕜 : Type u_1\nE : Type ?u.288872\nF : Type ?u.288875\nβ : Type ?u.288878\nι : Type u_2\ninst✝¹ : OrderedSemiring 𝕜\ninst✝ : Fintype ι\nf : ι → 𝕜\n⊢ f ∈ stdSimplex 𝕜 ι ↔ f ∈ (⋂ (x : ι), {f | 0 ≤ f x}) ∩ {f | ∑ x : ι, f x = 1}",
"state_before": "𝕜 : Type u_1\nE : Type ?u.288872\... | [
624,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
622,
1
] |
Mathlib/Data/List/Basic.lean | List.getLast?_isSome | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.34657\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\n⊢ Option.isSome (getLast? []) = true ↔ [] ≠ []",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "ι : Type ?u.34657\nα : Type u\nβ : Type v\nγ : T... | [
786,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
783,
1
] |
src/lean/Init/Prelude.lean | Nat.le_refl | [] | [
1606,
14
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1605,
11
] |
Mathlib/Order/Filter/Bases.lean | Filter.IsBasis.hasBasis | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.12014\nγ : Type ?u.12017\nι : Sort u_2\nι' : Sort ?u.12023\nl l' : Filter α\np : ι → Prop\ns : ι → Set α\nt✝ : Set α\ni : ι\np' : ι' → Prop\ns' : ι' → Set α\ni' : ι'\nh : IsBasis p s\nt : Set α\n⊢ t ∈ IsBasis.filter h ↔ ∃ i, p i ∧ s i ⊆... | [
287,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
11
] |
Mathlib/Data/ZMod/Basic.lean | ZMod.cast_mul | [
{
"state_after": "case zero\nR : Type u_1\ninst✝¹ : Ring R\nm : ℕ\ninst✝ : CharP R m\nh : m ∣ Nat.zero\na b : ZMod Nat.zero\n⊢ ↑(a * b) = ↑a * ↑b\n\ncase succ\nR : Type u_1\ninst✝¹ : Ring R\nm : ℕ\ninst✝ : CharP R m\nn✝ : ℕ\nh : m ∣ Nat.succ n✝\na b : ZMod (Nat.succ n✝)\n⊢ ↑(a * b) = ↑a * ↑b",
"state_before... | [
318,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
1
] |
Mathlib/Control/Traversable/Basic.lean | ApplicativeTransformation.ext_iff | [] | [
135,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_neg | [
{
"state_after": "no goals",
"state_before": "x y : ℝ\n⊢ sin (-x) = -sin x",
"tactic": "simp [sin, exp_neg, (neg_div _ _).symm, add_mul]"
}
] | [
1181,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1181,
1
] |
Mathlib/LinearAlgebra/Matrix/Nondegenerate.lean | Matrix.Nondegenerate.exists_not_ortho_of_ne_zero | [] | [
44,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
42,
1
] |
Mathlib/Data/Num/Lemmas.lean | PosNum.to_nat_to_int | [] | [
67,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/Data/Setoid/Basic.lean | Setoid.eq_top_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.6005\ns : Setoid α\n⊢ (∀ {x y : α}, ⊤ x y → Rel s x y) ↔ ∀ (x y : α), Rel s x y",
"state_before": "α : Type u_1\nβ : Type ?u.6005\ns : Setoid α\n⊢ s = ⊤ ↔ ∀ (x y : α), Rel s x y",
"tactic": "rw [_root_.eq_top_iff, Setoid.le_def, Setoid.top_def]"
},
{
"... | [
199,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Order/JordanHolder.lean | JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup | [
{
"state_after": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nx y : X\nhxz : IsMaximal x (x ⊔ y)\nhyz : IsMaximal y (x ⊔ y)\n⊢ IsMaximal (y ⊓ x) y",
"state_before": "X : Type u\ninst✝¹ : Lattice X\ninst✝ : JordanHolderLattice X\nx y : X\nhxz : IsMaximal x (x ⊔ y)\nhyz : IsMaximal y (x ⊔ y... | [
104,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Std/Data/List/Basic.lean | List.zipWithLeft'_eq_zipWithLeft'TR | [
{
"state_after": "case h.h.h.h.h.h\nα : Type u_3\nβ : Type u_2\nγ : Type u_1\nf : α → Option β → γ\nas : List α\nbs : List β\n⊢ zipWithLeft' f as bs = zipWithLeft'TR f as bs",
"state_before": "⊢ @zipWithLeft' = @zipWithLeft'TR",
"tactic": "funext α β γ f as bs"
},
{
"state_after": "case h.h.h.h.... | [
1305,
28
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1298,
10
] |
Mathlib/Data/Complex/Exponential.lean | Real.sin_pos_of_pos_of_le_two | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : 0 < x\nhx : x ≤ 2\n⊢ 0 < 2",
"tactic": "norm_num"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : 0 < x\nhx : x ≤ 2\n⊢ x ≤ 1 * 2",
"tactic": "simpa"
},
{
"state_after": "no goals",
"state_before": "x : ℝ... | [
1906,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1900,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | Submodule.iInf_colon_iSup | [] | [
389,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
378,
1
] |
Mathlib/Analysis/Calculus/FDeriv/RestrictScalars.lean | hasFDerivAt_of_restrictScalars | [
{
"state_after": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝⁹ : NontriviallyNormedField 𝕜'\ninst✝⁸ : NormedAlgebra 𝕜 𝕜'\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : IsScalarTower 𝕜 𝕜' E\nF : Type u_3\ninst✝³ : ... | [
101,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
] |
Mathlib/Analysis/Calculus/MeanValue.lean | monotone_of_deriv_nonneg | [] | [
927,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
923,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | nat_abs_sum_le | [
{
"state_after": "case empty\nι✝ : Type ?u.986696\nβ : Type u\nα : Type v\nγ : Type w\ns s₁ s₂ : Finset α\na : α\nf✝ g : α → β\nι : Type u_1\nf : ι → ℤ\n⊢ Int.natAbs (∑ i in ∅, f i) ≤ ∑ i in ∅, Int.natAbs (f i)\n\ncase insert\nι✝ : Type ?u.986696\nβ : Type u\nα : Type v\nγ : Type w\ns✝ s₁ s₂ : Finset α\na : α\n... | [
2279,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2273,
1
] |
Mathlib/Data/Int/Log.lean | Int.log_of_right_le_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝¹ : LinearOrderedSemifield R\ninst✝ : FloorSemiring R\nb : ℕ\nr : R\nhr : r ≤ 0\n⊢ log b r = 0",
"tactic": "rw [log_of_right_le_one _ (hr.trans zero_le_one),\n Nat.clog_of_right_le_one ((Nat.ceil_eq_zero.mpr <| inv_nonpos.2 hr).trans_le z... | [
93,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
Mathlib/Geometry/Euclidean/Angle/Unoriented/Affine.lean | EuclideanGeometry.angle_const_vsub | [] | [
88,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/RingTheory/IntegralClosure.lean | isIntegral_leadingCoeff_smul | [
{
"state_after": "R : Type u_1\nA : Type ?u.981430\nB : Type ?u.981433\nS : Type u_2\ninst✝⁶ : CommRing R\ninst✝⁵ : CommRing A\ninst✝⁴ : CommRing B\ninst✝³ : CommRing S\ninst✝² : Algebra R A\ninst✝¹ : Algebra R B\nf : R →+* S\np : R[X]\nx : S\ninst✝ : Algebra R S\nh : eval₂ (algebraMap R S) x p = 0\n⊢ IsIntegra... | [
804,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
] |
Mathlib/Data/Nat/Factorization/Basic.lean | Nat.prod_pow_factorization_eq_self | [
{
"state_after": "f : ℕ →₀ ℕ\nhf : ∀ (p : ℕ), p ∈ f.support → Prime p\nh : ∀ (x : ℕ), x ∈ f.support → x ^ ↑f x ≠ 0\n⊢ factorization (Finsupp.prod f fun x x_1 => x ^ x_1) = f",
"state_before": "f : ℕ →₀ ℕ\nhf : ∀ (p : ℕ), p ∈ f.support → Prime p\n⊢ factorization (Finsupp.prod f fun x x_1 => x ^ x_1) = f",
... | [
315,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Analysis/InnerProductSpace/PiL2.lean | Complex.orthonormalBasisOneI_repr_symm_apply | [] | [
638,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
1
] |
Mathlib/RingTheory/Ideal/Operations.lean | RingHom.mem_ker | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nF : Type u_1\nG : Type ?u.1679598\ninst✝² : Semiring R\ninst✝¹ : Semiring S\ninst✝ : Semiring T\nrcf : RingHomClass F R S\nrcg : RingHomClass G T S\nf : F\ng : G\nr : R\n⊢ r ∈ ker f ↔ ↑f r = 0",
"tactic": "rw [ker, Ideal.m... | [
2001,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2001,
1
] |
Std/Data/Int/DivMod.lean | Int.emod_def | [
{
"state_after": "no goals",
"state_before": "a b : Int\n⊢ a % b = a - b * (a / b)",
"tactic": "rw [← Int.add_sub_cancel (a % b), emod_add_ediv]"
}
] | [
329,
51
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
328,
1
] |
Mathlib/Data/List/Basic.lean | List.zipRight_nil_right | [] | [
4222,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
4221,
1
] |
Mathlib/LinearAlgebra/Dual.lean | Basis.dualBasis_equivFun | [
{
"state_after": "no goals",
"state_before": "R : Type u\nM : Type v\nK : Type u₁\nV : Type u₂\nι : Type w\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : DecidableEq ι\nb : Basis ι R M\ninst✝ : Fintype ι\nl : Dual R M\ni : ι\n⊢ ↑(equivFun (dualBasis b)) l i = ↑l (↑b i)",
"t... | [
462,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
461,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.ind | [] | [
129,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Linear.lean | ContinuousLinearMap.hasFDerivAtFilter | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nG : Type ?u.18148\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedS... | [
70,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
11
] |
Mathlib/LinearAlgebra/LinearPMap.lean | LinearPMap.zero_domain | [] | [
393,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
393,
1
] |
Mathlib/Computability/Primrec.lean | Primrec.nat_div | [
{
"state_after": "α : Type ?u.161626\nβ : Type ?u.161629\nγ : Type ?u.161632\nδ : Type ?u.161635\nσ : Type ?u.161638\ninst✝⁴ : Primcodable α\ninst✝³ : Primcodable β\ninst✝² : Primcodable γ\ninst✝¹ : Primcodable δ\ninst✝ : Primcodable σ\n⊢ PrimrecRel fun a b => (fun x x_1 => x / x_1) a.fst a.snd = b",
"state... | [
831,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
815,
1
] |
Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.integral_Icc_eq_integral_Ico' | [] | [
617,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
615,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | toIcoDiv_add_right | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\nhα : Archimedean α\np : α\nhp : 0 < p\na✝ b✝ c : α\nn : ℤ\na b : α\n⊢ toIcoDiv hp a (b + p) = toIcoDiv hp a b + 1",
"tactic": "simpa only [one_zsmul] using toIcoDiv_add_zsmul hp a b 1"
}
] | [
300,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Init/Function.lean | Function.HasLeftInverse.injective | [] | [
102,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConcaveOn.convex_gt | [] | [
558,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
557,
1
] |
Mathlib/Topology/SubsetProperties.lean | continuousOn_boolIndicator_iff_clopen | [
{
"state_after": "α : Type u\nβ : Type v\nι : Type ?u.179439\nπ : ι → Type ?u.179444\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ns✝ t : Set α\nX : Type u_1\ninst✝ : TopologicalSpace X\ns U : Set X\n⊢ Continuous (restrict s (boolIndicator U)) ↔ Continuous (boolIndicator (Subtype.val ⁻¹' U))",
... | [
1676,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1673,
1
] |
Mathlib/Data/List/Basic.lean | List.length_insertNth_le_succ | [
{
"state_after": "case inl\nι : Type ?u.124260\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl : List α\nx : α\nn : ℕ\nhn : n ≤ length l\n⊢ length (insertNth n x l) ≤ length l + 1\n\ncase inr\nι : Type ?u.124260\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁ l₂ : List α\na : α\nl ... | [
1693,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1688,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Icc_ssubset_Icc_right | [
{
"state_after": "ι : Type ?u.27279\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁ a₂ b b₁ b₂ c x : α\nhI : a₂ ≤ b₂\nha : a₂ ≤ a₁\nhb : b₁ < b₂\n⊢ Set.Icc a₁ b₁ ⊂ Set.Icc a₂ b₂",
"state_before": "ι : Type ?u.27279\nα : Type u_1\ninst✝¹ : Preorder α\ninst✝ : LocallyFiniteOrder α\na a₁... | [
275,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Data/Prod/Basic.lean | Prod.eq_iff_fst_eq_snd_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.4899\nδ : Type ?u.4902\np₁ : α\np₂ : β\nq₁ : α\nq₂ : β\n⊢ (p₁, p₂) = (q₁, q₂) ↔ (p₁, p₂).fst = (q₁, q₂).fst ∧ (p₁, p₂).snd = (q₁, q₂).snd",
"tactic": "simp"
}
] | [
214,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.separatingLeft_iff_ker_eq_bot | [] | [
719,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Data/Polynomial/Mirror.lean | Polynomial.mirror_zero | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\ninst✝ : Semiring R\np q : R[X]\n⊢ mirror 0 = 0",
"tactic": "simp [mirror]"
}
] | [
47,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
Mathlib/MeasureTheory/Function/SimpleFuncDenseLp.lean | MeasureTheory.SimpleFunc.memℒp_top | [] | [
303,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Algebra/Algebra/Unitization.lean | Unitization.ext | [] | [
98,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Data/Set/Basic.lean | Set.union_eq_right_iff_subset | [] | [
805,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
804,
1
] |
Mathlib/Analysis/NormedSpace/QuaternionExponential.lean | Quaternion.exp_coe | [] | [
37,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.le_cons_erase | [
{
"state_after": "α : Type u_1\nβ : Type ?u.96069\nγ : Type ?u.96072\ninst✝ : DecidableEq α\ns✝ t : Multiset α\na✝ b : α\ns : Multiset α\na : α\nh : ¬a ∈ s\n⊢ s ≤ a ::ₘ s",
"state_before": "α : Type u_1\nβ : Type ?u.96069\nγ : Type ?u.96072\ninst✝ : DecidableEq α\ns✝ t : Multiset α\na✝ b : α\ns : Multiset α... | [
1040,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1038,
1
] |
Mathlib/AlgebraicGeometry/PrimeSpectrum/Basic.lean | PrimeSpectrum.isClosed_iff_zeroLocus_ideal | [] | [
428,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
425,
1
] |
Mathlib/Topology/Order/Lattice.lean | continuous_inf | [] | [
89,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/RingTheory/Noetherian.lean | IsNoetherian.disjoint_partialSups_eventually_bot | [
{
"state_after": "R : Type u_1\nM : Type u_2\nP : Type ?u.278074\nN : Type w\ninst✝⁶ : Ring R\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\ninst✝¹ : AddCommGroup P\ninst✝ : Module R P\nI : IsNoetherian R M\nf : ℕ → Submodule R M\nh : ∀ (n : ℕ), Disjoint (↑(partialS... | [
464,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
450,
1
] |
Mathlib/Analysis/LocallyConvex/Basic.lean | Absorbent.absorbs_finite | [
{
"state_after": "𝕜 : Type u_2\n𝕝 : Type ?u.10601\nE : Type u_1\nι : Sort ?u.10607\nκ : ι → Sort ?u.10612\ninst✝¹ : SeminormedRing 𝕜\ninst✝ : SMul 𝕜 E\ns✝ t u v✝ A B s : Set E\nhs : Absorbent 𝕜 s\nv : Set E\nhv : Set.Finite v\n⊢ Absorbs 𝕜 s (⋃ (x : E) (_ : x ∈ v), {x})",
"state_before": "𝕜 : Type u_2... | [
155,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
152,
1
] |
Mathlib/Combinatorics/Quiver/Path.lean | Prefunctor.mapPath_cons | [] | [
227,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/Algebra/Operations.lean | Submodule.map_op_one | [
{
"state_after": "case h\nι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\ninst✝¹ : Semiring A\ninst✝ : Algebra R A\nS T : Set A\nM N P Q : Submodule R A\nm n : A\nx : Aᵐᵒᵖ\n⊢ x ∈ map (↑(opLinearEquiv R)) 1 ↔ x ∈ 1",
"state_before": "ι : Sort uι\nR : Type u\ninst✝² : CommSemiring R\nA : Type v\... | [
137,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.filter_false_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.323235\nγ : Type ?u.323238\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\ns : Finset α\nh : ∀ (x : α), x ∈ s → ¬p x\n⊢ ∀ (x : α), ¬x ∈ filter p s",
"tactic": "simpa only [eq_empty_iff_forall_not_mem, mem_filter,... | [
2704,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2702,
1
] |
Mathlib/Analysis/NormedSpace/Banach.lean | ContinuousLinearMap.NonlinearRightInverse.bound | [] | [
54,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Topology/Basic.lean | isClosed_iInter | [] | [
223,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Analysis/SpecialFunctions/Integrals.lean | integral_sin_pow_even | [
{
"state_after": "case zero\na b : ℝ\nn : ℕ\n⊢ (∫ (x : ℝ) in 0 ..π, sin x ^ (2 * zero)) = π * ∏ i in Finset.range zero, (2 * ↑i + 1) / (2 * ↑i + 2)\n\ncase succ\na b : ℝ\nn k : ℕ\nih : (∫ (x : ℝ) in 0 ..π, sin x ^ (2 * k)) = π * ∏ i in Finset.range k, (2 * ↑i + 1) / (2 * ↑i + 2)\n⊢ (∫ (x : ℝ) in 0 ..π, sin x ^ ... | [
679,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
674,
1
] |
Mathlib/SetTheory/Ordinal/FixedPoint.lean | Ordinal.deriv_id_of_nfp_id | [
{
"state_after": "no goals",
"state_before": "f✝ : Ordinal → Ordinal\nf : Ordinal → Ordinal\nh : nfp f = id\n⊢ deriv f 0 = id 0 ∧ ∀ (a : Ordinal), deriv f a = id a → deriv f (succ a) = id (succ a)",
"tactic": "simp [h]"
}
] | [
535,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
534,
1
] |
Mathlib/Analysis/NormedSpace/ConformalLinearMap.lean | IsConformalMap.smul | [
{
"state_after": "case intro.intro.intro\nR : Type u_1\nM : Type u_2\nN : Type u_3\nG : Type ?u.124862\nM' : Type ?u.124865\ninst✝⁸ : NormedField R\ninst✝⁷ : SeminormedAddCommGroup M\ninst✝⁶ : SeminormedAddCommGroup N\ninst✝⁵ : SeminormedAddCommGroup G\ninst✝⁴ : NormedSpace R M\ninst✝³ : NormedSpace R N\ninst✝²... | [
68,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.mk_finsupp_lift_of_fintype | [
{
"state_after": "no goals",
"state_before": "α✝ β✝ α : Type u\nβ : Type v\ninst✝¹ : Fintype α\ninst✝ : Zero β\n⊢ (#α →₀ β) = lift (#β) ^ Fintype.card α",
"tactic": "simpa using (@Finsupp.equivFunOnFinite α β _ _).cardinal_eq"
}
] | [
1329,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1327,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | AffineIndependent.affineSpan_eq_of_le_of_card_eq_finrank_add_one | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_4\nι : Type u_1\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\ninst✝¹ : Fintype ι\np : ι → P\nhi : AffineIndependent k p\nsp : AffineSubspace k P\ninst✝ : FiniteDimensional k { x // x ∈ direction sp }\nhl... | [
257,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/GroupTheory/Index.lean | Subgroup.index_dvd_of_le | [] | [
108,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Algebra/Algebra/Subalgebra/Basic.lean | Subalgebra.coe_toSubmodule | [] | [
348,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
348,
1
] |
Mathlib/Topology/Filter.lean | Filter.nhds_eq | [] | [
80,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/RingTheory/PowerSeries/Basic.lean | MvPowerSeries.constantCoeff_X | [] | [
519,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.cycleOf_pow_apply_self | [
{
"state_after": "ι : Type ?u.2116608\nα : Type u_1\nβ : Type ?u.2116614\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf✝ g : Perm α\nx✝ y : α\nf : Perm α\nx : α\nn : ℕ\n⊢ ↑(cycleOf f x ^ n) x = ↑(f ^ n) x",
"state_before": "ι : Type ?u.2116608\nα : Type u_1\nβ : Type ?u.2116614\ninst✝¹ : DecidableEq α\ninst✝... | [
988,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
983,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Cardinal.mk_ord_out | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.229879\nβ : Type ?u.229882\nγ : Type ?u.229885\nr : α → α → Prop\ns : β → β → Prop\nt : γ → γ → Prop\nc : Cardinal\n⊢ (#(Quotient.out (ord c)).α) = c",
"tactic": "simp"
}
] | [
1447,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Order/Heyting/Basic.lean | compl_compl_compl | [] | [
912,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.dvd_of_mem_factors | [] | [
460,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
459,
1
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.Integrable.locallyIntegrable | [] | [
137,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
136,
1
] |
Mathlib/Algebra/Order/ToIntervalMod.lean | QuotientAddGroup.btw_coe_iff' | [] | [
934,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
1
] |
Mathlib/Topology/MetricSpace/PiNat.lean | PiNat.eq_of_dist_eq_zero | [
{
"state_after": "case inl\nE : ℕ → Type u_1\nx : (n : ℕ) → E n\nhxy : dist x x = 0\n⊢ x = x\n\ncase inr\nE : ℕ → Type u_1\nx y : (n : ℕ) → E n\nhxy : dist x y = 0\nh : x ≠ y\n⊢ x = y",
"state_before": "E : ℕ → Type u_1\nx y : (n : ℕ) → E n\nhxy : dist x y = 0\n⊢ x = y",
"tactic": "rcases eq_or_ne x y w... | [
314,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
311,
11
] |
Mathlib/Analysis/Complex/RealDeriv.lean | HasDerivWithinAt.complexToReal_fderiv' | [
{
"state_after": "no goals",
"state_before": "e : ℂ → ℂ\ne' : ℂ\nz : ℝ\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\ns : Set ℂ\nx : ℂ\nf' : E\nh : HasDerivWithinAt f f' s x\n⊢ HasFDerivWithinAt f (ContinuousLinearMap.smulRight reClm f' + I • ContinuousLinearMap.smulRight ... | [
118,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Polynomial/Div.lean | Polynomial.eval₂_modByMonic_eq_self_of_root | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\nA : Type z\na b : R\nn : ℕ\ninst✝¹ : CommRing R\np✝ q✝ : R[X]\ninst✝ : CommRing S\nf : R →+* S\np q : R[X]\nhq : Monic q\nx : S\nhx : eval₂ f x q = 0\n⊢ eval₂ f x (p %ₘ q) = eval₂ f x p",
"tactic": "rw [modByMonic_eq_sub_m... | [
464,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
462,
1
] |
Std/Data/Int/Lemmas.lean | Int.sub_nonneg_of_le | [
{
"state_after": "a b : Int\nh✝ : b ≤ a\nh : b + -b ≤ a + -b\n⊢ 0 ≤ a - b",
"state_before": "a b : Int\nh : b ≤ a\n⊢ 0 ≤ a - b",
"tactic": "have h := Int.add_le_add_right h (-b)"
},
{
"state_after": "no goals",
"state_before": "a b : Int\nh✝ : b ≤ a\nh : b + -b ≤ a + -b\n⊢ 0 ≤ a - b",
"t... | [
920,
31
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
918,
11
] |
Mathlib/CategoryTheory/Over.lean | CategoryTheory.Under.w | [
{
"state_after": "T : Type u₁\ninst✝ : Category T\nX : T\nA B : Under X\nf : A ⟶ B\nthis : (Functor.fromPUnit X).map f.left ≫ B.hom = A.hom ≫ (𝟭 T).map f.right\n⊢ A.hom ≫ f.right = B.hom",
"state_before": "T : Type u₁\ninst✝ : Category T\nX : T\nA B : Under X\nf : A ⟶ B\n⊢ A.hom ≫ f.right = B.hom",
"ta... | [
350,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
350,
1
] |
Mathlib/Data/Nat/Fib.lean | Nat.fast_fib_aux_eq | [
{
"state_after": "n : ℕ\n⊢ fastFibAux 0 = (fib 0, fib (0 + 1))\n\nn : ℕ\n⊢ ∀ (b : Bool) (n' : ℕ),\n fastFibAux n' = (fib n', fib (n' + 1)) → fastFibAux (bit b n') = (fib (bit b n'), fib (bit b n' + 1))",
"state_before": "n : ℕ\n⊢ fastFibAux n = (fib n, fib (n + 1))",
"tactic": "apply Nat.binaryRec _ ... | [
245,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Order/SuccPred/Basic.lean | Order.Ico_pred_left | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : PredOrder α\na b : α\nh : pred a < b\n⊢ Ico (pred a) b = insert (pred a) (Ico a b)",
"tactic": "simp_rw [← Ici_inter_Iio, Ici_pred, insert_inter_of_mem (mem_Iio.2 h)]"
}
] | [
818,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Data/Dfinsupp/Basic.lean | Dfinsupp.filter_ne_eq_erase' | [
{
"state_after": "ι : Type u\nγ : Type w\nβ : ι → Type v\nβ₁ : ι → Type v₁\nβ₂ : ι → Type v₂\ndec : DecidableEq ι\ninst✝ : (i : ι) → Zero (β i)\ns : Finset ι\nx : (i : ↑↑s) → β ↑i\ni✝ : ι\nf : Π₀ (i : ι), β i\ni : ι\n⊢ filter ((fun x x_1 => x ≠ x_1) i) f = filter (fun x => x ≠ i) f",
"state_before": "ι : Ty... | [
790,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
787,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPushout.inl_iso_hom | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nW X Y Z : C\nh : X ⟶ Z\nk : Y ⟶ Z\nf : W ⟶ X\ng : W ⟶ Y\ncomm : f ≫ h = g ≫ k\ninst✝² : PreservesColimit (span f g) G\ninst✝¹ : HasPushout f g\ninst✝ : HasPushout (G.map f) (G.map g)\n⊢ pushout.inl ≫\n (IsColim... | [
230,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
227,
1
] |
Mathlib/RingTheory/AlgebraicIndependent.lean | IsTranscendenceBasis.isAlgebraic | [
{
"state_after": "ι : Type u_2\nι' : Type ?u.1381427\nR : Type u_1\nK : Type ?u.1381433\nA : Type u_3\nA' : Type ?u.1381439\nA'' : Type ?u.1381442\nV : Type u\nV' : Type ?u.1381447\nx : ι → A\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing A\ninst✝⁵ : CommRing A'\ninst✝⁴ : CommRing A''\ninst✝³ : Algebra R A\ninst✝² : A... | [
559,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
] |
Mathlib/MeasureTheory/Measure/OuterMeasure.lean | MeasureTheory.OuterMeasure.smul_iSup | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type ?u.70023\nR : Type u_1\nR' : Type ?u.70029\nms : Set (OuterMeasure α)\nm : OuterMeasure α\ninst✝¹ : SMul R ℝ≥0∞\ninst✝ : IsScalarTower R ℝ≥0∞ ℝ≥0∞\nι : Sort u_2\nf : ι → OuterMeasure α\nc : R\ns : Set α\n⊢ ↑(c • ⨆ (i : ι), f i) s = ↑(⨆ (i ... | [
434,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.