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/Fintype/Card.lean | Fintype.card_ofFinset | [] | [
137,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.abs_arg_le_pi_div_two_iff | [
{
"state_after": "no goals",
"state_before": "z : ℂ\n⊢ Abs.abs (arg z) ≤ π / 2 ↔ 0 ≤ z.re",
"tactic": "rw [abs_le, arg_le_pi_div_two_iff, neg_pi_div_two_le_arg_iff, ← or_and_left, ← not_le,\n and_not_self_iff, or_false_iff]"
}
] | [
362,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
360,
1
] |
Mathlib/Topology/ContinuousFunction/Compact.lean | ContinuousMap.dist_lt_of_dist_lt_modulus | [] | [
392,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
390,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.pred_succ | [] | [
687,
6
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
686,
19
] |
Mathlib/Order/BooleanAlgebra.lean | compl_bijective | [] | [
650,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
649,
1
] |
Mathlib/GroupTheory/MonoidLocalization.lean | Submonoid.LocalizationMap.lift_injective_iff | [
{
"state_after": "case mp\nM : Type u_3\ninst✝² : CommMonoid M\nS : Submonoid M\nN : Type u_1\ninst✝¹ : CommMonoid N\nP : Type u_2\ninst✝ : CommMonoid P\nf : LocalizationMap S N\ng : M →* P\nhg : ∀ (y : { x // x ∈ S }), IsUnit (↑g ↑y)\n⊢ Injective ↑(lift f hg) → ∀ (x y : M), ↑(toMap f) x = ↑(toMap f) y ↔ ↑g x =... | [
1114,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1101,
1
] |
Mathlib/Algebra/Associated.lean | isUnit_of_associated_mul | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.351988\nγ : Type ?u.351991\nδ : Type ?u.351994\ninst✝ : CancelCommMonoidWithZero α\np b : α\nhp : p ≠ 0\na : αˣ\nha : p * b * ↑a = p\n⊢ IsUnit b",
"state_before": "α : Type u_1\nβ : Type ?u.351988\nγ : Type ?u.351991\nδ : Type ?u.351994\ninst✝ : Cancel... | [
1189,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1185,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_coe | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.564690\nT : Type ?u.564693\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ ↑normSq ↑x = x ^ 2",
"tactic": "rw [normSq_def, star_coe, ← coe_mul, coe_re, sq]"
}
] | [
1207,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1206,
1
] |
Mathlib/Data/Finmap.lean | Finmap.mem_toFinmap | [] | [
185,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
184,
1
] |
Mathlib/Logic/Small/Basic.lean | small_type | [] | [
77,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
1
] |
Mathlib/Deprecated/Submonoid.lean | Additive.isAddSubmonoid | [] | [
66,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
64,
1
] |
Mathlib/Algebra/GroupWithZero/Units/Lemmas.lean | mul_div_cancel_of_imp' | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.11359\nM₀ : Type ?u.11362\nG₀ : Type u_1\nM₀' : Type ?u.11368\nG₀' : Type ?u.11371\nF : Type ?u.11374\nF' : Type ?u.11377\ninst✝¹ : MonoidWithZero M₀\ninst✝ : CommGroupWithZero G₀\na✝ b✝ c d a b : G₀\nh : b = 0 → a = 0\n⊢ b * (a / b) = a",
"tacti... | [
172,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
171,
1
] |
Mathlib/Analysis/SpecialFunctions/Complex/Arg.lean | Complex.arg_mul_coe_angle | [
{
"state_after": "case h.e'_2.h.e'_1.h.e'_1\nx y : ℂ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ x * y = ↑(↑abs x * ↑abs y) * (↑(Angle.cos (↑(arg x) + ↑(arg y))) + ↑(Angle.sin (↑(arg x) + ↑(arg y))) * I)",
"state_before": "x y : ℂ\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ ↑(arg (x * y)) = ↑(arg x) + ↑(arg y)",
"tactic": "convert arg_m... | [
483,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
475,
1
] |
Mathlib/Order/CompleteLattice.lean | sInf_empty | [] | [
490,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
489,
1
] |
Mathlib/Order/Monotone/Basic.lean | monotone_comp_ofDual_iff | [] | [
138,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
137,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | CochainComplex.mk'_X_0 | [] | [
1037,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1036,
1
] |
Mathlib/Algebra/Homology/HomologicalComplex.lean | HomologicalComplex.dFrom_comp_xNextIsoSelf | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nV : Type u\ninst✝¹ : Category V\ninst✝ : HasZeroMorphisms V\nc : ComplexShape ι\nC : HomologicalComplex V c\ni : ι\nh : ¬ComplexShape.Rel c i (ComplexShape.next c i)\n⊢ dFrom C i ≫ (xNextIsoSelf C h).hom = 0",
"tactic": "simp [h]"
}
] | [
450,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
449,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.contractNth_apply_of_gt | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\nα : Type u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nh : ↑j < ↑k\n⊢ contractNth j op g k = g (succ k)",
"tactic": "rw [contractNth, if_neg (not_lt_of_gt h), if_neg (Ne.symm <| ne_of_lt h)]"
}
] | [
975,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
973,
1
] |
Mathlib/Algebra/GroupWithZero/Commute.lean | Commute.inv_right₀ | [] | [
81,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Order/SuccPred/Basic.lean | WithTop.pred_top | [] | [
1100,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1099,
1
] |
Mathlib/MeasureTheory/Function/StronglyMeasurable/Basic.lean | MeasureTheory.FinStronglyMeasurable.stronglyMeasurable | [] | [
1025,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1023,
11
] |
Mathlib/Combinatorics/Catalan.lean | Tree.treesOfNumNodesEq_succ | [
{
"state_after": "n : ℕ\n⊢ (Finset.biUnion (attach (Nat.antidiagonal n)) fun ijh =>\n pairwiseNode (treesOfNumNodesEq (↑ijh).fst) (treesOfNumNodesEq (↑ijh).snd)) =\n Finset.biUnion (Nat.antidiagonal n) fun ij => pairwiseNode (treesOfNumNodesEq ij.fst) (treesOfNumNodesEq ij.snd)",
"state_before": "n ... | [
191,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/LinearAlgebra/Projection.lean | Submodule.quotientEquivOfIsCompl_apply_mk_coe | [] | [
91,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
89,
1
] |
Mathlib/Order/Basic.lean | forall_lt_iff_le' | [] | [
549,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
548,
1
] |
Mathlib/Geometry/Euclidean/Sphere/Basic.lean | EuclideanGeometry.Sphere.center_eq_iff_eq_of_mem | [
{
"state_after": "V : Type ?u.4387\nP : Type u_1\ninst✝ : MetricSpace P\ns₁ s₂ : Sphere P\np : P\nhs₁ : p ∈ s₁\nhs₂ : p ∈ s₂\nh : s₁.center = s₂.center\n⊢ s₁.radius = s₂.radius",
"state_before": "V : Type ?u.4387\nP : Type u_1\ninst✝ : MetricSpace P\ns₁ s₂ : Sphere P\np : P\nhs₁ : p ∈ s₁\nhs₂ : p ∈ s₂\n⊢ s₁... | [
129,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
1
] |
Mathlib/CategoryTheory/EssentiallySmall.lean | CategoryTheory.ShrinkHoms.from_to | [] | [
160,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/LinearAlgebra/ProjectiveSpace/Basic.lean | Projectivization.mk_eq_mk_iff | [] | [
103,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Data/Finsupp/Basic.lean | Finsupp.sumFinsuppAddEquivProdFinsupp_symm_inr | [] | [
1400,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1398,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.ext_num_den | [
{
"state_after": "case a.num\np q : ℚ≥0\nhn : num p = num q\nhd : den p = den q\n⊢ (↑p).num = (↑q).num\n\ncase a.den\np q : ℚ≥0\nhn : num p = num q\nhd : den p = den q\n⊢ (↑p).den = (↑q).den",
"state_before": "p q : ℚ≥0\nhn : num p = num q\nhd : den p = den q\n⊢ p = q",
"tactic": "ext"
},
{
"sta... | [
477,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
472,
1
] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | derivWithin_const_smul | [] | [
148,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Std/Data/RBMap/WF.lean | Std.RBNode.All.balRight | [
{
"state_after": "α✝ : Type u_1\np : α✝ → Prop\nl : RBNode α✝\nv : α✝\nr : RBNode α✝\nhl : All p l\nhv : p v\nhr : All p r\n⊢ All p\n (match r with\n | node red b y c => node red l v (node black b y c)\n | r =>\n match l with\n | node black a x b => balance1 (node red a x b) v r\n | node... | [
271,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
269,
11
] |
Mathlib/Analysis/NormedSpace/ENorm.lean | ENorm.coe_inj | [] | [
81,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieIdeal.map_sup | [] | [
849,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
848,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.add_smul_mem_interior' | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.124932\n𝕜 : Type u_2\nE : Type u_1\ninst✝⁵ : LinearOrderedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nh... | [
223,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/Data/Set/Intervals/WithBotTop.lean | WithTop.image_coe_Ici | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ some '' Ici a = Ico ↑a ⊤",
"tactic": "rw [← preimage_coe_Ici, image_preimage_eq_inter_range, range_coe, Ici_inter_Iio]"
}
] | [
95,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
94,
1
] |
Mathlib/Analysis/NormedSpace/TrivSqZeroExt.lean | TrivSqZeroExt.exp_def | [] | [
148,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/LinearAlgebra/Lagrange.lean | Lagrange.eval_basis_not_at_node | [
{
"state_after": "no goals",
"state_before": "F : Type u_2\ninst✝¹ : Field F\nι : Type u_1\ns : Finset ι\nv : ι → F\ni : ι\nr : ι → F\nx : F\ninst✝ : DecidableEq ι\nhi : i ∈ s\nhxi : x ≠ v i\n⊢ eval x (Lagrange.basis s v i) = eval x (nodal s v) * (nodalWeight s v i * (x - v i)⁻¹)",
"tactic": "rw [mul_co... | [
590,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/Logic/Basic.lean | congr_heq | [
{
"state_after": "case refl\nα : Sort u_1\nγ : Sort u_2\nf : α → γ\nx : α\ng : α → γ\nh₁ : HEq f g\n⊢ f x = g x",
"state_before": "α β : Sort u_1\nγ : Sort u_2\nf : α → γ\ng : β → γ\nx : α\ny : β\nh₁ : HEq f g\nh₂ : HEq x y\n⊢ f x = g y",
"tactic": "cases h₂"
},
{
"state_after": "case refl.refl\... | [
63,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/List/AList.lean | AList.lookup_insert | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : AList β\n⊢ lookup a (insert a b s) = some b",
"tactic": "simp only [lookup, insert, dlookup_kinsert]"
}
] | [
305,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/List/BigOperators/Lemmas.lean | List.pow_card_le_prod | [] | [
53,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
50,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.coe_int_dvd_coe_int | [
{
"state_after": "d a b : ℤ\n⊢ a ∣ (↑b).re ∧ a ∣ (↑b).im ↔ a ∣ b",
"state_before": "d a b : ℤ\n⊢ ↑a ∣ ↑b ↔ a ∣ b",
"tactic": "rw [coe_int_dvd_iff]"
},
{
"state_after": "case mp\nd a b : ℤ\n⊢ a ∣ (↑b).re ∧ a ∣ (↑b).im → a ∣ b\n\ncase mpr\nd a b : ℤ\n⊢ a ∣ b → a ∣ (↑b).re ∧ a ∣ (↑b).im",
"stat... | [
378,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/LinearAlgebra/Matrix/Hermitian.lean | Matrix.IsHermitian.eq | [] | [
48,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.raised_iff | [
{
"state_after": "case mp\nα : Type ?u.243566\nn m : ℕ\n⊢ Raised n m → n ≤ m ∧ m ≤ n + 1\n\ncase mpr\nα : Type ?u.243566\nn m : ℕ\n⊢ n ≤ m ∧ m ≤ n + 1 → Raised n m",
"state_before": "α : Type ?u.243566\nn m : ℕ\n⊢ Raised n m ↔ n ≤ m ∧ m ≤ n + 1",
"tactic": "constructor"
},
{
"state_after": "case... | [
789,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
782,
1
] |
Mathlib/Algebra/Group/Basic.lean | ite_one_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.2448\nβ : Type ?u.2451\nG : Type ?u.2454\nM : Type u\ninst✝¹ : MulOneClass M\nP : Prop\ninst✝ : Decidable P\na b : M\n⊢ (if P then 1 else a * b) = (if P then 1 else a) * if P then 1 else b",
"tactic": "by_cases h:P <;> simp [h]"
}
] | [
68,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
66,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MonoidHom.mrange_top_iff_surjective | [
{
"state_after": "no goals",
"state_before": "M : Type u_2\nN : Type u_1\nP : Type ?u.118478\ninst✝³ : MulOneClass M\ninst✝² : MulOneClass N\ninst✝¹ : MulOneClass P\nS : Submonoid M\nA : Type ?u.118499\ninst✝ : SetLike A M\nhA : SubmonoidClass A M\nS' : A\nF : Type u_3\nmc : MonoidHomClass F M N\nf : F\n⊢ ↑... | [
1070,
93
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1069,
1
] |
Mathlib/GroupTheory/Perm/Sign.lean | Equiv.Perm.sign_mul | [] | [
550,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
549,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.mul_re | [
{
"state_after": "no goals",
"state_before": "S : Type ?u.416499\nT : Type ?u.416502\nR : Type u_1\ninst✝ : CommRing R\nr x y z : R\na b c : ℍ[R]\n⊢ a.re * b.re + -1 * a.imI * b.imI + -1 * a.imJ * b.imJ - -1 * -1 * a.imK * b.imK =\n a.re * b.re - a.imI * b.imI - a.imJ * b.imJ - a.imK * b.imK",
"tacti... | [
949,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
948,
1
] |
Mathlib/NumberTheory/Liouville/Basic.lean | Liouville.transcendental | [
{
"state_after": "case intro.intro\nx : ℝ\nlx : Liouville x\nf : ℤ[X]\nf0 : f ≠ 0\nef0 : ↑(aeval x) f = 0\n⊢ False",
"state_before": "x : ℝ\nlx : Liouville x\n⊢ Transcendental ℤ x",
"tactic": "rintro ⟨f : ℤ[X], f0, ef0⟩"
},
{
"state_after": "case ef0\nx : ℝ\nlx : Liouville x\nf : ℤ[X]\nf0 : f ≠ ... | [
218,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
11
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Mathlib/SetTheory/ZFC/Basic.lean | Class.classToCong_empty | [
{
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"state_before": "⊢ classToCong ∅ = ∅",
"tactic": "ext"
},
{
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] | [
1587,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1585,
1
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_zero_left' | [] | [
705,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
703,
1
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Mathlib/Algebra/Order/Floor.lean | Int.sub_floor_div_mul_nonneg | [] | [
1026,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1025,
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Mathlib/LinearAlgebra/Dfinsupp.lean | Submodule.mem_biSup_iff_exists_dfinsupp | [] | [
374,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
369,
1
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Mathlib/GroupTheory/Submonoid/Basic.lean | Submonoid.nontrivial_iff | [] | [
375,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
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Mathlib/MeasureTheory/MeasurableSpace.lean | Measurable.prod | [
{
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673,
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Mathlib/Topology/Algebra/ConstMulAction.lean | continuous_const_smul_iff | [
{
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230,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
229,
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Mathlib/MeasureTheory/MeasurableSpace.lean | measurable_quotient_mk' | [] | [
495,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
494,
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Mathlib/Analysis/Calculus/BumpFunctionInner.lean | ContDiffBump.normed_def | [] | [
489,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
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Mathlib/Order/Max.lean | IsBot.snd | [] | [
422,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
422,
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Mathlib/CategoryTheory/Adjunction/Opposites.lean | CategoryTheory.Adjunction.unit_rightAdjointUniq_hom | [
{
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259,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/Data/Multiset/Basic.lean | Multiset.countp_pos | [] | [
2301,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2300,
1
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Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.coe_nat_mul_eq_nsmul | [
{
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}
] | [
111,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Data/Pi/Algebra.lean | Pi.mulSingle_op₂ | [] | [
317,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
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Mathlib/Data/PNat/Prime.lean | PNat.lcm_dvd | [] | [
99,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
98,
1
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Mathlib/Data/Real/NNReal.lean | NNReal.orderIsoIccZeroCoe_symm_apply_coe | [] | [
467,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
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Mathlib/Data/Multiset/Basic.lean | Multiset.countp_cons | [
{
"state_after": "no goals",
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"tactic": "simp [List.countp_co... | [
2222,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2221,
1
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Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.subgroupOf_bot_eq_bot | [] | [
1651,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1650,
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Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | summable_star_iff' | [] | [
1418,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1417,
1
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Mathlib/Order/Basic.lean | PUnit.min_eq | [] | [
1371,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1370,
1
] |
Mathlib/GroupTheory/Perm/List.lean | List.formPerm_ext_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.792756\ninst✝ : DecidableEq α\nl✝ : List α\nx✝ x y x' y' : α\nl l' : List α\nhd : Nodup (x :: y :: l)\nhd' : Nodup (x' :: y' :: l')\nh : formPerm (x :: y :: l) = formPerm (x' :: y' :: l')\n⊢ (x :: y :: l) ~r (x' :: y' :: l')",
"state_before": "α : Type u_1\nβ : Ty... | [
379,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
344,
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Mathlib/CategoryTheory/Monoidal/Category.lean | CategoryTheory.MonoidalCategory.rightUnitor_conjugation | [
{
"state_after": "no goals",
"state_before": "C✝ : Type u\n𝒞 : Category C✝\ninst✝² : MonoidalCategory C✝\nC : Type u\ninst✝¹ : Category C\ninst✝ : MonoidalCategory C\nU V W X✝ Y✝ Z X Y : C\nf : X ⟶ Y\n⊢ f ⊗ 𝟙 (𝟙_ C) = (ρ_ X).hom ≫ f ≫ (ρ_ Y).inv",
"tactic": "rw [← rightUnitor_naturality_assoc, Iso.ho... | [
253,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
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Mathlib/Order/Partition/Finpartition.lean | Finpartition.nonempty_of_mem_parts | [] | [
465,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
464,
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.ball_subset_closedBall | [] | [
524,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
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Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Ioo_left | [] | [
440,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
439,
1
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Mathlib/Algebra/DirectSum/Ring.lean | DirectSum.ofPow | [
{
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291,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
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Mathlib/Data/List/Rdrop.lean | List.rtakeWhile_concat_pos | [
{
"state_after": "no goals",
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"tactic": "rw [rtakeWhile_concat, if_pos h]"
}
] | [
208,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Logic/Equiv/Fintype.lean | Equiv.Perm.viaFintypeEmbedding_apply_image | [
{
"state_after": "α : Type u_2\nβ : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\ne : Perm α\nf : α ↪ β\na : α\n⊢ ↑(extendDomain e (Function.Embedding.toEquivRange f)) (↑f a) = ↑f (↑e a)",
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77,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
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Mathlib/CategoryTheory/Sites/Subsheaf.lean | CategoryTheory.GrothendieckTopology.Subpresheaf.lift_ι | [
{
"state_after": "case w.h.h\nC : Type u\ninst✝ : Category C\nJ : GrothendieckTopology C\nF F' F'' : Cᵒᵖ ⥤ Type w\nG G' : Subpresheaf F\nf : F' ⟶ F\nhf : ∀ (U : Cᵒᵖ) (x : F'.obj U), f.app U x ∈ obj G U\nx✝ : Cᵒᵖ\na✝ : F'.obj x✝\n⊢ (lift G f hf ≫ ι G).app x✝ a✝ = f.app x✝ a✝",
"state_before": "C : Type u\nin... | [
151,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
148,
1
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Mathlib/FieldTheory/Subfield.lean | Subfield.pow_mem | [] | [
321,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
320,
11
] |
Mathlib/Data/Matrix/Block.lean | Matrix.fromBlocks_toBlocks | [
{
"state_after": "case a.h\nl : Type u_4\nm : Type u_3\nn : Type u_2\no : Type u_1\np : Type ?u.4504\nq : Type ?u.4507\nm' : o → Type ?u.4512\nn' : o → Type ?u.4517\np' : o → Type ?u.4522\nR : Type ?u.4525\nS : Type ?u.4528\nα : Type u_5\nβ : Type ?u.4534\nM : Matrix (n ⊕ o) (l ⊕ m) α\ni : n ⊕ o\nj : l ⊕ m\n⊢ f... | [
104,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
101,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | Summable.sigma_factor | [] | [
1194,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1192,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.liminf_eq_sSup_sInf | [] | [
799,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
797,
1
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Mathlib/Data/Fintype/Basic.lean | Finset.Nonempty.eq_univ | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.1716\nγ : Type ?u.1719\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : Subsingleton α\nx : α\nhx : x ∈ s\n⊢ s = univ",
"state_before": "α : Type u_1\nβ : Type ?u.1716\nγ : Type ?u.1719\ninst✝¹ : Fintype α\ns t : Finset α\ninst✝ : Subsingleton α\n⊢ Finset.... | [
101,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
99,
1
] |
Mathlib/LinearAlgebra/Matrix/Charpoly/LinearMap.lean | PiToModule.fromEnd_apply_single_one | [
{
"state_after": "ι : Type u_1\ninst✝⁴ : Fintype ι\nM : Type u_3\ninst✝³ : AddCommGroup M\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : Module R M\nI : Ideal R\nb : ι → M\nhb : Submodule.span R (Set.range b) = ⊤\ninst✝ : DecidableEq ι\nf : Module.End R M\ni : ι\n⊢ ↑f (↑(↑(Fintype.total R R) b) (Pi.single i 1)) =... | [
70,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
65,
1
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Mathlib/CategoryTheory/Pi/Basic.lean | CategoryTheory.Functor.pi'_eval | [
{
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260,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
255,
1
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Mathlib/MeasureTheory/Function/SimpleFunc.lean | MeasureTheory.SimpleFunc.add_lintegral | [
{
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1017,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1007,
1
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Mathlib/Order/RelClasses.lean | trans_trichotomous_left | [
{
"state_after": "α : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsTrans α r\ninst✝ : IsTrichotomous α r\na b c : α\nh₁ : ¬r b a\nh₂ : r b c\n⊢ r a c",
"state_before": "α : Type u\nβ : Type v\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : IsTrans α r\ninst✝ : IsTrichotomous α r\na b c :... | [
167,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/Topology/SubsetProperties.lean | ClosedEmbedding.tendsto_cocompact | [] | [
906,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
903,
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] |
Mathlib/LinearAlgebra/TensorProduct.lean | TensorProduct.smul_tmul_smul | [
{
"state_after": "no goals",
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309,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.continuousOn_of_dominated | [
{
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1071,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1064,
1
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Mathlib/CategoryTheory/Preadditive/Generator.lean | CategoryTheory.Preadditive.isCoseparating_iff | [
{
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"state_before": "C : Type u\ninst✝¹ : Category C\ninst✝ : Preadditive C\n𝒢 : Set C\nh𝒢 : IsCoseparating 𝒢\nX Y : C\nf : X ⟶ Y\nhf : ∀ (G : C), G ∈ 𝒢 → ∀ (h : Y ⟶ G), f ≫ h = 0\n⊢ ∀ (G : C), G ∈ 𝒢 → ∀ (h : Y ⟶ G), f ≫ h = 0 ≫ h",
"tactic": "simpa only [Limits.zero_comp] ... | [
40,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/Topology/ContinuousOn.lean | Set.LeftInvOn.map_nhdsWithin_eq | [
{
"state_after": "case a\nα : Type u_2\nβ : Type u_1\nγ : Type ?u.338607\nδ : Type ?u.338610\ninst✝³ : TopologicalSpace α\ninst✝² : TopologicalSpace β\ninst✝¹ : TopologicalSpace γ\ninst✝ : TopologicalSpace δ\nf : α → β\ng : β → α\nx : β\ns : Set β\nh : LeftInvOn f g s\nhx : f (g x) = x\nhf : ContinuousWithinAt ... | [
940,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
932,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Projections.lean | AlgebraicTopology.DoldKan.P_add_Q | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ P q + (𝟙 K[X] - P q) = 𝟙 K[X]",
"state_before": "C : Type u_2\ninst✝¹ : Category C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\n⊢ P q + Q q = 𝟙 K[X]",
"tactic": "rw [Q]"
},
{
... | [
79,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/LinearAlgebra/Determinant.lean | LinearEquiv.isUnit_det' | [] | [
439,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
437,
1
] |
Mathlib/SetTheory/Ordinal/Arithmetic.lean | Ordinal.IsNormal.lt_iff | [] | [
432,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
431,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coeFn_mk | [] | [
87,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
86,
1
] |
Mathlib/Data/Nat/Order/Basic.lean | Nat.eq_zero_of_mul_le | [] | [
110,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
1
] |
Mathlib/Data/List/Sort.lean | List.length_mergeSort | [] | [
404,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
403,
1
] |
Mathlib/MeasureTheory/Lattice.lean | Finset.measurable_range_sup'' | [
{
"state_after": "case h.e'_5\nM : Type ?u.1462833\ninst✝³ : MeasurableSpace M\nα : Type u_2\nm : MeasurableSpace α\nμ : MeasureTheory.Measure α\nf✝ g : α → M\nδ : Type u_1\ninst✝² : MeasurableSpace δ\ninst✝¹ : SemilatticeSup α\ninst✝ : MeasurableSup₂ α\nf : ℕ → δ → α\nn : ℕ\nhf : ∀ (k : ℕ), k ≤ n → Measurable ... | [
263,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
259,
1
] |
Mathlib/Analysis/Convex/Star.lean | starConvex_iUnion | [
{
"state_after": "𝕜 : Type u_3\nE : Type u_2\nF : Type ?u.8423\ninst✝⁴ : OrderedSemiring 𝕜\ninst✝³ : AddCommMonoid E\ninst✝² : AddCommMonoid F\ninst✝¹ : SMul 𝕜 E\ninst✝ : SMul 𝕜 F\nx : E\ns✝ t : Set E\nι : Sort u_1\ns : ι → Set E\nhs : ∀ (i : ι), StarConvex 𝕜 x (s i)\ny : E\nhy : y ∈ ⋃ (i : ι), s i\na b : ... | [
135,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.sub_ne_zero_of_lt | [
{
"state_after": "no goals",
"state_before": "b : Nat\nx✝ : 0 < succ b\n⊢ succ b - 0 ≠ 0",
"tactic": "simp"
},
{
"state_after": "a b : Nat\nh : succ a < succ b\n⊢ b - a ≠ 0",
"state_before": "a b : Nat\nh : succ a < succ b\n⊢ succ b - succ a ≠ 0",
"tactic": "rw [Nat.succ_sub_succ]"
},
... | [
573,
103
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
569,
1
] |
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