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/RingTheory/JacobsonIdeal.lean | Ideal.isPrimary_of_isMaximal_radical | [
{
"state_after": "R : Type u\nS : Type v\ninst✝ : CommRing R\nI : Ideal R\nhi : IsMaximal (radical I)\nthis : radical I = jacobson I\nx y : R\nhxy : x * y ∈ I\nx✝ : ∃ y_1, y_1 * y - 1 ∈ I\nz : R\nhz : z * y - 1 ∈ I\n⊢ z * (x * y) - x * (z * y - 1) ∈ I",
"state_before": "R : Type u\nS : Type v\ninst✝ : CommR... | [
411,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
401,
1
] |
Mathlib/Algebra/Order/UpperLower.lean | UpperSet.Ici_one | [] | [
167,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
166,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.lift.isLift_inv | [] | [
214,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.neg | [
{
"state_after": "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 F\nG : Type uG\ninst✝³ : Normed... | [
1275,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1274,
1
] |
Mathlib/Data/Polynomial/Degree/Definitions.lean | Polynomial.natDegree_X_le | [] | [
480,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
479,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.repr_total | [
{
"state_after": "ι : Type u_1\nι' : Type ?u.48934\nR : Type u_2\nR₂ : Type ?u.48940\nK : Type ?u.48943\nM : Type u_3\nM' : Type ?u.48949\nM'' : Type ?u.48952\nV : Type u\nV' : Type ?u.48957\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : Module R M\ninst✝¹ : AddCommMonoid M'\ninst✝ : Module R M'\nb b₁... | [
183,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
181,
1
] |
Std/Data/Nat/Lemmas.lean | Nat.lt_le_antisymm | [] | [
348,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
347,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.sin_ne_zero_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ sin θ ≠ 0 ↔ θ ≠ 0 ∧ θ ≠ ↑π",
"tactic": "rw [← not_or, ← sin_eq_zero_iff]"
}
] | [
372,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
371,
1
] |
Mathlib/Data/List/Sort.lean | List.Sorted.nodup | [] | [
80,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
78,
11
] |
Mathlib/Algebra/Quaternion.lean | QuaternionAlgebra.imK_star | [] | [
631,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
630,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.gcd_eq_natAbs | [] | [
186,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.union_sdiff_left | [] | [
2130,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2129,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.ringHom_ext' | [] | [
469,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
467,
1
] |
Mathlib/Data/Nat/Interval.lean | Nat.multiset_Ico_map_mod | [
{
"state_after": "case h.e'_2\na✝ b c n a : ℕ\n⊢ Multiset.map (fun x => x % a) (Multiset.Ico n (n + a)) = (image (fun x => x % a) (Finset.Ico n (n + a))).val",
"state_before": "a✝ b c n a : ℕ\n⊢ Multiset.map (fun x => x % a) (Multiset.Ico n (n + a)) = Multiset.range a",
"tactic": "convert congr_arg Fins... | [
318,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
314,
1
] |
Mathlib/NumberTheory/LucasLehmer.lean | LucasLehmer.X.int_coe_fst | [] | [
323,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
322,
1
] |
Std/Data/Option/Init/Lemmas.lean | Option.map_some' | [] | [
20,
79
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
20,
9
] |
Mathlib/LinearAlgebra/FiniteDimensional.lean | FiniteDimensional.finrank_eq_rank' | [] | [
194,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/GroupTheory/Complement.lean | Subgroup.isComplement'_of_disjoint_and_mul_eq_univ | [
{
"state_after": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nh1 : Disjoint H K\nh2 : ↑H * ↑K = Set.univ\ng : G\n⊢ ∃ a, (fun x => ↑x.fst * ↑x.snd) a = g",
"state_before": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nS T : Set G\nh1 : Disjoint H K\nh2 : ↑H * ↑K = Set.univ\n⊢ IsCompleme... | [
532,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
528,
1
] |
Mathlib/Analysis/Asymptotics/Asymptotics.lean | Asymptotics.IsBigO.mono | [] | [
452,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
451,
1
] |
Mathlib/Algebra/Ring/Defs.lean | distrib_three_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nR : Type x\ninst✝² : Mul R\ninst✝¹ : Add R\ninst✝ : RightDistribClass R\na b c d : R\n⊢ (a + b + c) * d = a * d + b * d + c * d",
"tactic": "simp [right_distrib]"
}
] | [
98,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
97,
1
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | ContDiffAt.rpow | [] | [
508,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Tactic/Ring/Basic.lean | Mathlib.Tactic.Ring.sub_pf | [
{
"state_after": "u : Lean.Level\nR✝ : Type ?u.219701\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : Type u_1\ninst✝ : Ring R\na b : R\n⊢ a - b = a + -b",
"state_before": "u : Lean.Level\nR✝ : Type ?u.219701\nα : Q(Type u)\nsα : Q(CommSemiring «$α»)\ninst✝¹ : CommSemiring R✝\nR : T... | [
572,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Data/Set/Opposite.lean | Set.singleton_unop | [
{
"state_after": "case h\nα : Type u_1\nx : αᵒᵖ\nx✝ : α\n⊢ x✝ ∈ Set.unop {x} ↔ x✝ ∈ {x.unop}",
"state_before": "α : Type u_1\nx : αᵒᵖ\n⊢ Set.unop {x} = {x.unop}",
"tactic": "ext"
},
{
"state_after": "case h.mp\nα : Type u_1\nx : αᵒᵖ\nx✝ : α\n⊢ x✝ ∈ Set.unop {x} → x✝ ∈ {x.unop}\n\ncase h.mpr\nα :... | [
92,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
88,
1
] |
Mathlib/SetTheory/Ordinal/Basic.lean | Ordinal.lift.initialSeg_coe | [] | [
842,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
841,
1
] |
Mathlib/Data/Set/Function.lean | Set.range_extend_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_3\nβ : Type u_2\nγ : Type u_1\nι : Sort ?u.4057\nπ : α → Type ?u.4062\nf : α → β\ng : α → γ\ng' : β → γ\n⊢ range (extend f g g') ⊆ range g ∪ g' '' range fᶜ",
"tactic": "classical\nrintro _ ⟨y, rfl⟩\nrw [extend_def]\nsplit_ifs with h\nexacts [Or.in... | [
139,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
133,
1
] |
Mathlib/Algebra/Order/Group/Defs.lean | inv_mul_lt_one_iff | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝² : Group α\ninst✝¹ : LT α\ninst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1\na b c : α\n⊢ b < a * 1 ↔ b < a",
"tactic": "rw [mul_one]"
}
] | [
206,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_strictMono | [] | [
350,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Analysis/Convex/Between.lean | affineSegment_comm | [
{
"state_after": "R : Type u_2\nV : Type u_3\nV' : Type ?u.8362\nP : Type u_1\nP' : Type ?u.8368\ninst✝⁶ : OrderedRing R\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'\nx y z : P\n⊢ z ∈ affineSegment R x y ↔ z ∈ affi... | [
61,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
55,
1
] |
Mathlib/Algebra/Order/SMul.lean | smul_upperBounds_subset_upperBounds_smul | [] | [
152,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
150,
1
] |
Mathlib/Data/Vector/Basic.lean | Vector.insertNth_val | [] | [
529,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/Order/Filter/Basic.lean | Filter.mem_bind' | [] | [
2736,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2734,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.zero_lt_of_ne_zero | [
{
"state_after": "no goals",
"state_before": "a : Nat\nh : a ≠ 0\n⊢ 0 < a",
"tactic": "match a with\n| 0 => contradiction\n| a+1 => apply Nat.zero_lt_succ"
},
{
"state_after": "no goals",
"state_before": "a : Nat\nh : 0 ≠ 0\n⊢ 0 < 0",
"tactic": "contradiction"
},
{
"state_after":... | [
325,
34
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
322,
1
] |
Mathlib/LinearAlgebra/StdBasis.lean | LinearMap.stdBasis_same | [] | [
71,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/LinearAlgebra/Finsupp.lean | Finsupp.total_fin_zero | [
{
"state_after": "case h.h\nα : Type ?u.435535\nM : Type u_1\nN : Type ?u.435541\nP : Type ?u.435544\nR : Type u_2\nS : Type ?u.435550\ninst✝¹² : Semiring R\ninst✝¹¹ : Semiring S\ninst✝¹⁰ : AddCommMonoid M\ninst✝⁹ : Module R M\ninst✝⁸ : AddCommMonoid N\ninst✝⁷ : Module R N\ninst✝⁶ : AddCommMonoid P\ninst✝⁵ : Mo... | [
719,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
717,
1
] |
Mathlib/Analysis/InnerProductSpace/Basic.lean | inner_map_polarization' | [
{
"state_after": "𝕜 : Type ?u.2732526\nE : Type ?u.2732529\nF : Type ?u.2732532\ninst✝⁶ : IsROrC 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : InnerProductSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ndec_E : DecidableEq E\nV : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerPr... | [
1238,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1229,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrictₗ_apply | [] | [
1503,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1501,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.le_centralizer_iff_isCommutative | [] | [
2392,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2390,
1
] |
Mathlib/Algebra/Group/Units.lean | Units.mul_inv_eq_iff_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c✝ u : αˣ\na c : α\nh : a * ↑b⁻¹ = c\n⊢ a = c * ↑b",
"tactic": "rw [← h, inv_mul_cancel_right]"
},
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : Monoid α\na✝ b c✝ u : αˣ\na c : α\nh : a = c *... | [
341,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.add_one_le_iff | [
{
"state_after": "case zero\nn m : ℕ\nk : Fin (zero + 1)\n⊢ k + 1 ≤ k ↔ k = last zero\n\ncase succ\nn m n✝ : ℕ\nk : Fin (Nat.succ n✝ + 1)\n⊢ k + 1 ≤ k ↔ k = last (Nat.succ n✝)",
"state_before": "n✝ m n : ℕ\nk : Fin (n + 1)\n⊢ k + 1 ≤ k ↔ k = last n",
"tactic": "cases n"
},
{
"state_after": "case... | [
973,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
963,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Icc_eq_empty | [] | [
363,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
362,
1
] |
Mathlib/Topology/LocalExtr.lean | IsLocalMax.comp_continuous | [] | [
311,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
309,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Deriv.lean | fderiv_ccos | [] | [
347,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
345,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | Matrix.compl_apply_diag | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.12260\ninst✝³ : DecidableEq α\ninst✝² : DecidableEq V\nA : Matrix V V α\ninst✝¹ : Zero α\ninst✝ : One α\ni : V\n⊢ compl A i i = 0",
"tactic": "simp [compl]"
}
] | [
108,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
108,
1
] |
Mathlib/AlgebraicTopology/DoldKan/SplitSimplicialObject.lean | SimplicialObject.Splitting.ι_πSummand_eq_id | [
{
"state_after": "C : Type u_2\ninst✝² : Category C\ninst✝¹ : HasFiniteCoproducts C\nX : SimplicialObject C\ns : Splitting X\ninst✝ : HasZeroMorphisms C\nΔ : SimplexCategoryᵒᵖ\nA : IndexSet Δ\n⊢ ((ιCoprod s.N A ≫ map X s.ι Δ) ≫\n inv (map X s.ι Δ) ≫\n Sigma.desc fun B =>\n if h : B = A then... | [
54,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/Data/Complex/Module.lean | skewAdjoint.I_smul_neg_I | [
{
"state_after": "no goals",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : { x // x ∈ skewAdjoint A }\n⊢ I • ↑(↑negISMul a) = ↑a",
"tactic": "simp only [smul_smul, skewAdjoint.negISMul_apply_coe, neg_smul, smul_neg, I_m... | [
429,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
427,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.union_def | [] | [
1695,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1694,
1
] |
Mathlib/Analysis/Asymptotics/AsymptoticEquivalent.lean | Asymptotics.isEquivalent_iff_tendsto_one | [
{
"state_after": "case mp\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedField β\nt u v w : α → β\nl : Filter α\nhz : ∀ᶠ (x : α) in l, v x ≠ 0\n⊢ u ~[l] v → Tendsto (u / v) l (𝓝 1)\n\ncase mpr\nα : Type u_1\nβ : Type u_2\ninst✝ : NormedField β\nt u v w : α → β\nl : Filter α\nhz : ∀ᶠ (x : α) in l, v x ≠ 0\n⊢ Tendst... | [
236,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.ofEquivFun_equivFun | [
{
"state_after": "no goals",
"state_before": "ι : Type u_1\nι' : Type ?u.694515\nR : Type u_2\nR₂ : Type ?u.694521\nK : Type ?u.694524\nM : Type u_3\nM' : Type ?u.694530\nM'' : Type ?u.694533\nV : Type u\nV' : Type ?u.694538\ninst✝⁵ : Semiring R\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\ninst✝² : AddCo... | [
980,
97
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/Data/Polynomial/Eval.lean | Polynomial.eval₂_finset_prod | [] | [
1114,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1112,
1
] |
Mathlib/Algebra/DirectSum/Basic.lean | DirectSum.fromAddMonoid_of | [
{
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232,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
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Mathlib/MeasureTheory/Function/SpecialFunctions/IsROrC.lean | aemeasurable_of_re_im | [
{
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86,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
82,
1
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Mathlib/Analysis/BoxIntegral/Partition/Basic.lean | BoxIntegral.Prepartition.iUnion_mono | [] | [
259,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
256,
1
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Mathlib/Data/Matrix/Rank.lean | Matrix.rank_eq_finrank_range_toLin | [
{
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147,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
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Mathlib/Analysis/Calculus/ContDiff.lean | ContDiffAt.fst' | [] | [
780,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
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Mathlib/Data/Seq/Computation.lean | Computation.liftRel_pure_left | [
{
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61
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Mathlib/Data/Set/Image.lean | Set.insert_image_compl_eq_range | [
{
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777,
15
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764,
1
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Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | WithTop.sInf_eq | [] | [
71,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
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Mathlib/Algebra/Homology/Additive.lean | ChainComplex.single₀MapHomologicalComplex_hom_app_zero | [] | [
374,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
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Mathlib/Topology/ContinuousFunction/Compact.lean | BoundedContinuousFunction.norm_toContinuousMap_eq | [] | [
194,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
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Mathlib/Algebra/Order/ToIntervalMod.lean | toIocMod_periodic | [] | [
754,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
753,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordSeparatingSet_comm | [] | [
175,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
174,
1
] |
Mathlib/CategoryTheory/Arrow.lean | CategoryTheory.Arrow.square_from_iso_invert | [
{
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"tactic": "simp only [Iso.inv_hom_id_assoc, Arrow.w, Arrow.mk_hom]"
}
] | [
267,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
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Std/Data/AssocList.lean | Std.AssocList.contains_eq | [
{
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"tactic": "induction l <;> simp [*, contains]"
}
] | [
152,
37
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
150,
9
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Mathlib/Topology/Basic.lean | IsClosed.frontier_eq | [
{
"state_after": "no goals",
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}
] | [
757,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
756,
1
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Mathlib/Algebra/Group/Commute.lean | Commute.units_val | [] | [
247,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
246,
1
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Mathlib/Topology/MetricSpace/Basic.lean | Metric.continuousOn_iff | [
{
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1065,
46
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1063,
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Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.lift_symm_apply | [] | [
913,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
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Mathlib/Data/Stream/Init.lean | Stream'.mem_of_mem_odd | [
{
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"tactic": "rw [h, nth_odd]"
}
] | [
519,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
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Mathlib/Topology/Algebra/Module/Multilinear.lean | ContinuousMultilinearMap.toMultilinearMap_add | [] | [
209,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
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Mathlib/Order/BoundedOrder.lean | top_le_iff | [] | [
159,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
158,
1
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Mathlib/Data/Real/CauSeq.lean | CauSeq.exists_gt | [
{
"state_after": "α : Type u_1\ninst✝ : LinearOrderedField α\nf : CauSeq α abs\nK : α\nH : ∀ (i : ℕ), abs (↑f i) < K\ni : ℕ\nx✝ : i ≥ 0\n⊢ ↑f i ≤ K",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedField α\nf : CauSeq α abs\nK : α\nH : ∀ (i : ℕ), abs (↑f i) < K\ni : ℕ\nx✝ : i ≥ 0\n⊢ 1 ≤ ↑(const (K + 1) ... | [
804,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
800,
1
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Mathlib/Geometry/Manifold/ChartedSpace.lean | hasGroupoid_of_le | [] | [
877,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
875,
1
] |
Mathlib/Computability/TuringMachine.lean | Turing.Tape.move_right_left | [
{
"state_after": "case mk\nΓ : Type u_1\ninst✝ : Inhabited Γ\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ move Dir.left (move Dir.right { head := head✝, left := left✝, right := right✝ }) =\n { head := head✝, left := left✝, right := right✝ }",
"state_before": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\n⊢... | [
544,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
542,
1
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Mathlib/SetTheory/Cardinal/Ordinal.lean | Cardinal.aleph_toPartENat | [] | [
311,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/Basic.lean | accPt_iff_nhds | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nι : Sort w\na : α\ns s₁ s₂ t : Set α\np p₁ p₂ : α → Prop\ninst✝ : TopologicalSpace α\nx : α\nC : Set α\n⊢ AccPt x (𝓟 C) ↔ ∀ (U : Set α), U ∈ 𝓝 x → ∃ y, y ∈ U ∩ C ∧ y ≠ x",
"tactic": "simp [acc_principal_iff_cluster, clusterPt_princi... | [
1185,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1183,
1
] |
Mathlib/Logic/Basic.lean | heq_rec_iff_heq | [
{
"state_after": "α : Sort u_1\nβ : Sort u_2\na : α\nC : α → Sort u_2\nx : β\ny : C a\n⊢ HEq x ((_ : a = a) ▸ y) ↔ HEq x y",
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"tactic": "subst e"
},
{
"state_after": "no ... | [
574,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
573,
1
] |
Mathlib/Data/MvPolynomial/Basic.lean | MvPolynomial.eval_sum | [] | [
1158,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1156,
1
] |
Mathlib/Topology/Instances/ENNReal.lean | ENNReal.hasSum_toReal | [
{
"state_after": "case intro\nα : Type u_1\nβ : Type ?u.307697\nγ : Type ?u.307700\na b c d : ℝ≥0∞\nr p q : ℝ≥0\nx y z ε ε₁ ε₂ : ℝ≥0∞\ns : Set ℝ≥0∞\nf : α → ℝ≥0\nhsum : (∑' (x : α), (fun i => ↑(f i)) x) ≠ ⊤\n⊢ HasSum (fun x => ENNReal.toReal ((fun i => ↑(f i)) x)) (∑' (x : α), ENNReal.toReal ((fun i => ↑(f i)) ... | [
1087,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
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Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.card_commonNeighbors_le_degree_left | [
{
"state_after": "ι : Sort ?u.297010\n𝕜 : Type ?u.297013\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\ninst✝¹ : Fintype V\ninst✝ : DecidableRel G.Adj\nv w : V\n⊢ Fintype.card ↑(commonNeighbors G v w) ≤ Fintype.card ↑(neighborSet G v)",
"state_bef... | [
1600,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1597,
1
] |
Mathlib/Data/Multiset/Basic.lean | Multiset.disjoint_of_le_left | [] | [
2925,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2924,
1
] |
Mathlib/Data/List/Basic.lean | List.concat_ne_nil | [
{
"state_after": "no goals",
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"tactic": "simp"
}
] | [
568,
72
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
568,
1
] |
Mathlib/Order/JordanHolder.lean | CompositionSeries.snoc_castSucc | [] | [
572,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
570,
1
] |
Mathlib/Order/UpperLower/Basic.lean | UpperSet.compl_iSup₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.85112\nγ : Type ?u.85115\nι : Sort u_2\nκ : ι → Sort u_3\ninst✝ : LE α\ns t : UpperSet α\na : α\nf : (i : ι) → κ i → UpperSet α\n⊢ compl (⨆ (i : ι) (j : κ i), f i j) = ⨆ (i : ι) (j : κ i), compl (f i j)",
"tactic": "simp_rw [UpperSe... | [
858,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
857,
1
] |
Mathlib/Order/Compare.lean | Ordering.Compares.ne_gt | [] | [
108,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean | CategoryTheory.CommSq.cocone_inl | [] | [
93,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.mem_div | [] | [
604,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
603,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometryEquiv.bijective | [] | [
990,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
989,
11
] |
Mathlib/Data/Polynomial/RingDivision.lean | Polynomial.count_map_roots_of_injective | [
{
"state_after": "case pos\nR : Type u\nS : Type v\nT : Type w\na b✝ : R\nn : ℕ\nA : Type u_1\nB : Type u_2\ninst✝² : CommRing A\ninst✝¹ : CommRing B\ninst✝ : IsDomain A\np : A[X]\nf : A →+* B\nhf : Function.Injective ↑f\nb : B\nhp0 : p = 0\n⊢ Multiset.count b (Multiset.map (↑f) (roots p)) ≤ rootMultiplicity b ... | [
1179,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1173,
1
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Mathlib/SetTheory/Ordinal/Exponential.lean | Ordinal.lt_opow_of_limit | [
{
"state_after": "a b c : Ordinal\nb0 : b ≠ 0\nh : IsLimit c\n⊢ ¬a < b ^ c ↔ ∀ (x : Ordinal), ¬(x < c ∧ a < b ^ x)",
"state_before": "a b c : Ordinal\nb0 : b ≠ 0\nh : IsLimit c\n⊢ a < b ^ c ↔ ∃ c', c' < c ∧ a < b ^ c'",
"tactic": "rw [← not_iff_not, not_exists]"
},
{
"state_after": "no goals",
... | [
76,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/Algebra/MonoidAlgebra/Basic.lean | MonoidAlgebra.single_mul_apply | [] | [
1058,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1056,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.fromEdgeSet_empty | [
{
"state_after": "case Adj.h.h.a\nι : Sort ?u.82740\n𝕜 : Type ?u.82743\nV : Type u\nW : Type v\nX : Type w\nG : SimpleGraph V\nG' : SimpleGraph W\na b c u v✝ w✝ : V\ne : Sym2 V\ns : Set (Sym2 V)\nv w : V\n⊢ Adj (fromEdgeSet ∅) v w ↔ Adj ⊥ v w",
"state_before": "ι : Sort ?u.82740\n𝕜 : Type ?u.82743\nV : Ty... | [
639,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
637,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.zero_add | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.173311\nn : Num\n⊢ 0 + n = n",
"tactic": "cases n <;> rfl"
}
] | [
213,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
213,
1
] |
Mathlib/AlgebraicGeometry/LocallyRingedSpace.lean | AlgebraicGeometry.LocallyRingedSpace.comp_val_c_app | [] | [
188,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean | CategoryTheory.Limits.coprod.diag_comp | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝¹ : Category C\nX✝ Y✝ X Y : C\ninst✝ : HasBinaryCoproduct X X\nf : X ⟶ Y\n⊢ codiag X ≫ f = desc f f",
"tactic": "simp"
}
] | [
838,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Mathlib/Analysis/SpecialFunctions/Log/Basic.lean | Real.log_le_sub_one_of_pos | [
{
"state_after": "x✝ y x : ℝ\nhx : 0 < x\n⊢ log x + 1 ≤ x",
"state_before": "x✝ y x : ℝ\nhx : 0 < x\n⊢ log x ≤ x - 1",
"tactic": "rw [le_sub_iff_add_le]"
},
{
"state_after": "case h.e'_4\nx✝ y x : ℝ\nhx : 0 < x\n⊢ x = exp (log x)",
"state_before": "x✝ y x : ℝ\nhx : 0 < x\n⊢ log x + 1 ≤ x",
... | [
274,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
271,
1
] |
Mathlib/Analysis/NormedSpace/lpSpace.lean | lp.coeFn_neg | [] | [
369,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
368,
1
] |
Mathlib/Data/List/Nodup.lean | List.not_nodup_pair | [] | [
84,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.IsSymm.isRefl | [
{
"state_after": "R : Type u_1\nR₁ : Type ?u.159549\nR₂ : Type ?u.159552\nR₃ : Type ?u.159555\nM : Type u_2\nM₁ : Type ?u.159561\nM₂ : Type ?u.159564\nMₗ₁ : Type ?u.159567\nMₗ₁' : Type ?u.159570\nMₗ₂ : Type ?u.159573\nMₗ₂' : Type ?u.159576\nK : Type ?u.159579\nK₁ : Type ?u.159582\nK₂ : Type ?u.159585\nV : Type ... | [
232,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.reachable | [] | [
1861,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1860,
11
] |
Mathlib/Analysis/SpecialFunctions/Pow/Deriv.lean | deriv_rpow_const | [] | [
601,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
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