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/CategoryTheory/Subobject/Lattice.lean | CategoryTheory.Subobject.inf_def | [] | [
484,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
483,
1
] |
src/lean/Init/SimpLemmas.lean | implies_congr_ctx | [] | [
39,
30
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
38,
1
] |
Std/Data/Int/Lemmas.lean | Int.toNat_zero | [] | [
1367,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1367,
9
] |
Mathlib/Topology/ContinuousFunction/Bounded.lean | BoundedContinuousFunction.coe_intCast | [] | [
1297,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1297,
1
] |
Mathlib/Data/Polynomial/Degree/TrailingDegree.lean | Polynomial.le_trailingDegree_C | [] | [
227,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
226,
1
] |
Mathlib/Order/Disjoint.lean | bot_codisjoint | [] | [
299,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
298,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.mem_sup | [
{
"state_after": "F : Type ?u.415321\nα✝ : Type ?u.415324\nβ✝ : Type ?u.415327\nγ : Type ?u.415330\nι : Type ?u.415333\nκ : Type ?u.415336\nα : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\ns : Finset α\nf : α → Finset β\nx : β\n⊢ x ∈ sup s f ↔ ∃ v, v ∈ s ∧ x ∈ (f v).val",
"state_before": "F : Type ?u.4153... | [
1784,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1780,
1
] |
Mathlib/Logic/Function/Iterate.lean | Function.iterate_succ' | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nf : α → α\nn : ℕ\n⊢ f^[Nat.succ n] = f ∘ f^[n]",
"tactic": "rw [iterate_succ, (Commute.self_iterate f n).comp_eq]"
}
] | [
176,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Std/Data/List/Lemmas.lean | List.foldr_map | [
{
"state_after": "no goals",
"state_before": "α₁ : Type u_1\nα₂ : Type u_2\nβ : Type u_3\nf : α₁ → α₂\ng : α₂ → β → β\nl : List α₁\ninit : β\n⊢ foldr g init (map f l) = foldr (fun x y => g (f x) y) init l",
"tactic": "induction l generalizing init <;> simp [*]"
}
] | [
1415,
45
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1413,
1
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Mathlib/Algebra/Order/Ring/Lemmas.lean | Left.neg_of_mul_neg_left | [] | [
584,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
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Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_coeIdeal_of_mem | [] | [
264,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
262,
1
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.map_le_iff_le_comap | [] | [
1650,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1648,
1
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Mathlib/Algebra/Tropical/BigOperators.lean | Multiset.trop_inf | [
{
"state_after": "case empty\nR : Type u_1\nS : Type ?u.25149\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\n⊢ trop (inf 0) = sum (map trop 0)\n\ncase cons\nR : Type u_1\nS : Type ?u.25149\ninst✝¹ : LinearOrder R\ninst✝ : OrderTop R\ns : R\nx : Multiset R\nIH : trop (inf x) = sum (map trop x)\n⊢ trop (inf (s ::ₘ ... | [
94,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
90,
1
] |
src/lean/Init/Data/Array/Basic.lean | Array.size_set | [] | [
62,
21
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
61,
9
] |
Mathlib/Algebra/Squarefree.lean | Squarefree.of_mul_right | [] | [
84,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/NumberTheory/SumFourSquares.lean | Int.sq_add_sq_of_two_mul_sq_add_sq | [
{
"state_after": "no goals",
"state_before": "m x y : ℤ\nh : ↑2 * m = x ^ 2 + y ^ 2\n⊢ Even (x ^ 2 + y ^ 2)",
"tactic": "simp [← h, even_mul]"
},
{
"state_after": "no goals",
"state_before": "m x y : ℤ\nh : ↑2 * m = x ^ 2 + y ^ 2\nthis : Even (x ^ 2 + y ^ 2)\n⊢ Even (x + y)",
"tactic": "... | [
66,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
54,
1
] |
Mathlib/Data/Set/Prod.lean | Set.mem_prod | [] | [
60,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
59,
1
] |
Mathlib/Data/Real/CauSeq.lean | rat_inv_continuous_lemma | [
{
"state_after": "α : Type u_2\nβ✝ : Type ?u.21186\ninst✝⁴ : LinearOrderedField α\ninst✝³ : Ring β✝\nabv✝ : β✝ → α\ninst✝² : IsAbsoluteValue abv✝\nβ : Type u_1\ninst✝¹ : DivisionRing β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nε K : α\nε0 : 0 < ε\nK0 : 0 < K\na b : β\nha : K ≤ abv a\nhb : K ≤ abv b\nh : abv (a... | [
88,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | PSet.equiv_of_isEmpty | [
{
"state_after": "no goals",
"state_before": "x : PSet\ny : PSet\ninst✝¹ : IsEmpty (Type x)\ninst✝ : IsEmpty (Type y)\n⊢ (∀ (i : Type x), ∃ j, Equiv (Func x i) (Func y j)) ∧ ∀ (j : Type y), ∃ i, Equiv (Func x i) (Func y j)",
"tactic": "simp"
}
] | [
206,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.tan_neg_of_neg_of_pi_div_two_lt | [
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : x < 0\nhpx : -(π / 2) < x\n⊢ 0 < -x",
"tactic": "linarith"
},
{
"state_after": "no goals",
"state_before": "x : ℝ\nhx0 : x < 0\nhpx : -(π / 2) < x\n⊢ -x < π / 2",
"tactic": "linarith [pi_pos]"
}
] | [
952,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
951,
1
] |
Std/Data/Int/Lemmas.lean | Int.eq_nat_or_neg | [] | [
166,
81
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
166,
1
] |
Mathlib/RingTheory/Adjoin/Tower.lean | Algebra.adjoin_algebraMap | [] | [
37,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Data/PNat/Defs.lean | PNat.coe_eq_one_iff | [] | [
202,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.coe_sub | [] | [
944,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
943,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundle.continuous_proj | [] | [
251,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.ndinter_le_right | [] | [
269,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
268,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.Sized.dual_iff | [
{
"state_after": "α : Type u_1\nt : Ordnode α\nh : Sized (Ordnode.dual t)\n⊢ Sized (Ordnode.dual (Ordnode.dual t))",
"state_before": "α : Type u_1\nt : Ordnode α\nh : Sized (Ordnode.dual t)\n⊢ Sized t",
"tactic": "rw [← dual_dual t]"
},
{
"state_after": "no goals",
"state_before": "α : Type ... | [
408,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
407,
1
] |
Mathlib/Logic/Equiv/Fintype.lean | Function.Embedding.toEquivRange_symm_apply_self | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq β\ne : Equiv.Perm α\nf : α ↪ β\na : α\n⊢ ↑(toEquivRange f).symm { val := ↑f a, property := (_ : ↑f a ∈ Set.range ↑f) } = a",
"tactic": "simp [Equiv.symm_apply_eq]"
}
] | [
53,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
52,
1
] |
Mathlib/Order/Monotone/Basic.lean | StrictAnti.imp | [] | [
376,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
375,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.zpow_apply_eq_of_apply_apply_eq_self | [
{
"state_after": "α : Type u_1\nf g h : Perm α\nx : α\nhffx : ↑f (↑f x) = x\nn : ℕ\n⊢ ↑(f ^ (n + 1 + 1)) x = x ∨ ↑(f ^ (n + 1 + 1)) x = ↑f x",
"state_before": "α : Type u_1\nf g h : Perm α\nx : α\nhffx : ↑f (↑f x) = x\nn : ℕ\n⊢ ↑(f ^ Int.negSucc n) x = x ∨ ↑(f ^ Int.negSucc n) x = ↑f x",
"tactic": "rw [... | [
176,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/GroupTheory/Perm/Support.lean | Equiv.Perm.disjoint_iff_disjoint_support | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\n⊢ Disjoint f g ↔ _root_.Disjoint (support f) (support g)",
"tactic": "simp [disjoint_iff_eq_or_eq, disjoint_iff, disjoint_iff, Finset.ext_iff, not_and_or,\n imp_iff_not_or]"
}
] | [
396,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
394,
1
] |
Mathlib/Order/Interval.lean | Interval.coe_iInf | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.65135\nγ : Type ?u.65138\nδ : Type ?u.65141\nι : Sort u_2\nκ : ι → Sort ?u.65149\ninst✝¹ : CompleteLattice α\ninst✝ : DecidableRel fun x x_1 => x ≤ x_1\nf : ι → Interval α\n⊢ ↑(⨅ (i : ι), f i) = ⋂ (i : ι), ↑(f i)",
"tactic": "simp [... | [
781,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
780,
1
] |
Mathlib/LinearAlgebra/Quotient.lean | Submodule.liftQ_apply | [] | [
356,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
Mathlib/Data/Set/Basic.lean | Set.subset_union_left | [] | [
817,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
817,
1
] |
Mathlib/Data/MvPolynomial/Variables.lean | MvPolynomial.degreeOf_add_le | [
{
"state_after": "R : Type u\nS : Type v\nσ : Type u_1\nτ : Type ?u.308701\nr : R\ne : ℕ\nn✝ m : σ\ns : σ →₀ ℕ\ninst✝ : CommSemiring R\np q : MvPolynomial σ R\nn : σ\nf g : MvPolynomial σ R\nthis : DecidableEq σ := Classical.decEq σ\n⊢ degreeOf n (f + g) ≤ max (degreeOf n f) (degreeOf n g)",
"state_before":... | [
536,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
530,
1
] |
Mathlib/Data/List/Zip.lean | List.unzip_zip | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type u_1\nγ : Type ?u.87252\nδ : Type ?u.87255\nε : Type ?u.87258\nl₁ : List α\nl₂ : List β\nh : length l₁ = length l₂\n⊢ unzip (zip l₁ l₂) = (l₁, l₂)",
"tactic": "rw [← Prod.mk.eta (p := unzip (zip l₁ l₂)),\n unzip_zip_left (le_of_eq h), un... | [
248,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
245,
1
] |
Mathlib/Topology/Connected.lean | isPreconnected_empty | [] | [
85,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/Deprecated/Subgroup.lean | IsGroupHom.one_iff_ker_inv | [] | [
380,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
Mathlib/Order/Monotone/Basic.lean | Subtype.strictMono_coe | [] | [
1143,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1141,
1
] |
Mathlib/Algebra/Group/Basic.lean | mul_inv_eq_of_eq_mul | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.51063\nβ : Type ?u.51066\nG : Type u_1\ninst✝ : Group G\na b c d : G\nh : a = c * b\n⊢ a * b⁻¹ = c",
"tactic": "simp [h]"
}
] | [
643,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
643,
1
] |
Mathlib/Data/List/Basic.lean | List.injective_foldl_comp | [
{
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2514,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2507,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ioo_subset_Iio_self | [] | [
527,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
527,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.quotQuotMkₐ_toRingHom | [] | [
720,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
718,
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] |
Mathlib/Analysis/Normed/Group/Hom.lean | NormedAddGroupHom.bounds_bddBelow | [] | [
234,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
232,
1
] |
Mathlib/Data/Int/Order/Basic.lean | Int.ediv_pos_of_pos_of_dvd | [
{
"state_after": "no goals",
"state_before": "a✝ b✝ : ℤ\nn : ℕ\na b : ℤ\nH1 : 0 < a\nH2 : 0 ≤ b\nH3 : b ∣ a\n⊢ 0 * b < a",
"tactic": "rwa [zero_mul]"
}
] | [
477,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
476,
1
] |
Mathlib/Topology/Algebra/InfiniteSum/Basic.lean | tsum_bool | [
{
"state_after": "no goals",
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"tactic... | [
519,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
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Mathlib/Order/Height.lean | Set.chainHeight_le_chainHeight_iff | [] | [
203,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
201,
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Mathlib/Algebra/Star/StarAlgHom.lean | NonUnitalStarAlgHom.inl_apply | [] | [
584,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/Data/Real/Basic.lean | Real.mul_pos | [
{
"state_after": "case h\nx y b : ℝ\na : CauSeq ℚ abs\n⊢ 0 < mk a → 0 < b → 0 < mk a * b",
"state_before": "x y a b : ℝ\n⊢ 0 < a → 0 < b → 0 < a * b",
"tactic": "induction' a using Real.ind_mk with a"
},
{
"state_after": "case h.h\nx y : ℝ\na b : CauSeq ℚ abs\n⊢ 0 < mk a → 0 < mk b → 0 < mk a * ... | [
415,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
412,
11
] |
Mathlib/Data/Rat/Defs.lean | Rat.add_assoc | [
{
"state_after": "a b c : ℚ\nn₁ : ℤ\nd₁ : ℕ\nh₁ : d₁ ≠ 0\nn₂ : ℤ\nd₂ : ℕ\nh₂ : d₂ ≠ 0\nn₃ : ℤ\nd₃ : ℕ\nh₃ : d₃ ≠ 0\n⊢ ((n₁ * ↑d₂ + n₂ * ↑d₁) * ↑d₃ + n₃ * (↑d₁ * ↑d₂)) /. (↑d₁ * ↑d₂ * ↑d₃) =\n (n₁ * (↑d₂ * ↑d₃) + (n₂ * ↑d₃ + n₃ * ↑d₂) * ↑d₁) /. (↑d₁ * (↑d₂ * ↑d₃))",
"state_before": "a b c : ℚ\nn₁ : ℤ\nd₁ ... | [
223,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
11
] |
Mathlib/NumberTheory/Liouville/LiouvilleWith.lean | Liouville.frequently_exists_num | [
{
"state_after": "x : ℝ\nhx : Liouville x\nn : ℕ\nH : ¬∃ᶠ (b : ℕ) in atTop, ∃ a, x ≠ ↑a / ↑b ∧ abs (x - ↑a / ↑b) < 1 / ↑b ^ n\n⊢ False",
"state_before": "x : ℝ\nhx : Liouville x\nn : ℕ\n⊢ ∃ᶠ (b : ℕ) in atTop, ∃ a, x ≠ ↑a / ↑b ∧ abs (x - ↑a / ↑b) < 1 / ↑b ^ n",
"tactic": "refine Classical.not_not.1 fun H... | [
371,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
347,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.add_right_inj | [] | [
1084,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1083,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.coe_finTwoProd_repr | [] | [
1351,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1349,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.Memℒp.smul_of_top_right | [
{
"state_after": "α : Type u_2\nE : Type u_1\nF : Type ?u.5938996\nG : Type ?u.5938999\nm m0 : MeasurableSpace α\np✝ : ℝ≥0∞\nq : ℝ\nμ ν : Measure α\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedAddCommGroup G\n𝕜 : Type u_3\ninst✝⁴ : NormedRing 𝕜\ninst✝³ : MulActionWithZero 𝕜 E... | [
1531,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1528,
1
] |
Mathlib/Data/Complex/Exponential.lean | Complex.cos_sub | [
{
"state_after": "no goals",
"state_before": "x y : ℂ\n⊢ cos (x - y) = cos x * cos y + sin x * sin y",
"tactic": "simp [sub_eq_add_neg, cos_add, sin_neg, cos_neg]"
}
] | [
873,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
872,
1
] |
Mathlib/Order/BoundedOrder.lean | OrderTop.ext_top | [
{
"state_after": "case refl\nα✝ : Type u\nβ : Type v\nγ : Type ?u.18268\nδ : Type ?u.18271\nα : Type u_1\nhA : PartialOrder α\nA B : OrderTop α\nH : ∀ (x y : α), x ≤ y ↔ x ≤ y\n⊢ ⊤ = ⊤",
"state_before": "α✝ : Type u\nβ : Type v\nγ : Type ?u.18268\nδ : Type ?u.18271\nα : Type u_1\nhA : PartialOrder α\nA : Or... | [
230,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
225,
1
] |
Mathlib/Algebra/IsPrimePow.lean | IsPrimePow.not_unit | [] | [
50,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
48,
1
] |
Mathlib/CategoryTheory/Iso.lean | CategoryTheory.Iso.self_symm_id | [] | [
208,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
207,
1
] |
Mathlib/Algebra/Module/PointwisePi.lean | smul_pi₀ | [] | [
60,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
58,
1
] |
Mathlib/Algebra/Star/Basic.lean | starRingEnd_self_apply | [] | [
402,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/Deprecated/Subgroup.lean | Group.conjugatesOf_subset | [
{
"state_after": "case intro\nG : Type u_1\nH : Type ?u.142727\nA : Type ?u.142730\na✝ a₁ a₂ b c✝ : G\ns : Set G\ninst✝ : Group G\nt : Set G\nht : IsNormalSubgroup t\na : G\nh : a ∈ t\nx : G\nhc : x ∈ conjugatesOf a\nc : G\nw : c * a * c⁻¹ = x\n⊢ x ∈ t",
"state_before": "G : Type u_1\nH : Type ?u.142727\nA ... | [
689,
12
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Mathlib/Algebra/FreeMonoid/Basic.lean | FreeMonoid.casesOn_of_mul | [] | [
198,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/Topology/MetricSpace/Lipschitz.lean | LipschitzOnWith.of_dist_le' | [
{
"state_after": "case h\nα : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝² : PseudoMetricSpace α\ninst✝¹ : PseudoMetricSpace β\ninst✝ : PseudoMetricSpace γ\nK✝ : ℝ≥0\ns : Set α\nf : α → β\nK : ℝ\nh : ∀ (x : α), x ∈ s → ∀ (y : α), y ∈ s → dist (f x) (f y) ≤ K * dist x y\nx : α\nhx : x ∈ s\ny : α\nhy : y ∈ ... | [
536,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
533,
11
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | LowerSemicontinuous.measurable | [] | [
1060,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1058,
1
] |
Mathlib/MeasureTheory/Measure/Portmanteau.lean | MeasureTheory.tendsto_measure_of_null_frontier | [] | [
255,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
248,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_one_iff | [] | [
354,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
353,
1
] |
Mathlib/Algebra/GCDMonoid/Basic.lean | pow_dvd_of_mul_eq_pow | [
{
"state_after": "α : Type u_1\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : GCDMonoid α\na b c d₁ d₂ : α\nha : a ≠ 0\nhab : IsUnit (gcd a b)\nk : ℕ\nh : a * b = c ^ k\nhc : c = d₁ * d₂\nhd₁ : d₁ ∣ a\nh1 : IsUnit (gcd (d₁ ^ k) b)\nh2 : d₁ ^ k ∣ a * b\n⊢ d₁ ^ k ≠ 0 ∧ d₁ ^ k ∣ a",
"state_before": "α : Type u_... | [
611,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_ite | [] | [
1378,
18
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1376,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Equiv.lean | ContinuousLinearEquiv.comp_fderivWithin | [
{
"state_after": "case pos\n𝕜 : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_4\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_1\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nG' : Type ?u.139... | [
165,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
1
] |
Mathlib/GroupTheory/Sylow.lean | Sylow.coe_subgroup_smul | [] | [
246,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
244,
1
] |
Mathlib/Algebra/TrivSqZeroExt.lean | TrivSqZeroExt.algebraMap_eq_inlHom | [] | [
767,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Algebra/Hom/Group.lean | MonoidHom.coe_copy | [] | [
868,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
866,
1
] |
Mathlib/Data/Num/Lemmas.lean | ZNum.of_to_int | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.1060897\nn : ZNum\n⊢ ↑↑n = n",
"tactic": "rw [← ofInt'_eq, of_to_int']"
}
] | [
1552,
87
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1552,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.fg_of_isUnit | [] | [
884,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
883,
1
] |
Mathlib/Data/Vector3.lean | Vector3.recOn_cons | [] | [
149,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
147,
1
] |
Mathlib/Topology/UniformSpace/Equicontinuity.lean | Filter.HasBasis.uniformEquicontinuous_iff | [
{
"state_after": "ι : Type u_5\nκ : Type ?u.127632\nX : Type ?u.127635\nY : Type ?u.127638\nZ : Type ?u.127641\nα : Type u_4\nβ : Type u_3\nγ : Type ?u.127650\n𝓕 : Type ?u.127653\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : TopologicalSpace Y\ninst✝³ : TopologicalSpace Z\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpa... | [
335,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
1
] |
Mathlib/MeasureTheory/MeasurableSpace.lean | MeasurableSpace.comap_map_le | [] | [
180,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
179,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.val_add_one_of_lt | [
{
"state_after": "case zero\nn m : ℕ\ni : Fin (Nat.succ zero)\nh : i < last zero\n⊢ ↑(i + 1) = ↑i + 1\n\ncase succ\nn m n✝ : ℕ\ni : Fin (Nat.succ (Nat.succ n✝))\nh : i < last (Nat.succ n✝)\n⊢ ↑(i + 1) = ↑i + 1",
"state_before": "n✝ m n : ℕ\ni : Fin (Nat.succ n)\nh : i < last n\n⊢ ↑(i + 1) = ↑i + 1",
"ta... | [
744,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
738,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.toNNReal_mul | [] | [
2197,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2196,
1
] |
Mathlib/LinearAlgebra/SymplecticGroup.lean | SymplecticGroup.coe_inv | [] | [
189,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Std/Data/List/Lemmas.lean | List.Chain.imp' | [
{
"state_after": "no goals",
"state_before": "case nil\nα : Type u_1\nR S : α → α → Prop\nHRS : ∀ ⦃a b : α⦄, R a b → S a b\na : α\nl : List α\na✝ b : α\nHab : ∀ ⦃c : α⦄, R a✝ c → S b c\n⊢ Chain S b []",
"tactic": "constructor"
},
{
"state_after": "case cons.a\nα : Type u_1\nR S : α → α → Prop\nH... | [
1793,
24
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1786,
1
] |
Mathlib/CategoryTheory/Limits/Types.lean | CategoryTheory.Limits.Types.FilteredColimit.colimit_eq_iff_aux | [
{
"state_after": "J : Type v\ninst✝¹ : SmallCategory J\nF : J ⥤ TypeMax\ninst✝ : IsFilteredOrEmpty J\ni j : J\nxi : F.obj i\nxj : F.obj j\n⊢ Quot.mk (Quot.Rel F) { fst := i, snd := xi } = Quot.mk (Quot.Rel F) { fst := j, snd := xj } ↔\n FilteredColimit.Rel F { fst := i, snd := xi } { fst := j, snd := xj }",
... | [
477,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
473,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.mk_mul | [] | [
162,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iInter₂_subset_of_subset | [] | [
369,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
367,
1
] |
Mathlib/CategoryTheory/Preadditive/Basic.lean | CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift | [] | [
340,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
338,
1
] |
Mathlib/Order/Heyting/Basic.lean | hnot_hnot_sup_distrib | [
{
"state_after": "ι : Type ?u.178832\nα : Type u_1\nβ : Type ?u.178838\ninst✝ : CoheytingAlgebra α\na✝ b✝ c a b : α\n⊢ ￢￢(a ⊔ b) ≤ ￢￢a ⊔ ￢￢b",
"state_before": "ι : Type ?u.178832\nα : Type u_1\nβ : Type ?u.178838\ninst✝ : CoheytingAlgebra α\na✝ b✝ c a b : α\n⊢ ￢￢(a ⊔ b) = ￢￢a ⊔ ￢￢b",
"tactic": "refine' ... | [
1113,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1109,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.mk_repr | [] | [
1136,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1135,
1
] |
Mathlib/Data/List/Sigma.lean | List.mem_keys | [] | [
70,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
69,
1
] |
Mathlib/SetTheory/Cardinal/Cofinality.lean | Ordinal.nfpBFamily_lt_ord_lift | [
{
"state_after": "no goals",
"state_before": "α : Type ?u.34204\nr : α → α → Prop\no : Ordinal\nf : (a : Ordinal) → a < o → Ordinal → Ordinal\nc : Ordinal\nhc : ℵ₀ < cof c\nhc' : Cardinal.lift (card o) < cof c\nhf : ∀ (i : Ordinal) (hi : i < o) (b : Ordinal), b < c → f i hi b < c\na : Ordinal\n⊢ Cardinal.li... | [
400,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
397,
1
] |
Mathlib/Topology/MetricSpace/HausdorffDistance.lean | Metric.cthickening_subset_thickening | [] | [
1104,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1102,
1
] |
Mathlib/MeasureTheory/Covering/BesicovitchVectorSpace.lean | Besicovitch.isEmpty_satelliteConfig_multiplicity | [
{
"state_after": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\na : SatelliteConfig E (multiplicity E) (goodτ E)\n⊢ False",
"state_before": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\n⊢ Satelli... | [
550,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
541,
1
] |
Mathlib/Data/Set/Basic.lean | Disjoint.subset_right_of_subset_union | [] | [
2981,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2980,
1
] |
Mathlib/Analysis/Calculus/ContDiffDef.lean | ContDiffOn.mono | [] | [
712,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
Mathlib/CategoryTheory/Subobject/Basic.lean | CategoryTheory.Subobject.underlying_arrow | [] | [
233,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
231,
1
] |
Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.restrict_apply₀' | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.283441\nγ : Type ?u.283444\nδ : Type ?u.283447\nι : Type ?u.283450\nR : Type ?u.283453\nR' : Type ?u.283456\nm0 : MeasurableSpace α\ninst✝¹ : MeasurableSpace β\ninst✝ : MeasurableSpace γ\nμ μ₁ μ₂ μ₃ ν ν' ν₁ ν₂ : Measure α\ns s' t : Set ... | [
1568,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1565,
1
] |
Mathlib/Data/Dfinsupp/WellFounded.lean | Dfinsupp.Lex.acc_of_single | [
{
"state_after": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : (i : ι) → Zero (α i)\nr : ι → ι → Prop\ns : (i : ι) → α i → α i → Prop\nhbot : ∀ ⦃i : ι⦄ ⦃a : α i⦄, ¬s i a 0\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → (x : α i) → Decidable (x ≠ 0)\nx : Π₀ (i : ι), α i\nt : Finset ι\nht : support x = t\n⊢ (∀ (i : ι), i... | [
131,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Basic.lean | Real.cos_eq_one_iff_of_lt_of_lt | [
{
"state_after": "case intro\nn : ℤ\nhx₁ : -(2 * π) < ↑n * (2 * π)\nhx₂ : ↑n * (2 * π) < 2 * π\nh : cos (↑n * (2 * π)) = 1\n⊢ ↑n * (2 * π) = 0",
"state_before": "x : ℝ\nhx₁ : -(2 * π) < x\nhx₂ : x < 2 * π\nh : cos x = 1\n⊢ x = 0",
"tactic": "rcases(cos_eq_one_iff _).1 h with ⟨n, rfl⟩"
},
{
"stat... | [
553,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
545,
1
] |
Mathlib/Order/Hom/Lattice.lean | BoundedLatticeHom.coe_toLatticeHom | [] | [
1236,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1235,
1
] |
Mathlib/Algebra/GCDMonoid/Finset.lean | Finset.dvd_gcd_iff | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.12267\ninst✝¹ : CancelCommMonoidWithZero α\ninst✝ : NormalizedGCDMonoid α\ns s₁ s₂ : Finset β\nf : β → α\na : α\n⊢ (∀ (b : α), b ∈ Multiset.map f s.val → a ∣ b) ↔ ∀ (b : β), b ∈ s → a ∣ f b",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.1... | [
156,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
153,
1
] |
Mathlib/Data/Polynomial/Laurent.lean | Polynomial.toLaurent_injective | [] | [
381,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
379,
1
] |
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