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/Equivalence.lean | CategoryTheory.Equivalence.Equivalence_mk'_unitInv | [] | [
144,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/WithBot.lean | WithTop.forall | [] | [
589,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
588,
11
] |
Mathlib/Data/Nat/Count.lean | Nat.count_lt_count_succ_iff | [
{
"state_after": "no goals",
"state_before": "p : ℕ → Prop\ninst✝ : DecidablePred p\nn : ℕ\n⊢ count p n < count p (n + 1) ↔ p n",
"tactic": "by_cases h : p n <;> simp [count_succ, h]"
}
] | [
106,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/Data/Set/Basic.lean | Set.Nontrivial.exists_ne | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nhs : Set.Nontrivial s\nz : α\nH : ∀ (x : α), x ∈ s → x = z\n⊢ False",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Sort x\na b : α\ns s₁ s₂ t t₁ t₂ u : Set α\nhs : Set.Nontrivial s\nz : α\n⊢ ∃ x... | [
2493,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2489,
1
] |
Mathlib/NumberTheory/Liouville/LiouvilleNumber.lean | liouville_liouvilleNumber | [
{
"state_after": "m : ℕ\nhm : 2 ≤ m\nmZ1 : 1 < ↑m\n⊢ Liouville (liouvilleNumber ↑m)",
"state_before": "m : ℕ\nhm : 2 ≤ m\n⊢ Liouville (liouvilleNumber ↑m)",
"tactic": "have mZ1 : 1 < (m : ℤ) := by norm_cast"
},
{
"state_after": "m : ℕ\nhm : 2 ≤ m\nmZ1 : 1 < ↑m\nm1 : 1 < ↑m\n⊢ Liouville (liouvill... | [
208,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
195,
1
] |
Mathlib/Data/List/ToFinsupp.lean | List.toFinsupp_cons_apply_succ | [] | [
110,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
107,
1
] |
Mathlib/Data/List/Sort.lean | List.orderedInsert_eq_take_drop | [
{
"state_after": "α : Type uu\nr : α → α → Prop\ninst✝ : DecidableRel r\na b : α\nl : List α\n⊢ (if r a b then a :: b :: l else b :: orderedInsert r a l) =\n takeWhile (fun b => decide ¬r a b) (b :: l) ++ a :: dropWhile (fun b => decide ¬r a b) (b :: l)",
"state_before": "α : Type uu\nr : α → α → Prop\ni... | [
215,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
209,
1
] |
Mathlib/Analysis/Complex/ReImTopology.lean | Complex.frontier_reProdIm | [
{
"state_after": "no goals",
"state_before": "s t : Set ℝ\n⊢ frontier (s ×ℂ t) = closure s ×ℂ frontier t ∪ frontier s ×ℂ closure t",
"tactic": "simpa only [← preimage_eq_preimage equivRealProdClm.symm.toHomeomorph.surjective,\n equivRealProdClm.symm.toHomeomorph.preimage_frontier] using frontier_prod_e... | [
188,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/Data/Fin/Tuple/NatAntidiagonal.lean | Finset.Nat.antidiagonalTuple_zero_right | [] | [
252,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | IsPreconnected.ordConnected | [] | [
223,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
222,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.digits.injective | [] | [
325,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
324,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.symm_image_target_inter_eq' | [] | [
510,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Set/Ncard.lean | Set.ncard_le_one_iff | [
{
"state_after": "α : Type u_1\nβ : Type ?u.150013\ns t : Set α\na b x y : α\nf : α → β\nhs : autoParam (Set.Finite s) _auto✝\n⊢ (∀ (a : α), a ∈ s → ∀ (b : α), b ∈ s → a = b) ↔ ∀ {a b : α}, a ∈ s → b ∈ s → a = b",
"state_before": "α : Type u_1\nβ : Type ?u.150013\ns t : Set α\na b x y : α\nf : α → β\nhs : a... | [
669,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
666,
1
] |
Mathlib/Data/PFun.lean | PFun.asSubtype_eq_of_mem | [] | [
134,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/NumberTheory/Padics/PadicVal.lean | padicValNat_def | [] | [
226,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
224,
1
] |
Mathlib/Data/ZMod/Quotient.lean | AddAction.orbitZmultiplesEquiv_symm_apply' | [
{
"state_after": "n : ℕ\nA : Type ?u.312437\nR : Type ?u.312440\ninst✝⁵ : AddGroup A\ninst✝⁴ : Ring R\nα✝ : Type ?u.312449\nβ✝ : Type ?u.312452\ninst✝³ : Group α✝\na✝ : α✝\ninst✝² : MulAction α✝ β✝\nb✝ : β✝\nα : Type u_1\nβ : Type u_2\ninst✝¹ : AddGroup α\na : α\ninst✝ : AddAction α β\nb : β\nk : ℤ\n⊢ (k % ↑(mi... | [
160,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Constructions/BorelSpace/Basic.lean | Continuous.isOpenPosMeasure_map | [
{
"state_after": "α : Type ?u.877436\nβ : Type u_1\nγ : Type u_2\nγ₂ : Type ?u.877445\nδ : Type ?u.877448\nι : Sort y\ns t u : Set α\ninst✝¹⁵ : TopologicalSpace α\ninst✝¹⁴ : MeasurableSpace α\ninst✝¹³ : OpensMeasurableSpace α\ninst✝¹² : TopologicalSpace β\ninst✝¹¹ : MeasurableSpace β\ninst✝¹⁰ : OpensMeasurableS... | [
837,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
832,
1
] |
Mathlib/Algebra/Order/Module.lean | upperBounds_smul_of_neg | [] | [
235,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/Order/LiminfLimsup.lean | Filter.cofinite.limsup_set_eq | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.182390\nγ : Type ?u.182393\nι : Type u_2\np : ι → Prop\ns : ι → Set α\n⊢ limsup s cofinite = {x | Set.Infinite {n | x ∈ s n}}",
"tactic": "simp only [← cofinite.blimsup_true s, cofinite.blimsup_set_eq, true_and_iff]"
}
] | [
1073,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1072,
1
] |
Mathlib/Order/SuccPred/Basic.lean | exists_succ_iterate_or | [] | [
1444,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1443,
1
] |
Mathlib/Order/Filter/Germ.lean | Filter.Germ.liftPred_const | [] | [
303,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
302,
1
] |
Mathlib/Algebra/BigOperators/Finprod.lean | MonoidHom.map_finprod_Prop | [] | [
309,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
307,
1
] |
Mathlib/Logic/Equiv/LocalEquiv.lean | LocalEquiv.trans_apply | [] | [
701,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
700,
1
] |
Mathlib/Analysis/NormedSpace/OperatorNorm.lean | ContinuousLinearMap.le_norm_flip | [
{
"state_after": "𝕜 : Type u_1\n𝕜₂ : Type u_6\n𝕜₃ : Type u_2\nE : Type u_3\nEₗ : Type ?u.1080046\nF : Type u_5\nFₗ : Type ?u.1080052\nG : Type u_4\nGₗ : Type ?u.1080058\n𝓕 : Type ?u.1080061\ninst✝¹⁷ : SeminormedAddCommGroup E\ninst✝¹⁶ : SeminormedAddCommGroup Eₗ\ninst✝¹⁵ : SeminormedAddCommGroup F\ninst✝¹⁴ ... | [
795,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
792,
9
] |
Mathlib/Topology/Order.lean | continuous_sup_dom | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type ?u.38234\nf : α → β\nι : Sort ?u.38241\nt₁ t₂ : TopologicalSpace α\nt₃ : TopologicalSpace β\n⊢ Continuous f ↔ Continuous f ∧ Continuous f",
"tactic": "simp only [continuous_iff_le_induced, sup_le_iff]"
}
] | [
738,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
736,
1
] |
Mathlib/Data/Finset/Basic.lean | Finset.inter_distrib_left | [] | [
1741,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1740,
1
] |
src/lean/Init/Prelude.lean | Fin.val_eq_of_eq | [] | [
1756,
10
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
1755,
1
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_val | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Algebra/Hom/NonUnitalAlg.lean | NonUnitalAlgHom.ext_iff | [
{
"state_after": "R : Type u\nA : Type v\nB : Type w\nC : Type w₁\ninst✝⁶ : Monoid R\ninst✝⁵ : NonUnitalNonAssocSemiring A\ninst✝⁴ : DistribMulAction R A\ninst✝³ : NonUnitalNonAssocSemiring B\ninst✝² : DistribMulAction R B\ninst✝¹ : NonUnitalNonAssocSemiring C\ninst✝ : DistribMulAction R C\nf : A →ₙₐ[R] B\nx : ... | [
164,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Mathlib/Topology/Algebra/Order/LiminfLimsup.lean | Filter.Tendsto.isBoundedUnder_ge_atTop | [] | [
123,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
121,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/ArctanDeriv.lean | ContDiff.arctan | [] | [
218,
25
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Logic/Embedding/Basic.lean | Function.Embedding.ext_iff | [] | [
107,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.lift_map_functor_map | [
{
"state_after": "C : Type u_2\ninst✝¹ : Category C\nr : HomRel C\nD : Type u_4\ninst✝ : Category D\nF : C ⥤ D\nH : ∀ (x y : C) (f₁ f₂ : x ⟶ y), r f₁ f₂ → F.map f₁ = F.map f₂\nX Y : C\nf : X ⟶ Y\n⊢ (lift r F H).map ((functor r).map f) =\n (lift.isLift r F H).inv.app X ≫ (functor r ⋙ lift r F H).map f ≫ (lift... | [
221,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Data/Real/Irrational.lean | Irrational.of_neg | [
{
"state_after": "no goals",
"state_before": "q✝ : ℚ\nx y : ℝ\nh : Irrational (-x)\nx✝ : x ∈ Set.range Rat.cast\nq : ℚ\nhx : ↑q = x\n⊢ ↑(-q) = -x",
"tactic": "rw [cast_neg, hx]"
}
] | [
267,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
267,
1
] |
Mathlib/Topology/Sets/Opens.lean | TopologicalSpace.Opens.coe_eq_empty | [] | [
193,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.eventually_ge_atTop | [] | [
186,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
185,
1
] |
Mathlib/RingTheory/FractionalIdeal.lean | FractionalIdeal.mem_map | [] | [
742,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
740,
1
] |
Mathlib/Data/Polynomial/Basic.lean | Polynomial.C_bit0 | [] | [
522,
8
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
521,
1
] |
Mathlib/LinearAlgebra/Matrix/Basis.lean | Basis.coePiBasisFun.toMatrix_eq_transpose | [
{
"state_after": "case h.a.h\nι : Type u_1\nι' : Type ?u.96253\nκ : Type ?u.96256\nκ' : Type ?u.96259\nR : Type u_2\nM✝ : Type ?u.96265\ninst✝⁶ : CommSemiring R\ninst✝⁵ : AddCommMonoid M✝\ninst✝⁴ : Module R M✝\nR₂ : Type ?u.96452\nM₂ : Type ?u.96455\ninst✝³ : CommRing R₂\ninst✝² : AddCommGroup M₂\ninst✝¹ : Modu... | [
83,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
80,
1
] |
Mathlib/Order/CompleteLattice.lean | iInf_iInf_eq_left | [] | [
1178,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1177,
1
] |
Mathlib/RingTheory/Ideal/Basic.lean | Ideal.subset_span | [] | [
145,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/LinearAlgebra/UnitaryGroup.lean | Matrix.UnitaryGroup.toGL_one | [
{
"state_after": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA : Matrix n n α\n⊢ LinearMap.id = ↑1",
"state_before": "n : Type u\ninst✝³ : DecidableEq n\ninst✝² : Fintype n\nα : Type v\ninst✝¹ : CommRing α\ninst✝ : StarRing α\nA : Matrix n n ... | [
185,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
183,
1
] |
Mathlib/Data/Finsupp/NeLocus.lean | Finsupp.neLocus_comm | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nM : Type ?u.4833\nN : Type u_2\nP : Type ?u.4839\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\n⊢ neLocus f g = neLocus g f",
"tactic": "simp_rw [neLocus, Finset.union_comm, ne_comm]"
}
] | [
73,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
72,
1
] |
Mathlib/Data/List/Dedup.lean | List.dedup_cons_of_mem' | [
{
"state_after": "no goals",
"state_before": "α : Type u\ninst✝ : DecidableEq α\na : α\nl : List α\nh : a ∈ dedup l\n⊢ ¬∀ (b : α), b ∈ pwFilter (fun x x_1 => x ≠ x_1) l → a ≠ b",
"tactic": "simpa only [forall_mem_ne, not_not] using h"
}
] | [
38,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
37,
1
] |
Mathlib/GroupTheory/OrderOfElement.lean | orderOf_eq_prime | [
{
"state_after": "no goals",
"state_before": "G : Type u\nA : Type v\nx y : G\na b : A\nn m : ℕ\ninst✝¹ : Monoid G\ninst✝ : AddMonoid A\np : ℕ\nhp : Fact (Nat.Prime p)\nhg : x ^ p = 1\nhg1 : x ≠ 1\n⊢ ¬IsFixedPt (fun x_1 => x * x_1) 1",
"tactic": "rwa [IsFixedPt, mul_one]"
}
] | [
454,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
452,
1
] |
Mathlib/Analysis/SpecialFunctions/Sqrt.lean | ContDiffOn.sqrt | [] | [
174,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Topology/MetricSpace/Completion.lean | UniformSpace.Completion.dist_self | [
{
"state_after": "case refine'_1\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx : Completion α\n⊢ IsClosed {a | dist a a = 0}\n\ncase refine'_2\nα : Type u\nβ : Type v\ninst✝ : PseudoMetricSpace α\nx : Completion α\n⊢ ∀ (a : α), dist (↑α a) (↑α a) = 0",
"state_before": "α : Type u\nβ : Type v\ninst... | [
67,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
62,
11
] |
Mathlib/Topology/Algebra/InfiniteSum/Ring.lean | Summable.mul_right | [] | [
50,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
49,
1
] |
Mathlib/Analysis/Calculus/ContDiff.lean | contDiff_pi | [
{
"state_after": "no goals",
"state_before": "𝕜 : Type u_1\ninst✝¹⁴ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝¹³ : NormedAddCommGroup D\ninst✝¹² : NormedSpace 𝕜 D\nE : Type uE\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nF : Type uF\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpac... | [
1165,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1164,
1
] |
Mathlib/Combinatorics/Additive/Etransform.lean | Finset.mulEtransformLeft.fst_mul_snd_subset | [
{
"state_after": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Group α\ne : α\nx : Finset α × Finset α\n⊢ op e • x.fst * e⁻¹ • x.snd ⊆ x.fst * x.snd",
"state_before": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Group α\ne : α\nx : Finset α × Finset α\n⊢ (mulEtransformLeft e x).fst * (mulEtransformLeft e... | [
148,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
1
] |
Mathlib/Topology/LocalExtr.lean | Filter.EventuallyEq.isLocalMinOn_iff | [] | [
580,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
8
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_hasFPowerSeriesOnBall | [] | [
441,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
440,
1
] |
Mathlib/Algebra/GeomSum.lean | geom_sum₂_comm | [] | [
252,
37
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
250,
1
] |
Mathlib/LinearAlgebra/Finrank.lean | Submodule.lt_of_le_of_finrank_lt_finrank | [
{
"state_after": "no goals",
"state_before": "K : Type u\nV : Type v\ninst✝⁴ : Ring K\ninst✝³ : AddCommGroup V\ninst✝² : Module K V\nV₂ : Type v'\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\ns t : Submodule K V\nle : s ≤ t\nlt : finrank K { x // x ∈ s } < finrank K { x // x ∈ t }\nh : s = t\n⊢ finrank K ... | [
284,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
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Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty | [
{
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973,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
956,
1
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Mathlib/LinearAlgebra/Dfinsupp.lean | CompleteLattice.lsum_comp_mapRange_toSpanSingleton | [
{
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473,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
465,
1
] |
Mathlib/Algebra/Order/LatticeGroup.lean | LatticeOrderedCommGroup.pos_one | [] | [
168,
11
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
167,
1
] |
Mathlib/Data/Matrix/Notation.lean | Matrix.mul_fin_two | [
{
"state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\ninst✝¹ : AddCommMonoid α\ninst✝ : Mul α\na₁₁ a₁₂ a₂₁ a₂₂ b₁₁ b₁₂ b₂₁ b₂₂ : α\ni j : Fin 2\n⊢ (↑of ![![a₁₁, a₁₂], ![a₂₁, a₂₂]] ⬝ ↑of ![![b₁₁, b₁₂], ![b₂₁, b₂₂]]) i j =\n ↑of ![![a₁₁ * b₁₁ + a₁₂ * b₂₁, a₁₁ * b... | [
442,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
436,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | Metric.eventually_nhds_iff_ball | [] | [
955,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/ZeroMorphisms.lean | CategoryTheory.Limits.zero_of_target_iso_zero | [
{
"state_after": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nX Y : C\nf : X ⟶ Y\ni : Y ≅ 0\nh : f = f ≫ i.hom ≫ 𝟙 0 ≫ i.inv\n⊢ f = 0",
"state_before": "C : Type u\ninst✝³ : Category C\nD : Type u'\ninst✝² : Category D\ninst✝¹ : H... | [
383,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
381,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.le_add_right | [] | [
342,
47
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
340,
1
] |
Mathlib/Topology/FiberBundle/Basic.lean | FiberBundleCore.localTrivAsLocalEquiv_coe | [] | [
658,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Algebra/Lie/Quotient.lean | LieSubmodule.Quotient.mk_eq_zero | [] | [
193,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
192,
1
] |
Mathlib/CategoryTheory/Limits/Fubini.lean | CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits_conePoints | [] | [
179,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean | ModelWithCorners.map_nhds_eq | [] | [
306,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.coe_carrier_toSubmonoid | [] | [
485,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
484,
1
] |
Std/Data/Option/Lemmas.lean | Option.map_eq_some' | [
{
"state_after": "no goals",
"state_before": "α✝¹ : Type u_1\nb : α✝¹\nα✝ : Type u_2\nx : Option α✝\nf : α✝ → α✝¹\n⊢ Option.map f x = some b ↔ ∃ a, x = some a ∧ f a = b",
"tactic": "cases x <;> simp"
}
] | [
127,
99
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
127,
9
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_bracket | [] | [
218,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Basic.lean | DifferentiableWithinAt.mono_of_mem | [] | [
577,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
575,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.iUnion_exists | [] | [
692,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
690,
1
] |
Mathlib/GroupTheory/FreeGroup.lean | FreeGroup.map_mul | [] | [
1046,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1045,
1
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.adjoin_simple_comm | [] | [
510,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
509,
1
] |
Mathlib/Data/Set/NAry.lean | Set.image2_swap | [
{
"state_after": "case h\nα : Type u_1\nα' : Type ?u.12485\nβ : Type u_2\nβ' : Type ?u.12491\nγ : Type u_3\nγ' : Type ?u.12497\nδ : Type ?u.12500\nδ' : Type ?u.12503\nε : Type ?u.12506\nε' : Type ?u.12509\nζ : Type ?u.12512\nζ' : Type ?u.12515\nν : Type ?u.12518\nf f' : α → β → γ\ng g' : α → β → γ → δ\ns✝ s' : ... | [
122,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
120,
1
] |
Mathlib/Data/Set/Lattice.lean | Set.Ici_iSup₂ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.296264\nγ : Type ?u.296267\nι : Sort u_2\nι' : Sort ?u.296273\nι₂ : Sort ?u.296276\nκ : ι → Sort u_3\nκ₁ : ι → Sort ?u.296286\nκ₂ : ι → Sort ?u.296291\nκ' : ι' → Sort ?u.296296\ninst✝ : CompleteLattice α\nf : (i : ι) → κ i → α\n⊢ Ici (⨆... | [
2133,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2132,
1
] |
Mathlib/Combinatorics/SimpleGraph/Subgraph.lean | SimpleGraph.Subgraph.edgeSet_subset | [] | [
239,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
238,
1
] |
Mathlib/Data/List/Nodup.lean | List.Nodup.erase_eq_filter | [
{
"state_after": "case nil\nα : Type u\nβ : Type v\nl✝ l₁ l₂ : List α\nr : α → α → Prop\na✝ b : α\ninst✝ : DecidableEq α\nl : List α\na : α\n⊢ List.erase [] a = List.filter (fun x => decide (x ≠ a)) []\n\ncase cons\nα : Type u\nβ : Type v\nl✝¹ l₁ l₂ : List α\nr : α → α → Prop\na✝¹ b✝ : α\ninst✝ : DecidableEq α\... | [
313,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
303,
1
] |
Mathlib/Topology/Category/TopCat/Opens.lean | TopologicalSpace.Opens.infLELeft_apply_mk | [] | [
102,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
1
] |
Mathlib/Algebra/CharP/MixedCharZero.lean | EqualCharZero.PNat.isUnit_natCast | [
{
"state_after": "R : Type u_1\ninst✝ : CommRing R\nh : Fact (∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I))\nn : ℕ+\n⊢ Ideal.span {↑↑n} = ⊤",
"state_before": "R : Type u_1\ninst✝ : CommRing R\nh : Fact (∀ (I : Ideal R), I ≠ ⊤ → CharZero (R ⧸ I))\nn : ℕ+\n⊢ IsUnit ↑↑n",
"tactic": "rw [← Ideal.span_singleton... | [
193,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
182,
1
] |
Mathlib/Order/Max.lean | NoMaxOrder.not_acc | [] | [
176,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/Data/Nat/Parity.lean | Nat.isCompl_even_odd | [
{
"state_after": "no goals",
"state_before": "m n : ℕ\n⊢ IsCompl {n | Even n} {n | Odd n}",
"tactic": "simp only [← Set.compl_setOf, isCompl_compl, odd_iff_not_even]"
}
] | [
71,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
70,
1
] |
Mathlib/Order/GaloisConnection.lean | GaloisInsertion.u_le_u_iff | [] | [
594,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
593,
1
] |
Mathlib/Data/Nat/Digits.lean | Nat.coe_ofDigits | [
{
"state_after": "case nil\nn : ℕ\nα : Type u_1\ninst✝ : Semiring α\nb : ℕ\n⊢ ↑(ofDigits b []) = ofDigits ↑b []\n\ncase cons\nn : ℕ\nα : Type u_1\ninst✝ : Semiring α\nb d : ℕ\nL : List ℕ\nih : ↑(ofDigits b L) = ofDigits (↑b) L\n⊢ ↑(ofDigits b (d :: L)) = ofDigits (↑b) (d :: L)",
"state_before": "n : ℕ\nα : ... | [
212,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Rat/NNRat.lean | NNRat.toNNRat_sum_of_nonneg | [
{
"state_after": "α : Type u_1\np q : ℚ≥0\ns : Finset α\nf : α → ℚ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ ∑ i in s, f i = ∑ a in s, ↑(toNNRat (f a))",
"state_before": "α : Type u_1\np q : ℚ≥0\ns : Finset α\nf : α → ℚ\nhf : ∀ (a : α), a ∈ s → 0 ≤ f a\n⊢ toNNRat (∑ a in s, f a) = ∑ a in s, toNNRat (f a)",
"t... | [
282,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_lt_iff_lt_right | [] | [
113,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Std/Data/HashMap/WF.lean | Std.HashMap.Imp.WF_iff | [] | [
294,
39
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
292,
1
] |
Mathlib/Algebra/Hom/GroupAction.lean | MulSemiringActionHom.coe_fn_coe' | [] | [
500,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
499,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.im_imJ | [] | [
811,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
811,
9
] |
Mathlib/Data/Holor.lean | HolorIndex.drop_drop | [
{
"state_after": "no goals",
"state_before": "ds₁ ds₂ ds₃ is : List ℕ\nh : Forall₂ (fun x x_1 => x < x_1) is (ds₁ ++ ds₂ ++ ds₃)\n⊢ ↑(drop (drop (assocRight { val := is, property := h }))) = ↑(drop { val := is, property := h })",
"tactic": "simp [add_comm, assocRight, drop, cast_type, List.drop_drop]"
... | [
85,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
] |
Mathlib/CategoryTheory/Preadditive/ProjectiveResolution.lean | CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝⁴ : Category C\ninst✝³ : HasZeroObject C\ninst✝² : Preadditive C\ninst✝¹ : HasEqualizers C\ninst✝ : HasImages C\nX : C\nP Q : ProjectiveResolution X\n⊢ (homotopyEquiv P Q).inv ≫ P.π = Q.π",
"tactic": "simp [homotopyEquiv]"
}
] | [
305,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
304,
1
] |
Mathlib/Data/Set/Pointwise/SMul.lean | Set.iUnion_smul_set | [] | [
302,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
301,
1
] |
Mathlib/Data/PFunctor/Univariate/Basic.lean | PFunctor.supp_eq | [
{
"state_after": "case h\nP : PFunctor\nα : Type u\na : P.A\nf : B P a → α\nx : α\n⊢ x ∈ supp { fst := a, snd := f } ↔ x ∈ f '' univ",
"state_before": "P : PFunctor\nα : Type u\na : P.A\nf : B P a → α\n⊢ supp { fst := a, snd := f } = f '' univ",
"tactic": "ext x"
},
{
"state_after": "case h\nP :... | [
244,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
233,
1
] |
Mathlib/Data/Matrix/Basic.lean | Matrix.two_mul_expl | [
{
"state_after": "case refine_4\nl : Type ?u.237230\nm : Type ?u.237233\nn : Type ?u.237236\no : Type ?u.237239\nm' : o → Type ?u.237244\nn' : o → Type ?u.237249\nR✝ : Type ?u.237252\nS : Type ?u.237255\nα : Type v\nβ : Type w\nγ : Type ?u.237262\nR : Type u_1\ninst✝ : CommRing R\nA B : Matrix (Fin 2) (Fin 2) R... | [
961,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
953,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | AffineSubspace.bot_coe | [] | [
768,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
767,
1
] |
Mathlib/CategoryTheory/Equivalence.lean | CategoryTheory.IsEquivalence.inv_fun_map | [
{
"state_after": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst✝¹ : Category D\nF : C ⥤ D\ninst✝ : IsEquivalence F\nX Y : C\nf : X ⟶ Y\n⊢ (Functor.inv F).map (F.map f) = ((asEquivalence F).functor ⋙ (asEquivalence F).inverse).map f",
"state_before": "C : Type u₁\ninst✝² : Category C\nD : Type u₂\ninst... | [
612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
609,
1
] |
Mathlib/Order/JordanHolder.lean | JordanHolderLattice.IsMaximal.iso_refl | [] | [
120,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Analysis/Convex/Side.lean | AffineSubspace.WOppSide.trans_sOppSide | [] | [
601,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
599,
1
] |
Mathlib/Algebra/Order/Floor.lean | Nat.floor_nat | [] | [
113,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
1
] |
Mathlib/Topology/Constructions.lean | closedEmbedding_sigmaMk | [] | [
1494,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1492,
1
] |
Mathlib/NumberTheory/Zsqrtd/Basic.lean | Zsqrtd.nonneg_antisymm | [
{
"state_after": "no goals",
"state_before": "d : ℕ\ndnsq : Nonsquare d\nx : ℕ\nxy : Nonneg { re := -[x+1], im := 0 }\nx✝ : Nonneg (-{ re := -[x+1], im := 0 })\n⊢ 0 < 1",
"tactic": "decide"
},
{
"state_after": "no goals",
"state_before": "d : ℕ\ndnsq : Nonsquare d\nx : ℕ\nx✝ : Nonneg { re :=... | [
943,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
928,
1
] |
Mathlib/Data/Int/Units.lean | Int.isUnit_eq_or_eq_neg | [
{
"state_after": "case inl\na : ℤ\nha : IsUnit a\nhb : IsUnit 1\n⊢ a = 1 ∨ a = -1\n\ncase inr\na : ℤ\nha : IsUnit a\nhb : IsUnit (-1)\n⊢ a = -1 ∨ a = - -1",
"state_before": "a b : ℤ\nha : IsUnit a\nhb : IsUnit b\n⊢ a = b ∨ a = -b",
"tactic": "rcases isUnit_eq_one_or hb with (rfl | rfl)"
},
{
"st... | [
50,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
47,
1
] |
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