file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Data/Finset/Basic.lean | Finset.right_eq_union_iff_subset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.151794\nγ : Type ?u.151797\ninst✝ : DecidableEq α\ns✝ s₁ s₂ t✝ t₁ t₂ u v : Finset α\na b : α\ns t : Finset α\n⊢ s = t ∪ s ↔ t ⊆ s",
"tactic": "rw [← union_eq_right_iff_subset, eq_comm]"
}
] | [
1481,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1480,
1
] |
Mathlib/Order/MinMax.lean | min_eq_iff | [
{
"state_after": "case mp\nα : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\n⊢ min a b = c → a = c ∧ a ≤ b ∨ b = c ∧ b ≤ a\n\ncase mpr\nα : Type u\nβ : Type v\ninst✝¹ : LinearOrder α\ninst✝ : LinearOrder β\nf : α → β\ns : Set α\na b c d : α\n⊢ a = c ∧ a ≤ ... | [
177,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/Data/Fin/Tuple/Basic.lean | Fin.contractNth_apply_of_ne | [
{
"state_after": "case inl\nm n : ℕ\nα : Type u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nhjk : ↑j ≠ ↑k\nh : ↑k < ↑j\n⊢ contractNth j op g k = g (↑(succAbove j) k)\n\ncase inr.inl\nm n : ℕ\nα : Type u_1\nj : Fin (n + 1)\nop : α → α → α\ng : Fin (n + 1) → α\nk : Fin n\nhjk : ↑j ≠ ↑k\nh ... | [
985,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
978,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Combination.lean | Finset.weightedVSub_apply_const | [
{
"state_after": "no goals",
"state_before": "k : Type u_1\nV : Type u_3\nP : Type u_4\ninst✝² : Ring k\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nS : AffineSpace V P\nι : Type u_2\ns : Finset ι\nι₂ : Type ?u.153989\ns₂ : Finset ι₂\nw : ι → k\np : P\nh : ∑ i in s, w i = 0\n⊢ ↑(weightedVSub s fun x => p) ... | [
282,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Multiset/Nodup.lean | Multiset.Nodup.erase | [] | [
178,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
177,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean | CategoryTheory.Limits.walkingParallelPairOp_one | [] | [
146,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/LinearAlgebra/Multilinear/Basic.lean | MultilinearMap.map_smul_univ | [
{
"state_after": "no goals",
"state_before": "R : Type u\nι : Type u'\nn : ℕ\nM : Fin (Nat.succ n) → Type v\nM₁ : ι → Type v₁\nM₂ : Type v₂\nM₃ : Type v₃\nM' : Type v'\ninst✝⁷ : CommSemiring R\ninst✝⁶ : (i : ι) → AddCommMonoid (M₁ i)\ninst✝⁵ : (i : Fin (Nat.succ n)) → AddCommMonoid (M i)\ninst✝⁴ : AddCommMo... | [
858,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
856,
1
] |
Mathlib/Order/Atoms.lean | isAtomic_iff_isCoatomic | [] | [
881,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
879,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_const_right | [] | [
821,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
819,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Finset.product_self_eq_disjUnion_perm | [
{
"state_after": "case a.mk\nι : Type ?u.3150272\nα : Type u_1\nβ : Type ?u.3150278\ninst✝ : DecidableEq α\nf : Perm α\ns : Finset α\nhf : IsCycleOn f ↑s\na b : α\n⊢ (a, b) ∈ s ×ˢ s ↔\n (a, b) ∈\n disjiUnion (range (card s))\n (fun k =>\n map\n { toFun := fun i => (i, ↑(f ^ k)... | [
1966,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1954,
1
] |
Mathlib/SetTheory/ZFC/Basic.lean | ZFSet.mem_insert_of_mem | [] | [
908,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
907,
1
] |
Mathlib/Topology/UniformSpace/UniformConvergence.lean | tendstoUniformly_iff_tendstoUniformlyOnFilter | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nι : Type x\ninst✝ : UniformSpace β\nF : ι → α → β\nf : α → β\ns s' : Set α\nx : α\np : Filter ι\np' : Filter α\ng : ι → α\n⊢ TendstoUniformly F f p ↔ TendstoUniformlyOnFilter F f p ⊤",
"tactic": "rw [← tendstoUniformlyOn_u... | [
146,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Mathlib/Data/Set/Intervals/OrdConnectedComponent.lean | Set.ordConnectedComponent_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrder α\ns t : Set α\nx y z : α\n⊢ ordConnectedComponent univ x = univ",
"tactic": "simp [ordConnectedComponent]"
}
] | [
76,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
75,
1
] |
Mathlib/Data/Fintype/Basic.lean | Set.toFinset_ssubset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.84031\nγ : Type ?u.84034\ns t✝ : Set α\ninst✝ : Fintype ↑s\nt : Finset α\n⊢ toFinset s ⊂ t ↔ s ⊂ ↑t",
"tactic": "rw [← Finset.coe_ssubset, coe_toFinset]"
}
] | [
658,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Logic/Hydra.lean | WellFounded.cutExpand | [] | [
157,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
156,
1
] |
Mathlib/Data/Set/Function.lean | Set.range_restrict | [] | [
74,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/Topology/Maps.lean | quotientMap_iff | [] | [
278,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
276,
1
] |
Mathlib/Algebra/Order/Monoid/Lemmas.lean | mul_le_of_le_one_of_le | [] | [
771,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
765,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.prod_principal_principal | [
{
"state_after": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.43185\nδ : Type ?u.43188\nι : Sort ?u.43191\ns✝ : Set α\nt✝ : Set β\nf : Filter α\ng : Filter β\ns : Set α\nt : Set β\n⊢ Prod.fst ⁻¹' s ∩ Prod.snd ⁻¹' t = prod s t",
"state_before": "α : Type u_1\nβ : Type u_2\nγ : Type ?u.43185\nδ : Type ?u.43188\nι... | [
402,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
400,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.prod_repr_inr | [] | [
723,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
722,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.coe_inf' | [] | [
912,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Data/Set/Prod.lean | Set.pi_if | [
{
"state_after": "case h\nι : Type u_1\nα : ι → Type u_2\nβ : ι → Type ?u.138170\ns✝ s₁ s₂ : Set ι\nt t₁✝ t₂✝ : (i : ι) → Set (α i)\ni : ι\np : ι → Prop\nh : DecidablePred p\ns : Set ι\nt₁ t₂ : (i : ι) → Set (α i)\nf : (i : ι) → α i\n⊢ (f ∈ pi s fun i => if p i then t₁ i else t₂ i) ↔ f ∈ pi {i | i ∈ s ∧ p i} t₁... | [
758,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
749,
1
] |
Mathlib/Algebra/Tropical/BigOperators.lean | Finset.untrop_sum | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder R\ns : Finset S\nf : S → Tropical (WithTop R)\n⊢ untrop (∑ i in s, f i) = ⨅ (i : { x // x ∈ s }), untrop (f ↑i)",
"tactic": "simpa [← _root_.untrop_sum] using sum_attach.symm"
}
] | [
148,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
146,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.darts_map | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nf : G →g G'\nf' : G' →g G''\nu v u' v' : V\np : Walk G u v\n⊢ darts (Walk.map f p) = List.map (Hom.mapDart f) (darts p)",
"tactic": "induction p <;> simp [*... | [
1515,
91
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1515,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.injective | [] | [
283,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
282,
11
] |
Mathlib/CategoryTheory/Bicategory/Free.lean | CategoryTheory.FreeBicategory.mk_right_unitor_hom | [] | [
300,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
299,
1
] |
Mathlib/Order/GameAdd.lean | Sym2.gameAdd_iff | [
{
"state_after": "case mk.mk\nα : Type u_1\nβ : Type ?u.5319\nrα : α → α → Prop\nrβ : β → β → Prop\nfst✝¹ snd✝¹ fst✝ snd✝ : α\n⊢ GameAdd rα (Quotient.mk (Rel.setoid α) (fst✝¹, snd✝¹)) (Quotient.mk (Rel.setoid α) (fst✝, snd✝)) ↔\n Prod.GameAdd rα rα (fst✝¹, snd✝¹) (fst✝, snd✝) ∨ Prod.GameAdd rα rα (Prod.swap ... | [
168,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
165,
1
] |
Mathlib/Data/Fintype/Powerset.lean | Finset.powerset_univ | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : Fintype α\n⊢ ↑(powerset univ) = ↑univ",
"tactic": "simp [-coe_eq_univ]"
}
] | [
34,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
33,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Iic_mem_atBot | [] | [
72,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Complex.lean | Complex.continuous_tan | [] | [
164,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/NumberTheory/LegendreSymbol/ZModChar.lean | ZMod.χ₈'_int_eq_if_mod_eight | [
{
"state_after": "n : ℤ\nhelp : ∀ (m : ℤ), 0 ≤ m → m < 8 → ↑χ₈' ↑m = if m % 2 = 0 then 0 else if m = 1 ∨ m = 3 then 1 else -1\n⊢ ↑χ₈' ↑n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1",
"state_before": "n : ℤ\n⊢ ↑χ₈' ↑n = if n % 2 = 0 then 0 else if n % 8 = 1 ∨ n % 8 = 3 then 1 else -1",... | [
204,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.toReal_nonneg_iff_sign_nonneg | [
{
"state_after": "case inl\nθ : Angle\nh : toReal θ < 0\n⊢ 0 ≤ toReal θ ↔ 0 ≤ sign θ\n\ncase inr.inl\nθ : Angle\nh : toReal θ = 0\n⊢ 0 ≤ toReal θ ↔ 0 ≤ sign θ\n\ncase inr.inr\nθ : Angle\nh : 0 < toReal θ\n⊢ 0 ≤ toReal θ ↔ 0 ≤ sign θ",
"state_before": "θ : Angle\n⊢ 0 ≤ toReal θ ↔ 0 ≤ sign θ",
"tactic": "... | [
919,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
911,
1
] |
Mathlib/Combinatorics/SimpleGraph/Coloring.lean | SimpleGraph.Coloring.card_colorClasses_le | [
{
"state_after": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑(colorClasses C)\n⊢ Fintype.card ↑(Setoid.classes (Setoid.ker ↑C)) ≤ Fintype.card α",
"state_before": "V : Type u\nG : SimpleGraph V\nα : Type v\nC : Coloring G α\ninst✝¹ : Fintype α\ninst✝ : ... | [
119,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
] |
Mathlib/Data/Nat/Prime.lean | Nat.prime_iff_prime_int | [
{
"state_after": "p : ℕ\nhp : Prime p\na b : ℤ\nh : p ∣ Int.natAbs a ∨ p ∣ Int.natAbs b\n⊢ ↑p ∣ a ∨ ↑p ∣ b",
"state_before": "p : ℕ\nhp : Prime p\na b : ℤ\nh : ↑p ∣ a * b\n⊢ ↑p ∣ a ∨ ↑p ∣ b",
"tactic": "rw [← Int.dvd_natAbs, Int.coe_nat_dvd, Int.natAbs_mul, hp.dvd_mul] at h"
},
{
"state_after": ... | [
755,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
746,
1
] |
Mathlib/Analysis/Asymptotics/SpecificAsymptotics.lean | Filter.Tendsto.cesaro_smul | [
{
"state_after": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nu : ℕ → E\nl : E\nh : Tendsto u atTop (𝓝 l)\n⊢ (fun n => (↑n)⁻¹ • ∑ i in range n, u i - l) =o[atTop] fun _x => 1",
"state_before": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nu : ℕ → E\nl : E\... | [
163,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
151,
1
] |
Mathlib/Topology/Separation.lean | inseparable_iff_eq | [] | [
222,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
221,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.cospanCompIso_app_right | [] | [
295,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
294,
1
] |
Mathlib/GroupTheory/SemidirectProduct.lean | SemidirectProduct.lift_comp_inl | [
{
"state_after": "case h\nN : Type u_1\nG : Type u_3\nH : Type u_2\ninst✝² : Group N\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* MulAut N\nf₁ : N →* H\nf₂ : G →* H\nh :\n ∀ (g : G),\n MonoidHom.comp f₁ (MulEquiv.toMonoidHom (↑φ g)) = MonoidHom.comp (MulEquiv.toMonoidHom (↑MulAut.conj (↑f₂ g))) f₁\nx✝ : N\n... | [
236,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
236,
1
] |
Mathlib/Data/Set/Prod.lean | Set.offDiag_singleton | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Set α\nx : α × α\na✝ a : α\n⊢ offDiag {a} = ∅",
"tactic": "simp"
}
] | [
578,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
578,
1
] |
Mathlib/Data/Set/Finite.lean | Set.Finite.coe_toFinset | [] | [
169,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
168,
11
] |
Mathlib/Analysis/SpecialFunctions/Exponential.lean | hasFDerivAt_exp_smul_const_of_mem_ball' | [
{
"state_after": "case h.e'_10\n𝕂 : Type u_3\n𝕊 : Type u_2\n𝔸 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕂\ninst✝⁸ : CharZero 𝕂\ninst✝⁷ : NormedCommRing 𝕊\ninst✝⁶ : NormedRing 𝔸\ninst✝⁵ : NormedSpace 𝕂 𝕊\ninst✝⁴ : NormedAlgebra 𝕂 𝔸\ninst✝³ : Algebra 𝕊 𝔸\ninst✝² : ContinuousSMul 𝕊 𝔸\ninst✝¹ : Is... | [
315,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
308,
1
] |
Mathlib/Algebra/Lie/Submodule.lean | LieSubmodule.coe_homOfLe | [] | [
587,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
586,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.adjugate_mul_distrib | [
{
"state_after": "m : Type u\nn : Type v\nα : Type w\ninst✝⁴ : DecidableEq n\ninst✝³ : Fintype n\ninst✝² : DecidableEq m\ninst✝¹ : Fintype m\ninst✝ : CommRing α\nA B : Matrix n n α\ng : Matrix n n α → Matrix n n α[X] := fun M => map M ↑C + X • 1\n⊢ adjugate (A ⬝ B) = adjugate B ⬝ adjugate A",
"state_before"... | [
507,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
486,
1
] |
Mathlib/Topology/Order.lean | isOpen_discrete | [] | [
281,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
280,
1
] |
Mathlib/Data/Seq/WSeq.lean | Stream'.WSeq.think_append | [] | [
785,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
784,
1
] |
Mathlib/RingTheory/Localization/AsSubring.lean | Localization.mem_range_mapToFractionRing_iff | [
{
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63,
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52,
1
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Mathlib/Data/Set/Finite.lean | Set.Finite.disjoint_toFinset | [] | [
236,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
8
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Mathlib/LinearAlgebra/LinearIndependent.lean | linearIndependent_of_finite | [] | [
430,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/LinearAlgebra/AffineSpace/Restrict.lean | AffineMap.restrict.bijective | [] | [
95,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
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Mathlib/Data/Real/NNReal.lean | NNReal.sSup_of_not_bddAbove | [
{
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"state_before": "ι : Sort ?u.272153\nf : ι → ℝ≥0\ns : Set ℝ≥0\nhs : ¬BddAbove s\n⊢ sSup s = 0",
"tactic": "rw [← bddAbove_coe] at hs"
},
{
"state_after": "ι : Sort ?u.272153\nf : ι → ℝ≥0\... | [
934,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
931,
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Mathlib/SetTheory/ZFC/Basic.lean | Class.coe_empty | [] | [
1644,
56
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1643,
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Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.SimpleFunc.setToSimpleFunc_mono_left | [
{
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520,
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518,
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Mathlib/MeasureTheory/Function/SpecialFunctions/Basic.lean | Complex.measurable_re | [] | [
78,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/Nat/ModEq.lean | Nat.ModEq.mul_right | [
{
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"state_before": "m n a b c✝ d c : ℕ\nh : a ≡ b [MOD n]\n⊢ a * c ≡ b * c [MOD n]",
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},
{
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"state_before": "m n a b c✝ d c : ℕ\nh : a ≡ b [MOD n]\... | [
126,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
125,
11
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Mathlib/LinearAlgebra/QuadraticForm/Basic.lean | QuadraticForm.map_sub | [
{
"state_after": "no goals",
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}
] | [
257,
80
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
257,
1
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Mathlib/Analysis/NormedSpace/WeakDual.lean | WeakDual.isClosed_image_coe_of_bounded_of_closed | [] | [
217,
99
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
214,
1
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Mathlib/Analysis/Calculus/FDeriv/Add.lean | DifferentiableAt.sub | [] | [
504,
55
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
502,
1
] |
Mathlib/Topology/Sheaves/PresheafOfFunctions.lean | TopCat.presheafToTypes_obj | [] | [
62,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
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Mathlib/Order/UpperLower/Basic.lean | isUpperSet_preimage_toDual_iff | [] | [
190,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
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Mathlib/Data/Nat/Log.lean | Nat.log_anti_left | [
{
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"state_before": "b c n : ℕ\nhc : 1 < c\nhb : c ≤ b\n⊢ log b n ≤ log c n",
"tactic": "rcases eq_or_ne n 0 with (rfl | hn)"
},
{
"state... | [
203,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
198,
1
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Mathlib/Algebra/Star/StarAlgHom.lean | StarAlgEquiv.ext | [] | [
782,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
781,
1
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Mathlib/Data/List/Sigma.lean | List.nodupKeys_dedupKeys | [
{
"state_after": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\nl : List (Sigma β)\n⊢ NodupKeys (foldr (fun x => kinsert x.fst x.snd) [] l)",
"state_before": "α : Type u\nβ : α → Type v\nl✝ l₁ l₂ : List (Sigma β)\ninst✝ : DecidableEq α\nl : List (Sigma β)\n⊢ NodupKeys (dedupK... | [
650,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
636,
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Mathlib/MeasureTheory/Measure/NullMeasurable.lean | MeasureTheory.nullMeasurableSet_singleton | [] | [
352,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
351,
1
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Mathlib/Data/Nat/Dist.lean | Nat.eq_of_dist_eq_zero | [] | [
43,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
38,
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Mathlib/LinearAlgebra/Basis.lean | Basis.coe_sumCoords_of_fintype | [
{
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252,
25
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246,
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Mathlib/Topology/Instances/ENNReal.lean | ENNReal.tendsto_toReal | [] | [
135,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
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Mathlib/Topology/FiberBundle/Trivialization.lean | Pretrivialization.mk_proj_snd | [] | [
132,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
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Mathlib/Data/PEquiv.lean | PEquiv.eq_some_iff | [] | [
115,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
114,
1
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Mathlib/Analysis/Normed/Group/Basic.lean | norm_le_of_mem_closedBall' | [
{
"state_after": "no goals",
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652,
92
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651,
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Mathlib/Algebra/Order/Field/Power.lean | zpow_le_max_iff_min_le | [
{
"state_after": "no goals",
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"tactic": "simp_rw [le_max_iff, min_le_iff, zpow_le_iff_le hx, neg_le_neg_iff]"
}
] | [
114,
70
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
112,
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Mathlib/MeasureTheory/Measure/MutuallySingular.lean | MeasureTheory.Measure.MutuallySingular.mono | [] | [
85,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
84,
1
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Mathlib/GroupTheory/CommutingProbability.lean | commProb_eq_one_iff | [
{
"state_after": "M : Type u_1\ninst✝¹ : Mul M\ninst✝ : Finite M\nh : Nonempty M\nthis : Fintype M\n⊢ commProb M = 1 ↔ Commutative fun x x_1 => x * x_1",
"state_before": "M : Type u_1\ninst✝¹ : Mul M\ninst✝ : Finite M\nh : Nonempty M\n⊢ commProb M = 1 ↔ Commutative fun x x_1 => x * x_1",
"tactic": "have... | [
70,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
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Mathlib/Order/Heyting/Basic.lean | PUnit.hnot_eq | [] | [
1365,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
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Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.projIcc_of_right_le | [
{
"state_after": "no goals",
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"tactic": "simp [projIcc, hx, h]"
}
] | [
51,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Topology/Algebra/Semigroup.lean | exists_idempotent_in_compact_subsemigroup | [
{
"state_after": "M : Type u_1\ninst✝² : Semigroup M\ninst✝¹ : TopologicalSpace M\ninst✝ : T2Space M\ncontinuous_mul_left : ∀ (r : M), Continuous fun x => x * r\ns : Set M\nsnemp : Set.Nonempty s\ns_compact : IsCompact s\ns_add : ∀ (x : M), x ∈ s → ∀ (y : M), y ∈ s → x * y ∈ s\nM' : Type u_1 := { m // m ∈ s }\n... | [
103,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/Data/List/Cycle.lean | List.next_cons_cons_eq | [] | [
164,
35
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
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Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear | [
{
"state_after": "no goals",
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108,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
100,
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Mathlib/MeasureTheory/Integral/SetIntegral.lean | MeasureTheory.set_integral_mono_ae_restrict | [] | [
686,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
684,
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Mathlib/LinearAlgebra/Dimension.lean | lift_rank_range_le | [
{
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167,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
155,
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] |
Mathlib/Algebra/ContinuedFractions/Computation/Translations.lean | GeneralizedContinuedFraction.IntFractPair.succ_nth_stream_eq_none_iff | [
{
"state_after": "K : Type u_1\ninst✝¹ : LinearOrderedField K\ninst✝ : FloorRing K\nv : K\nn : ℕ\n⊢ (Option.bind (IntFractPair.stream v n) fun ap_n => if ap_n.fr = 0 then none else some (IntFractPair.of ap_n.fr⁻¹)) =\n none ↔\n IntFractPair.stream v n = none ∨ ∃ ifp, IntFractPair.stream v n = some ifp ∧... | [
84,
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] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
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Mathlib/MeasureTheory/Measure/MeasureSpace.lean | MeasureTheory.Measure.sum_add_sum_compl | [
{
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2115,
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Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.apply_zero_curry0 | [
{
"state_after": "case H\n𝕜 : Type u\nι : Type v\nι' : Type v'\nn : ℕ\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nEi : Fin (Nat.succ n) → Type wEi\nG : Type wG\nG' : Type wG'\ninst✝¹⁴ : Fintype ι\ninst✝¹³ : Fintype ι'\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : (i : ι) → NormedAddCommGroup (E... | [
1649,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1646,
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] |
Mathlib/Topology/FiberBundle/Trivialization.lean | Trivialization.coe_coe_fst | [] | [
572,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
571,
1
] |
Mathlib/Topology/MetricSpace/Basic.lean | uniformContinuous_nndist | [] | [
1836,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1835,
1
] |
Mathlib/Analysis/Calculus/FDeriv/Bilinear.lean | IsBoundedBilinearMap.differentiable | [] | [
119,
32
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
118,
1
] |
Mathlib/Data/Multiset/Powerset.lean | Multiset.mem_powerset | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ns t : Multiset α\n⊢ ∀ (a b : List α),\n Quotient.mk (isSetoid α) a ∈ powerset (Quotient.mk (isSetoid α) b) ↔\n Quotient.mk (isSetoid α) a ≤ Quotient.mk (isSetoid α) b",
"tactic": "simp [Subperm, and_comm]"
}
] | [
111,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
110,
1
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Mathlib/Data/Polynomial/Eval.lean | Polynomial.ofNat_comp | [] | [
561,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
560,
1
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Mathlib/Data/Matrix/Notation.lean | Matrix.col_cons | [
{
"state_after": "case a.h\nα : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ\nx : α\nu : Fin m → α\ni : Fin (Nat.succ m)\nj : Unit\n⊢ col (vecCons x u) i j = vecCons (fun x_1 => x) (col u) i j",
"state_before": "α : Type u\no n m : ℕ\nm' : Type uₘ\nn' : Type uₙ\no' : Type uₒ\na b : ℕ... | [
175,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
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Mathlib/CategoryTheory/Limits/IsLimit.lean | CategoryTheory.Limits.IsColimit.hom_desc | [
{
"state_after": "J : Type u₁\ninst✝² : Category J\nK : Type u₂\ninst✝¹ : Category K\nC : Type u₃\ninst✝ : Category C\nF : J ⥤ C\nt : Cocone F\nh : IsColimit t\nW : C\nm : t.pt ⟶ W\nX✝ Y✝ : J\nf✝ : X✝ ⟶ Y✝\n⊢ F.map f✝ ≫ (fun b => t.ι.app b ≫ m) Y✝ = (fun b => t.ι.app b ≫ m) X✝ ≫ ((const J).obj W).map f✝",
"... | [
742,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
730,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.liftRingHom_apply_div' | [] | [
907,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
904,
1
] |
Mathlib/Logic/Relation.lean | Relation.comp_assoc | [
{
"state_after": "case h.h\nα : Type u_1\nβ : Type u_4\nγ : Type u_3\nδ : Type u_2\nr : α → β → Prop\np : β → γ → Prop\nq : γ → δ → Prop\na : α\nd : δ\n⊢ ((r ∘r p) ∘r q) a d = (r ∘r p ∘r q) a d",
"state_before": "α : Type u_1\nβ : Type u_4\nγ : Type u_3\nδ : Type u_2\nr : α → β → Prop\np : β → γ → Prop\nq :... | [
164,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
159,
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] |
Mathlib/Analysis/Calculus/Deriv/Mul.lean | deriv_smul | [] | [
87,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Topology/PathConnected.lean | IsPathConnected.joinedIn | [] | [
970,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
967,
1
] |
Mathlib/Data/List/Basic.lean | List.take_append_of_le_length | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.164866\nα : Type u\nβ : Type v\nγ : Type w\nδ : Type x\nl₁✝ l₂✝ l₁ l₂ : List α\nn : ℕ\nh : n ≤ length l₁\n⊢ take n (l₁ ++ l₂) = take n l₁",
"tactic": "simp [take_append_eq_append_take, tsub_eq_zero_iff_le.mpr h]"
}
] | [
1980,
101
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1979,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.Tendsto.atTop_of_const_mul | [] | [
962,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
959,
1
] |
Mathlib/Data/Complex/Module.lean | realPart_I_smul | [
{
"state_after": "case a\nA : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : A\n⊢ ↑(↑ℜ (I • a)) = ↑(-↑ℑ a)",
"state_before": "A : Type u_1\ninst✝³ : AddCommGroup A\ninst✝² : Module ℂ A\ninst✝¹ : StarAddMonoid A\ninst✝ : StarModule ℂ A\na : A\n⊢ ... | [
482,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
477,
1
] |
Mathlib/RingTheory/Subring/Basic.lean | Subring.top_prod | [
{
"state_after": "no goals",
"state_before": "R : Type u\nS : Type v\nT : Type w\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Ring T\ns : Subring S\nx : R × S\n⊢ x ∈ prod ⊤ s ↔ x ∈ comap (RingHom.snd R S) s",
"tactic": "simp [mem_prod, MonoidHom.coe_snd]"
}
] | [
1125,
53
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1124,
1
] |
Mathlib/Topology/ContinuousOn.lean | ContinuousOn.prod_map | [] | [
656,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
654,
1
] |
Mathlib/Data/Part.lean | Part.get_eq_of_mem | [] | [
155,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
154,
1
] |
Mathlib/MeasureTheory/Measure/Haar/Basic.lean | MeasureTheory.Measure.haar.prehaar_sup_le | [
{
"state_after": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : TopologicalGroup G\nK₀ : PositiveCompacts G\nU : Set G\nK₁ K₂ : Compacts G\nhU : Set.Nonempty (interior U)\n⊢ ↑(index (↑(K₁ ⊔ K₂)) U) / ↑(index (↑K₀) U) ≤ ↑(index (↑K₁) U) / ↑(index (↑K₀) U) + ↑(index (↑K₂) U) / ↑(index (↑K₀)... | [
339,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
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