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/Seq/Seq.lean | Stream'.Seq.map_append | [
{
"state_after": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns t : Seq α\n⊢ IsBisimulation fun s1 s2 => ∃ s t, s1 = map f (append s t) ∧ s2 = append (map f s) (map f t)",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nf : α → β\ns t : Seq α\n⊢ map f (append s t) = append (map f s) (map f t)",
... | [
736,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
723,
1
] |
Mathlib/Data/PEquiv.lean | PEquiv.symm_single | [] | [
356,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
355,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.not_ge_eq | [] | [
725,
16
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
724,
1
] |
Mathlib/Data/List/OfFn.lean | List.nthLe_ofFn | [
{
"state_after": "no goals",
"state_before": "α : Type u\nn : ℕ\nf : Fin n → α\ni : Fin n\n⊢ nthLe (ofFn f) ↑i (_ : ↑i < length (ofFn f)) = f i",
"tactic": "simp [nthLe]"
}
] | [
76,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean | NonUnitalSubsemiring.toAddSubmonoid_injective | [] | [
163,
46
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
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Mathlib/Geometry/Euclidean/Basic.lean | EuclideanGeometry.reflection_symm | [
{
"state_after": "case h\nV : Type u_1\nP : Type u_2\ninst✝⁵ : NormedAddCommGroup V\ninst✝⁴ : InnerProductSpace ℝ V\ninst✝³ : MetricSpace P\ninst✝² : NormedAddTorsor V P\ns : AffineSubspace ℝ P\ninst✝¹ : Nonempty { x // x ∈ s }\ninst✝ : CompleteSpace { x // x ∈ direction s }\nx✝ : P\n⊢ ↑(AffineIsometryEquiv.sym... | [
573,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
569,
1
] |
Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean | CategoryTheory.Limits.PreservesPushout.inr_iso_hom | [
{
"state_after": "C : Type u₁\ninst✝⁴ : Category C\nD : Type u₂\ninst✝³ : Category D\nG : C ⥤ D\nW X Y Z : C\nh : X ⟶ Z\nk : Y ⟶ Z\nf : W ⟶ X\ng : W ⟶ Y\ncomm : f ≫ h = g ≫ k\ninst✝² : PreservesColimit (span f g) G\ninst✝¹ : HasPushout f g\ninst✝ : HasPushout (G.map f) (G.map g)\n⊢ pushout.inr ≫\n (IsColim... | [
237,
7
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
234,
1
] |
Mathlib/LinearAlgebra/BilinearForm.lean | BilinForm.coe_add | [] | [
198,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
197,
1
] |
Mathlib/LinearAlgebra/Prod.lean | LinearEquiv.snd_comp_prodComm | [
{
"state_after": "no goals",
"state_before": "N : Type u_1\nR : Type u\nK : Type u'\nM : Type v\nV : Type v'\nM₂ : Type w\nV₂ : Type w'\nM₃ : Type y\nV₃ : Type y'\nM₄ : Type z\nι : Type x\nM₅ : Type ?u.405020\nM₆ : Type ?u.405023\ninst✝⁴ : Semiring R\ninst✝³ : AddCommMonoid M\ninst✝² : AddCommMonoid N\ninst... | [
759,
15
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
757,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.map_div_left_divisors | [
{
"state_after": "case a\nn : ℕ\n⊢ map (Equiv.toEmbedding (Equiv.prodComm ℕ ℕ))\n (map\n { toFun := fun d => (n / d, d),\n inj' :=\n (_ :\n ∀ (p₁ p₂ : ℕ),\n (fun d => (n / d, d)) p₁ = (fun d => (n / d, d)) p₂ →\n ((fun d => (n / d, d))... | [
282,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
277,
1
] |
Mathlib/Topology/Order/Hom/Esakia.lean | PseudoEpimorphism.coe_copy | [] | [
143,
100
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/Algebra/Hom/Ring.lean | RingHom.map_sub | [] | [
641,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
639,
11
] |
Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean | Real.Angle.abs_toReal_eq_pi_div_two_iff | [
{
"state_after": "no goals",
"state_before": "θ : Angle\n⊢ abs (toReal θ) = π / 2 ↔ θ = ↑(π / 2) ∨ θ = ↑(-π / 2)",
"tactic": "rw [abs_eq (div_nonneg Real.pi_pos.le two_pos.le), ← neg_div, toReal_eq_pi_div_two_iff,\n toReal_eq_neg_pi_div_two_iff]"
}
] | [
660,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Topology/UniformSpace/Cauchy.lean | TotallyBounded.image | [
{
"state_after": "α : Type u\nβ : Type v\ninst✝¹ : UniformSpace α\ninst✝ : UniformSpace β\nf : α → β\ns : Set α\nhs : TotallyBounded s\nhf : UniformContinuous f\nt : Set (β × β)\nht : t ∈ 𝓤 β\nthis : {p | (f p.fst, f p.snd) ∈ t} ∈ 𝓤 α\nc : Set α\nhfc : Set.Finite c\nhct : s ⊆ ⋃ (y : α) (_ : y ∈ c), {x | (x, y... | [
526,
20
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
518,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.mul_adjugate_apply | [
{
"state_after": "no goals",
"state_before": "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 : Matrix n n α\ni j k : n\n⊢ A i k * adjugate A k j = ↑(cramer Aᵀ) (Pi.single k (A i k)) j",
"tactic": "erw [← s... | [
289,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
286,
1
] |
Mathlib/Data/Set/Intervals/ProjIcc.lean | Set.projIcc_of_mem | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\nβ : Type ?u.7809\ninst✝ : LinearOrder α\na b : α\nh : a ≤ b\nx : α\nhx : x ∈ Icc a b\n⊢ projIcc a b h x = { val := x, property := hx }",
"tactic": "simp [projIcc, hx.1, hx.2]"
}
] | [
74,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
73,
1
] |
Mathlib/LinearAlgebra/Span.lean | LinearMap.ext_on_range | [] | [
972,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
970,
1
] |
Mathlib/Data/Multiset/Functor.lean | Multiset.bind_def | [] | [
78,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
77,
1
] |
Mathlib/Algebra/DirectSum/Decomposition.lean | DirectSum.decompose_symm_sum | [] | [
175,
41
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
173,
1
] |
Mathlib/LinearAlgebra/Orientation.lean | Orientation.map_symm | [] | [
88,
65
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
87,
1
] |
Mathlib/Analysis/NormedSpace/LpEquiv.lean | coe_ringEquiv_lpBcf_symm | [] | [
205,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
204,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_add_const_uIcc | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝ : LinearOrderedAddCommGroup α\na b c d : α\n⊢ (fun x => x + a) ⁻¹' [[b, c]] = [[b - a, c - a]]",
"tactic": "simpa only [add_comm] using preimage_const_add_uIcc a b c"
}
] | [
435,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
434,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.univ_mul | [] | [
1264,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1262,
1
] |
Mathlib/MeasureTheory/Group/FundamentalDomain.lean | MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier | [] | [
585,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
583,
1
] |
Mathlib/FieldTheory/RatFunc.lean | RatFunc.algebraMap_C | [] | [
1401,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1400,
1
] |
Mathlib/Topology/Algebra/Star.lean | continuousAt_star | [] | [
46,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
45,
1
] |
Mathlib/Algebra/EuclideanDomain/Basic.lean | EuclideanDomain.gcd_eq_gcd_ab | [
{
"state_after": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b : R\nthis : EuclideanDomain.P a b (xgcdAux a 1 0 b 0 1)\n⊢ gcd a b = a * gcdA a b + b * gcdB a b",
"state_before": "R : Type u\ninst✝¹ : EuclideanDomain R\ninst✝ : DecidableEq R\na b : R\n⊢ gcd a b = a * gcdA a b + b * gcdB... | [
232,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
228,
1
] |
Mathlib/Analysis/NormedSpace/LinearIsometry.lean | LinearIsometry.coe_mul | [] | [
434,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
433,
1
] |
Mathlib/CategoryTheory/Abelian/Transfer.lean | CategoryTheory.AbelianOfAdjunction.hasKernels | [
{
"state_after": "C : Type u₁\ninst✝⁵ : Category C\ninst✝⁴ : Preadditive C\nD : Type u₂\ninst✝³ : Category D\ninst✝² : Abelian D\nF : C ⥤ D\nG : D ⥤ C\ninst✝¹ : Functor.PreservesZeroMorphisms G\ni : F ⋙ G ≅ 𝟭 C\nadj : G ⊣ F\ninst✝ : PreservesFiniteLimits G\nX✝ Y✝ : C\nf : X✝ ⟶ Y✝\nthis : i.inv.app X✝ ≫ (F ⋙ G)... | [
66,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
60,
1
] |
Mathlib/Algebra/Order/Hom/Monoid.lean | OrderMonoidWithZeroHom.coe_comp_orderMonoidHom | [] | [
698,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
696,
1
] |
Mathlib/Algebra/Lie/Subalgebra.lean | LieSubalgebra.coe_submodule_le_coe_submodule | [] | [
429,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Set/Intervals/OrdConnected.lean | Set.OrdConnected.preimage_anti | [] | [
76,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
74,
1
] |
Mathlib/SetTheory/Cardinal/Basic.lean | Cardinal.aleph0_toNat | [] | [
1744,
34
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1743,
1
] |
Mathlib/Topology/LocallyConstant/Algebra.lean | LocallyConstant.inv_apply | [] | [
52,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
51,
1
] |
Mathlib/Data/Nat/Log.lean | Nat.log_mono_right | [] | [
194,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
193,
1
] |
Mathlib/Order/Lattice.lean | inf_eq_right | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\ninst✝ : SemilatticeInf α\na b c d : α\n⊢ a ⊓ b ≤ b ∧ b ≤ a ⊓ b ↔ b ≤ a",
"tactic": "simp [le_rfl]"
}
] | [
439,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
438,
1
] |
Mathlib/GroupTheory/Perm/Cycle/Basic.lean | Equiv.Perm.SameCycle.symm | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.30729\nα : Type u_1\nβ : Type ?u.30735\nf g : Perm α\np : α → Prop\nx y z : α\nx✝ : SameCycle f x y\ni : ℤ\nhi : ↑(f ^ i) x = y\n⊢ ↑(f ^ (-i)) y = x",
"tactic": "rw [zpow_neg, ← hi, inv_apply_self]"
}
] | [
94,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
93,
1
] |
Mathlib/Control/Functor.lean | Functor.Comp.comp_map | [
{
"state_after": "no goals",
"state_before": "F : Type u → Type w\nG : Type v → Type u\ninst✝³ : Functor F\ninst✝² : Functor G\ninst✝¹ : LawfulFunctor F\ninst✝ : LawfulFunctor G\nα β γ : Type v\ng' : α → β\nh : β → γ\nx : F (G α)\n⊢ Comp.map (h ∘ g') (mk x) = Comp.map h (Comp.map g' (mk x))",
"tactic": ... | [
217,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
215,
11
] |
Mathlib/Data/List/Intervals.lean | List.Ico.eq_cons | [
{
"state_after": "n m : ℕ\nh : n < m\n⊢ [n] ++ Ico (succ n) m = n :: Ico (n + 1) m",
"state_before": "n m : ℕ\nh : n < m\n⊢ Ico n m = n :: Ico (n + 1) m",
"tactic": "rw [← append_consecutive (Nat.le_succ n) h, succ_singleton]"
},
{
"state_after": "no goals",
"state_before": "n m : ℕ\nh : n <... | [
134,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
132,
1
] |
Mathlib/RingTheory/Subsemiring/Basic.lean | Subsemiring.list_prod_mem | [] | [
329,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
327,
8
] |
Mathlib/Order/Filter/Pointwise.lean | Filter.NeBot.zero_div_nonneg | [] | [
932,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
929,
1
] |
Mathlib/Data/Num/Lemmas.lean | Num.cast_zero | [] | [
275,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
274,
1
] |
Mathlib/Algebra/Lie/Normalizer.lean | LieSubmodule.le_normalizer | [
{
"state_after": "R : Type u_2\nL : Type u_3\nM : Type u_1\nM' : Type ?u.9664\ninst✝¹⁰ : CommRing R\ninst✝⁹ : LieRing L\ninst✝⁸ : LieAlgebra R L\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\ninst✝⁵ : LieRingModule L M\ninst✝⁴ : LieModule R L M\ninst✝³ : AddCommGroup M'\ninst✝² : Module R M'\ninst✝¹ : LieRingMo... | [
70,
30
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/GroupTheory/QuotientGroup.lean | QuotientGroup.kerLift_injective | [
{
"state_after": "no goals",
"state_before": "G : Type u\ninst✝¹ : Group G\nN : Subgroup G\nnN : Subgroup.Normal N\nH : Type v\ninst✝ : Group H\nφ : G →* H\na✝ b✝ : G ⧸ ker φ\na b : G\nh : ↑φ a = ↑φ b\n⊢ Setoid.r a b",
"tactic": "rw [leftRel_apply, mem_ker, φ.map_mul, ← h, φ.map_inv, inv_mul_self]"
}
... | [
367,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
365,
1
] |
Mathlib/Data/Subtype.lean | Subtype.coe_prop | [] | [
266,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
265,
1
] |
Mathlib/RingTheory/Polynomial/Bernstein.lean | bernsteinPolynomial.iterate_derivative_at_0_ne_zero | [
{
"state_after": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nn ν : ℕ\nh : ν ≤ n\n⊢ ¬eval (↑(n - (ν - 1))) (pochhammer R ν) = 0",
"state_before": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CharZero R\nn ν : ℕ\nh : ν ≤ n\n⊢ eval 0 ((↑derivative^[ν]) (bernsteinPolynomial R n ν)) ≠ 0",
"tactic"... | [
212,
68
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
202,
1
] |
Mathlib/Data/Finset/Sups.lean | Finset.disjSups_subset | [] | [
455,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
454,
1
] |
Mathlib/Algebra/CharP/Invertible.lean | not_ringChar_dvd_of_invertible | [
{
"state_after": "K : Type u_1\ninst✝¹ : Field K\nt : ℕ\ninst✝ : Invertible ↑t\n⊢ ↑t ≠ 0",
"state_before": "K : Type u_1\ninst✝¹ : Field K\nt : ℕ\ninst✝ : Invertible ↑t\n⊢ ¬ringChar K ∣ t",
"tactic": "rw [← ringChar.spec, ← Ne.def]"
},
{
"state_after": "no goals",
"state_before": "K : Type u... | [
38,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
36,
1
] |
Mathlib/LinearAlgebra/Basis.lean | Basis.constr_comp | [
{
"state_after": "no goals",
"state_before": "ι : Type u_4\nι' : Type ?u.538910\nR : Type u_1\nR₂ : Type ?u.538916\nK : Type ?u.538919\nM : Type u_3\nM' : Type u_2\nM'' : Type ?u.538928\nV : Type u\nV' : Type ?u.538933\ninst✝⁷ : Semiring R\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : Module R M\ninst✝⁴ : AddCommMono... | [
659,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
657,
1
] |
Mathlib/Data/Finset/Sort.lean | Finset.mem_sort | [] | [
62,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
Mathlib/Data/List/Sigma.lean | List.Perm.kunion_right | [
{
"state_after": "case nil\nα : Type u\nβ : α → Type v\nl✝ l₁✝ l₂✝ : List (Sigma β)\ninst✝ : DecidableEq α\nl₁ l₂ l : List (Sigma β)\n⊢ kunion [] l ~ kunion [] l\n\ncase cons\nα : Type u\nβ : α → Type v\nl✝ l₁✝¹ l₂✝¹ : List (Sigma β)\ninst✝ : DecidableEq α\nl₁ l₂ : List (Sigma β)\nx✝ : Sigma β\nl₁✝ l₂✝ : List (... | [
731,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Algebra/Support.lean | Function.mulSupport_add_one' | [] | [
430,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
428,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.exists_root_of_splits' | [
{
"state_after": "no goals",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝² : CommRing K\ninst✝¹ : Field L\ninst✝ : Field F\ni : K →+* L\nf : K[X]\nhs : Splits i f\nhf0 : degree (map i f) ≠ 0\nhf0' : map i f = 0\n⊢ ∃ x, eval₂ i x f = 0",
"tactic": "simp [eval₂_eq_eval_map, hf0']"
},
{
... | [
184,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
175,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | MonoidHom.coe_rangeRestrict | [] | [
2626,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2625,
1
] |
Mathlib/Combinatorics/SimpleGraph/Basic.lean | SimpleGraph.Dart.symm_involutive | [] | [
767,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
766,
1
] |
Mathlib/Topology/Algebra/ConstMulAction.lean | continuousWithinAt_const_smul_iff | [] | [
210,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
208,
1
] |
Mathlib/Data/Matrix/Kronecker.lean | Matrix.kroneckerMap_smul_left | [] | [
119,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
116,
1
] |
Mathlib/Topology/Instances/Matrix.lean | Matrix.conjTranspose_tsum | [
{
"state_after": "case pos\nX : Type u_4\nα : Type ?u.67432\nl : Type ?u.67435\nm : Type u_2\nn : Type u_3\np : Type ?u.67444\nS : Type ?u.67447\nR : Type u_1\nm' : l → Type ?u.67455\nn' : l → Type ?u.67460\ninst✝⁶ : Semiring α\ninst✝⁵ : AddCommMonoid R\ninst✝⁴ : TopologicalSpace R\ninst✝³ : Module α R\ninst✝² ... | [
340,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
335,
1
] |
Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean | GromovHausdorff.candidates_dist_inr | [] | [
147,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
145,
9
] |
Mathlib/SetTheory/ZFC/Basic.lean | Class.mem_wf | [
{
"state_after": "a x : ZFSet\nIH : ∀ (y : ZFSet), y ∈ x → Acc (fun x x_1 => x ∈ x_1) ↑y\n⊢ ∀ (y : Class), y ∈ ↑x → Acc (fun x x_1 => x ∈ x_1) y",
"state_before": "⊢ ∀ (x : ZFSet), Acc (fun x x_1 => x ∈ x_1) ↑x",
"tactic": "refine' fun a => ZFSet.inductionOn a fun x IH => ⟨_, _⟩"
},
{
"state_aft... | [
1539,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1531,
1
] |
Mathlib/Analysis/SpecificLimits/Basic.lean | summable_geometric_two' | [] | [
254,
31
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
253,
1
] |
Mathlib/Analysis/NormedSpace/Exponential.lean | expSeries_apply_eq_div | [
{
"state_after": "no goals",
"state_before": "𝕂 : Type u_2\n𝔸 : Type u_1\ninst✝⁴ : Field 𝕂\ninst✝³ : DivisionRing 𝔸\ninst✝² : Algebra 𝕂 𝔸\ninst✝¹ : TopologicalSpace 𝔸\ninst✝ : TopologicalRing 𝔸\nx : 𝔸\nn : ℕ\n⊢ (↑(expSeries 𝕂 𝔸 n) fun x_1 => x) = x ^ n / ↑n !",
"tactic": "rw [div_eq_mul_inv, ... | [
172,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
170,
1
] |
Mathlib/Order/LocallyFinite.lean | Finset.subtype_Ici_eq | [] | [
1320,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1319,
1
] |
Mathlib/Data/Ordmap/Ordset.lean | Ordnode.balanceL_eq_balance' | [
{
"state_after": "case H1\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : Balanced l\nhr : Balanced r\nsl : Sized l\nsr : Sized r\nH : (∃ l', Raised l' (size l) ∧ BalancedSz l' (size r)) ∨ ∃ r', Raised (size r) r' ∧ BalancedSz (size l) r'\n⊢ size l = 0 → size r ≤ 1\n\ncase H2\nα : Type u_1\nl : Ordnode... | [
834,
43
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
818,
1
] |
Mathlib/CategoryTheory/Subobject/Limits.lean | CategoryTheory.Limits.kernelSubobjectMap_arrow | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninst✝³ : Category C\nX Y Z : C\ninst✝² : HasZeroMorphisms C\nf : X ⟶ Y\ninst✝¹ : HasKernel f\nX' Y' : C\nf' : X' ⟶ Y'\ninst✝ : HasKernel f'\nsq : Arrow.mk f ⟶ Arrow.mk f'\n⊢ kernelSubobjectMap sq ≫ arrow (kernelSubobject f') = arrow (kernelSubobject ... | [
163,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
161,
1
] |
Std/Data/BinomialHeap.lean | Std.BinomialHeapImp.Heap.WellFormed.singleton | [
{
"state_after": "no goals",
"state_before": "α✝ : Type u_1\na : α✝\nle : α✝ → α✝ → Bool\n⊢ 0 ≤ 0",
"tactic": "decide"
}
] | [
338,
95
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
338,
1
] |
Mathlib/Data/Quot.lean | Quotient.induction_on_pi | [
{
"state_after": "α✝ : Sort ?u.35644\nβ : Sort ?u.35647\nι : Type u_1\nα : ι → Sort u_2\ns : (i : ι) → Setoid (α i)\np : ((i : ι) → Quotient (s i)) → Prop\nf : (i : ι) → Quotient (s i)\nh : ∀ (a : (i : ι) → α i), p fun i => Quotient.mk (s i) (a i)\n⊢ p fun i => Quotient.mk (s i) (out (f i))",
"state_before"... | [
436,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
432,
1
] |
Mathlib/RingTheory/DedekindDomain/PID.lean | Ideal.IsPrincipal.of_finite_maximals_of_isUnit | [] | [
182,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
178,
1
] |
Mathlib/Topology/LocalHomeomorph.lean | LocalHomeomorph.trans_target | [] | [
838,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
837,
1
] |
Std/Logic.lean | and_congr_left | [] | [
165,
55
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
164,
1
] |
Mathlib/Data/Nat/Basic.lean | Nat.one_lt_succ_succ | [] | [
190,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
189,
1
] |
Mathlib/RingTheory/HahnSeries.lean | HahnSeries.add_coeff' | [] | [
373,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
372,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_right_mono | [] | [
979,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
979,
1
] |
Mathlib/Data/Polynomial/Splits.lean | Polynomial.image_rootSet | [
{
"state_after": "no goals",
"state_before": "F : Type u\nK : Type v\nL : Type w\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Field F\ni : K →+* L\ninst✝¹ : Algebra F K\ninst✝ : Algebra F L\np : F[X]\nh : Splits (algebraMap F K) p\nf : K →ₐ[F] L\n⊢ ↑f '' rootSet p K = rootSet p L",
"tactic": "classical... | [
341,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
336,
1
] |
Mathlib/Algebra/Category/ModuleCat/Monoidal/Basic.lean | ModuleCat.MonoidalCategory.pentagon_aux | [
{
"state_after": "case H\nR : Type u\ninst✝⁸ : CommRing R\nW : Type u_1\nX : Type u_2\nY : Type u_3\nZ : Type u_4\ninst✝⁷ : AddCommMonoid W\ninst✝⁶ : AddCommMonoid X\ninst✝⁵ : AddCommMonoid Y\ninst✝⁴ : AddCommMonoid Z\ninst✝³ : Module R W\ninst✝² : Module R X\ninst✝¹ : Module R Y\ninst✝ : Module R Z\n⊢ ∀ (w : W... | [
117,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
109,
9
] |
Mathlib/RingTheory/IntegralClosure.lean | is_integral_of_mem_closure'' | [] | [
630,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
628,
1
] |
Mathlib/RingTheory/UniqueFactorizationDomain.lean | UniqueFactorizationMonoid.factors_zero | [
{
"state_after": "no goals",
"state_before": "α : Type u_1\ninst✝² : CancelCommMonoidWithZero α\ninst✝¹ : DecidableEq α\ninst✝ : UniqueFactorizationMonoid α\n⊢ factors 0 = 0",
"tactic": "simp [factors]"
}
] | [
474,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
474,
1
] |
Mathlib/Order/Filter/Extr.lean | IsMinFilter.sub | [
{
"state_after": "no goals",
"state_before": "α : Type u\nβ : Type v\nγ : Type w\nδ : Type x\ninst✝ : OrderedAddCommGroup β\nf g : α → β\na : α\ns : Set α\nl : Filter α\nhf : IsMinFilter f l a\nhg : IsMaxFilter g l a\n⊢ IsMinFilter (fun x => f x - g x) l a",
"tactic": "simpa only [sub_eq_add_neg] using ... | [
507,
95
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
506,
1
] |
Mathlib/Algebra/Field/Basic.lean | RingHom.injective | [] | [
260,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
258,
11
] |
Mathlib/FieldTheory/Adjoin.lean | IntermediateField.finrank_bot | [
{
"state_after": "no goals",
"state_before": "F : Type u_1\ninst✝² : Field F\nE : Type u_2\ninst✝¹ : Field E\ninst✝ : Algebra F E\nα : E\nS : Set E\nK L : IntermediateField F E\n⊢ finrank F { x // x ∈ ⊥ } = 1",
"tactic": "rw [finrank_eq_one_iff]"
}
] | [
728,
94
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
728,
1
] |
Mathlib/Logic/Basic.lean | by_contradiction | [] | [
216,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/Data/Finset/LocallyFinite.lean | Finset.Ico_filter_le | [
{
"state_after": "no goals",
"state_before": "ι : Type ?u.139276\nα : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : LocallyFiniteOrder α\na✝ b✝ a b c : α\n⊢ filter (fun x => c ≤ x) (Ico a b) = Ico (max a c) b",
"tactic": "cases le_total a c with\n| inl h => rw [Ico_filter_le_of_left_le h, max_eq_right h]\n|... | [
798,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
795,
1
] |
Mathlib/AlgebraicTopology/DoldKan/Compatibility.lean | AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq | [
{
"state_after": "case w.w.h\nA : Type u_4\nA' : Type u_5\nB : Type u_1\nB' : Type u_6\ninst✝³ : Category A\ninst✝² : Category A'\ninst✝¹ : Category B\ninst✝ : Category B'\neA : A ≌ A'\neB : B ≌ B'\ne' : A' ≌ B'\nF : A ⥤ B'\nhF : eA.functor ⋙ e'.functor ≅ F\nG : B ⥤ A\nhG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.func... | [
148,
60
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
143,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean | CategoryTheory.Limits.kernelComparison_comp_ι | [] | [
1106,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1104,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.mem_subgroupOf | [] | [
1627,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1626,
1
] |
Mathlib/Algebra/Quaternion.lean | Cardinal.mk_quaternionAlgebra_of_infinite | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nc₁ c₂ : R\ninst✝ : Infinite R\n⊢ (#ℍ[R,c₁,c₂]) = (#R)",
"tactic": "rw [mk_quaternionAlgebra, pow_four]"
}
] | [
1436,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1435,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.inv_eq_top | [] | [
1403,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1403,
9
] |
Mathlib/MeasureTheory/Function/LocallyIntegrable.lean | MeasureTheory.locallyIntegrable_const | [
{
"state_after": "X : Type u_1\nY : Type ?u.128412\nE : Type u_2\nR : Type ?u.128418\ninst✝⁵ : MeasurableSpace X\ninst✝⁴ : TopologicalSpace X\ninst✝³ : MeasurableSpace Y\ninst✝² : TopologicalSpace Y\ninst✝¹ : NormedAddCommGroup E\nf : X → E\nμ : Measure X\ns : Set X\ninst✝ : IsLocallyFiniteMeasure μ\nc : E\nx :... | [
210,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean | SimpleGraph.isAdjMatrix_adjMatrix | [
{
"state_after": "no goals",
"state_before": "V : Type u_2\nα : Type u_1\nβ : Type ?u.28278\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\ninst✝¹ : Zero α\ninst✝ : One α\ni j : V\n⊢ adjMatrix α G i j = 0 ∨ adjMatrix α G i j = 1",
"tactic": "by_cases G.Adj i j <;> simp [h]"
}
] | [
188,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
187,
1
] |
Mathlib/RingTheory/FinitePresentation.lean | AlgHom.FinitePresentation.of_comp_finiteType | [] | [
531,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
529,
8
] |
Mathlib/Data/Nat/Pow.lean | Nat.pow_lt_iff_lt_left | [] | [
143,
47
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
142,
1
] |
Mathlib/Order/BoundedOrder.lean | max_top_left | [] | [
839,
13
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
838,
1
] |
Mathlib/Topology/Compactification/OnePoint.lean | OnePoint.le_nhds_infty | [
{
"state_after": "no goals",
"state_before": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nt : Set X\nf : Filter (OnePoint X)\n⊢ f ≤ 𝓝 ∞ ↔ ∀ (s : Set X), IsClosed s → IsCompact s → some '' sᶜ ∪ {∞} ∈ f",
"tactic": "simp only [hasBasis_nhds_infty.ge_iff, and_imp]"
}
] | [
351,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/MeasureTheory/Integral/SetToL1.lean | MeasureTheory.L1.SimpleFunc.setToL1S_const | [] | [
826,
81
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
823,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousLinearEquiv.compContinuousMultilinearMapL_symm | [] | [
1004,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1002,
1
] |
Mathlib/Order/Bounded.lean | Set.unbounded_lt_of_unbounded_le | [] | [
107,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/MeasureTheory/Measure/VectorMeasure.lean | MeasureTheory.VectorMeasure.MutuallySingular.neg_left | [
{
"state_after": "case intro.intro.intro\nα : Type u_2\nβ : Type ?u.681547\nm : MeasurableSpace α\nL : Type ?u.681553\nM✝ : Type ?u.681556\nN : Type u_3\ninst✝⁸ : AddCommMonoid L\ninst✝⁷ : TopologicalSpace L\ninst✝⁶ : AddCommMonoid M✝\ninst✝⁵ : TopologicalSpace M✝\ninst✝⁴ : AddCommMonoid N\ninst✝³ : Topological... | [
1251,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1246,
1
] |
Mathlib/Topology/Algebra/Order/IntermediateValue.lean | intermediate_value_Ioo' | [] | [
598,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Data/Fin/Basic.lean | Fin.cast_addNat_right | [] | [
1387,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1385,
1
] |
Mathlib/Analysis/Convex/Function.lean | ConvexOn.le_left_of_right_le' | [] | [
720,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
711,
1
] |
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