ruc-ai4math/mathlib_handler_benchmark_410 huggingface dataset:
-- Down.compression_idem
@[simp]
theorem compression_idem (a : α) (𝒜 : Finset (Finset α)) : 𝓓 a (𝓓 a 𝒜) = 𝓓 a 𝒜 
Arguments: {α : Type u_1} [DecidableEq α] (a : α) (𝒜 : Finset (Finset α))
Goal: Down.compression a (Down.compression a 𝒜) = Down.compression a 𝒜
-- Down.card_compression
@[simp]
theorem card_compression (a : α) (𝒜 : Finset (Finset α)) : (𝓓 a 𝒜).card = 𝒜.card 
Arguments: {α : Type u_1} [DecidableEq α] (a : α) (𝒜 : Finset (Finset α))
Goal: (Down.compression a 𝒜).card = 𝒜.card
-- SemistandardYoungTableau.zeros'
structure SemistandardYoungTableau (μ : YoungDiagram) where
    entry : ℕ → ℕ → ℕ
    row_weak' : ∀ {i j1 j2 : ℕ}, j1 < j2 → (i, j2) ∈ μ → entry i j1 ≤ entry i j2
    col_strict' : ∀ {i1 i2 j : ℕ}, i1 < i2 → (i2, j) ∈ μ → entry i1 j < entry i2 j
    zeros' : ∀ {i j}, (i, j) ∉ μ → entry i j = 0
Arguments: {μ : YoungDiagram} (self : SemistandardYoungTableau μ) {i j : ℕ}
Goal: (i, j) ∉ μ → self.entry i j = 0
-- SemistandardYoungTableau.col_strict'
structure SemistandardYoungTableau (μ : YoungDiagram) where
    entry : ℕ → ℕ → ℕ
    row_weak' : ∀ {i j1 j2 : ℕ}, j1 < j2 → (i, j2) ∈ μ → entry i j1 ≤ entry i j2
    col_strict' : ∀ {i1 i2 j : ℕ}, i1 < i2 → (i2, j) ∈ μ → entry i1 j < entry i2 j
    zeros' : ∀ {i j}, (i, j) ∉ μ → entry i j = 0
Arguments: {μ : YoungDiagram} (self : SemistandardYoungTableau μ) {i1 i2 j : ℕ}
Goal: i1 < i2 → (i2, j) ∈ μ → self.entry i1 j < self.entry i2 j
-- SemistandardYoungTableau.row_weak'
structure SemistandardYoungTableau (μ : YoungDiagram) where
    entry : ℕ → ℕ → ℕ
    row_weak' : ∀ {i j1 j2 : ℕ}, j1 < j2 → (i, j2) ∈ μ → entry i j1 ≤ entry i j2
    col_strict' : ∀ {i1 i2 j : ℕ}, i1 < i2 → (i2, j) ∈ μ → entry i1 j < entry i2 j
    zeros' : ∀ {i j}, (i, j) ∉ μ → entry i j = 0
Arguments: {μ : YoungDiagram} (self : SemistandardYoungTableau μ) {i j1 j2 : ℕ}
Goal: j1 < j2 → (i, j2) ∈ μ → self.entry i j1 ≤ self.entry i j2
-- SemistandardYoungTableau.to_fun_eq_coe
@[simp]
theorem to_fun_eq_coe {μ : YoungDiagram} {T : SemistandardYoungTableau μ} :
    T.entry = (T : ℕ → ℕ → ℕ) 
Arguments: {μ : YoungDiagram} {T : SemistandardYoungTableau μ}
Goal: T.entry = ⇑T
-- SemistandardYoungTableau.ext
@[ext]
theorem ext {μ : YoungDiagram} {T T' : SemistandardYoungTableau μ} (h : ∀ i j, T i j = T' i j) :
    T = T' 
Arguments: {μ : YoungDiagram} {T T' : SemistandardYoungTableau μ} (h : ∀ (i j : ℕ), T i j = T' i j)
Goal: T = T'
-- SemistandardYoungTableau.coe_copy
@[simp]
theorem coe_copy {μ : YoungDiagram} (T : SemistandardYoungTableau μ) (entry' : ℕ → ℕ → ℕ)
    (h : entry' = T) : ⇑(T.copy entry' h) = entry' 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) (entry' : ℕ → ℕ → ℕ) (h : entry' = ⇑T)
Goal: ⇑(T.copy entry' h) = entry'
-- SemistandardYoungTableau.copy_eq
theorem copy_eq {μ : YoungDiagram} (T : SemistandardYoungTableau μ) (entry' : ℕ → ℕ → ℕ)
    (h : entry' = T) : T.copy entry' h = T 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) (entry' : ℕ → ℕ → ℕ) (h : entry' = ⇑T)
Goal: T.copy entry' h = T
-- SemistandardYoungTableau.row_weak
theorem row_weak {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j1 j2 : ℕ} (hj : j1 < j2)
    (hcell : (i, j2) ∈ μ) : T i j1 ≤ T i j2 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j1 j2 : ℕ} (hj : j1 < j2) (hcell : (i, j2) ∈ μ)
Goal: T i j1 ≤ T i j2
-- SemistandardYoungTableau.col_strict
theorem col_strict {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i1 i2 j : ℕ} (hi : i1 < i2)
    (hcell : (i2, j) ∈ μ) : T i1 j < T i2 j 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i1 i2 j : ℕ} (hi : i1 < i2) (hcell : (i2, j) ∈ μ)
Goal: T i1 j < T i2 j
-- SemistandardYoungTableau.zeros
theorem zeros {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j : ℕ}
    (not_cell : (i, j) ∉ μ) : T i j = 0 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j : ℕ} (not_cell : (i, j) ∉ μ)
Goal: T i j = 0
-- SemistandardYoungTableau.row_weak_of_le
theorem row_weak_of_le {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j1 j2 : ℕ}
    (hj : j1 ≤ j2) (cell : (i, j2) ∈ μ) : T i j1 ≤ T i j2 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i j1 j2 : ℕ} (hj : j1 ≤ j2) (cell : (i, j2) ∈ μ)
Goal: T i j1 ≤ T i j2
-- SemistandardYoungTableau.col_weak
theorem col_weak {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i1 i2 j : ℕ} (hi : i1 ≤ i2)
    (cell : (i2, j) ∈ μ) : T i1 j ≤ T i2 j 
Arguments: {μ : YoungDiagram} (T : SemistandardYoungTableau μ) {i1 i2 j : ℕ} (hi : i1 ≤ i2) (cell : (i2, j) ∈ μ)
Goal: T i1 j ≤ T i2 j
-- SemistandardYoungTableau.highestWeight_apply
@[simp]
theorem highestWeight_apply {μ : YoungDiagram} {i j : ℕ} :
    highestWeight μ i j = if (i, j) ∈ μ then i else 0 
Arguments: {μ : YoungDiagram} {i j : ℕ}
Goal: (SemistandardYoungTableau.highestWeight μ) i j = if (i, j) ∈ μ then i else 0
-- Prefunctor.star_fst
@[simps]
def Prefunctor.star (u : U) : Quiver.Star u → Quiver.Star (φ.obj u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: ∀ (a : Quiver.Star u), (φ.star u a).fst = φ.obj a.fst
-- Prefunctor.star_snd
@[simps]
def Prefunctor.star (u : U) : Quiver.Star u → Quiver.Star (φ.obj u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: ∀ (a : Quiver.Star u), (φ.star u a).snd = φ.map a.snd
-- Prefunctor.costar_fst
@[simps]
def Prefunctor.costar (u : U) : Quiver.Costar u → Quiver.Costar (φ.obj u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: ∀ (a : Quiver.Costar u), (φ.costar u a).fst = φ.obj a.fst
-- Prefunctor.costar_snd
@[simps]
def Prefunctor.costar (u : U) : Quiver.Costar u → Quiver.Costar (φ.obj u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: ∀ (a : Quiver.Costar u), (φ.costar u a).snd = φ.map a.snd
-- Prefunctor.star_apply
@[simp]
theorem Prefunctor.star_apply {u v : U} (e : u ⟶ v) :
    φ.star u (Quiver.Star.mk e) = Quiver.Star.mk (φ.map e) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) {u v : U} (e : u ⟶ v)
Goal: φ.star u (Quiver.Star.mk e) = Quiver.Star.mk (φ.map e)
-- Prefunctor.costar_apply
@[simp]
theorem Prefunctor.costar_apply {u v : U} (e : u ⟶ v) :
    φ.costar v (Quiver.Costar.mk e) = Quiver.Costar.mk (φ.map e) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) {u v : U} (e : u ⟶ v)
Goal: φ.costar v (Quiver.Costar.mk e) = Quiver.Costar.mk (φ.map e)
-- Prefunctor.star_comp
theorem Prefunctor.star_comp (u : U) : (φ ⋙q ψ).star u = ψ.star (φ.obj u) ∘ φ.star u 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_3} [Quiver V] (φ : U ⥤q V) {W : Type u_2} [Quiver W] (ψ : V ⥤q W) (u : U)
Goal: (φ ⋙q ψ).star u = ψ.star (φ.obj u) ∘ φ.star u
-- Prefunctor.costar_comp
theorem Prefunctor.costar_comp (u : U) : (φ ⋙q ψ).costar u = ψ.costar (φ.obj u) ∘ φ.costar u 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_3} [Quiver V] (φ : U ⥤q V) {W : Type u_2} [Quiver W] (ψ : V ⥤q W) (u : U)
Goal: (φ ⋙q ψ).costar u = ψ.costar (φ.obj u) ∘ φ.costar u
-- Prefunctor.IsCovering.star_bijective
protected structure Prefunctor.IsCovering : Prop where
  star_bijective : ∀ u, Bijective (φ.star u)
  costar_bijective : ∀ u, Bijective (φ.costar u)
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] {φ : U ⥤q V} (self : φ.IsCovering) (u : U)
Goal: Function.Bijective (φ.star u)
-- Prefunctor.IsCovering.costar_bijective
protected structure Prefunctor.IsCovering : Prop where
  star_bijective : ∀ u, Bijective (φ.star u)
  costar_bijective : ∀ u, Bijective (φ.costar u)
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] {φ : U ⥤q V} (self : φ.IsCovering) (u : U)
Goal: Function.Bijective (φ.costar u)
-- Prefunctor.IsCovering.map_injective
@[simp]
theorem Prefunctor.IsCovering.map_injective (hφ : φ.IsCovering) {u v : U} :
    Injective fun f : u ⟶ v => φ.map f 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (hφ : φ.IsCovering) {u v : U}
Goal: Function.Injective fun f => φ.map f
-- Prefunctor.IsCovering.comp
theorem Prefunctor.IsCovering.comp (hφ : φ.IsCovering) (hψ : ψ.IsCovering) : (φ ⋙q ψ).IsCovering 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) {W : Type u_3} [Quiver W] (ψ : V ⥤q W) (hφ : φ.IsCovering) (hψ : ψ.IsCovering)
Goal: (φ ⋙q ψ).IsCovering
-- Prefunctor.IsCovering.of_comp_right
theorem Prefunctor.IsCovering.of_comp_right (hψ : ψ.IsCovering) (hφψ : (φ ⋙q ψ).IsCovering) :
    φ.IsCovering 
Arguments: {U : Type u_3} [Quiver U] {V : Type u_1} [Quiver V] (φ : U ⥤q V) {W : Type u_2} [Quiver W] (ψ : V ⥤q W) (hψ : ψ.IsCovering) (hφψ : (φ ⋙q ψ).IsCovering)
Goal: φ.IsCovering
-- Prefunctor.IsCovering.of_comp_left
theorem Prefunctor.IsCovering.of_comp_left (hφ : φ.IsCovering) (hφψ : (φ ⋙q ψ).IsCovering)
    (φsur : Surjective φ.obj) : ψ.IsCovering 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) {W : Type u_3} [Quiver W] (ψ : V ⥤q W) (hφ : φ.IsCovering) (hφψ : (φ ⋙q ψ).IsCovering) (φsur : Function.Surjective φ.obj)
Goal: ψ.IsCovering
-- Prefunctor.symmetrifyStar
theorem Prefunctor.symmetrifyStar (u : U) :
    φ.symmetrify.star u =
      (Quiver.symmetrifyStar _).symm ∘ Sum.map (φ.star u) (φ.costar u) ∘
        Quiver.symmetrifyStar u 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: φ.symmetrify.star u =
  ⇑(Quiver.symmetrifyStar (φ.obj u)).symm ∘ Sum.map (φ.star u) (φ.costar u) ∘ ⇑(Quiver.symmetrifyStar u)
-- Prefunctor.symmetrifyCostar
protected theorem Prefunctor.symmetrifyCostar (u : U) :
    φ.symmetrify.costar u =
      (Quiver.symmetrifyCostar _).symm ∘
        Sum.map (φ.costar u) (φ.star u) ∘ Quiver.symmetrifyCostar u 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (u : U)
Goal: φ.symmetrify.costar u =
  ⇑(Quiver.symmetrifyCostar (φ.obj u)).symm ∘ Sum.map (φ.costar u) (φ.star u) ∘ ⇑(Quiver.symmetrifyCostar u)
-- Prefunctor.IsCovering.symmetrify
protected theorem Prefunctor.IsCovering.symmetrify (hφ : φ.IsCovering) :
    φ.symmetrify.IsCovering 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (hφ : φ.IsCovering)
Goal: φ.symmetrify.IsCovering
-- Prefunctor.pathStar_apply
@[simp]
theorem Prefunctor.pathStar_apply {u v : U} (p : Path u v) :
    φ.pathStar u (Quiver.PathStar.mk p) = Quiver.PathStar.mk (φ.mapPath p) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) {u v : U} (p : Quiver.Path u v)
Goal: φ.pathStar u (Quiver.PathStar.mk p) = Quiver.PathStar.mk (φ.mapPath p)
-- Prefunctor.pathStar_injective
theorem Prefunctor.pathStar_injective (hφ : ∀ u, Injective (φ.star u)) (u : U) :
    Injective (φ.pathStar u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (hφ : ∀ (u : U), Function.Injective (φ.star u)) (u : U)
Goal: Function.Injective (φ.pathStar u)
-- Prefunctor.pathStar_surjective
theorem Prefunctor.pathStar_surjective (hφ : ∀ u, Surjective (φ.star u)) (u : U) :
    Surjective (φ.pathStar u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (hφ : ∀ (u : U), Function.Surjective (φ.star u)) (u : U)
Goal: Function.Surjective (φ.pathStar u)
-- Prefunctor.pathStar_bijective
theorem Prefunctor.pathStar_bijective (hφ : ∀ u, Bijective (φ.star u)) (u : U) :
    Bijective (φ.pathStar u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) (hφ : ∀ (u : U), Function.Bijective (φ.star u)) (u : U)
Goal: Function.Bijective (φ.pathStar u)
-- Prefunctor.IsCovering.pathStar_bijective
protected theorem pathStar_bijective (hφ : φ.IsCovering) (u : U) : Bijective (φ.pathStar u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] {φ : U ⥤q V} (hφ : φ.IsCovering) (u : U)
Goal: Function.Bijective (φ.pathStar u)
-- Quiver.starEquivCostar_symm_apply_fst
@[simps]
def Quiver.starEquivCostar (u : U) : Quiver.Star u ≃ Quiver.Costar u 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] (u : U) (e : Quiver.Costar u)
Goal: ((Quiver.starEquivCostar u).symm e).fst = e.fst
-- Quiver.starEquivCostar_apply_fst
@[simps]
def Quiver.starEquivCostar (u : U) : Quiver.Star u ≃ Quiver.Costar u 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] (u : U) (e : Quiver.Star u)
Goal: ((Quiver.starEquivCostar u) e).fst = e.fst
-- Quiver.starEquivCostar_apply_snd
@[simps]
def Quiver.starEquivCostar (u : U) : Quiver.Star u ≃ Quiver.Costar u 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] (u : U) (e : Quiver.Star u)
Goal: ((Quiver.starEquivCostar u) e).snd = Quiver.reverse e.snd
-- Quiver.starEquivCostar_symm_apply_snd
@[simps]
def Quiver.starEquivCostar (u : U) : Quiver.Star u ≃ Quiver.Costar u 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] (u : U) (e : Quiver.Costar u)
Goal: ((Quiver.starEquivCostar u).symm e).snd = Quiver.reverse e.snd
-- Quiver.starEquivCostar_apply
@[simp]
theorem Quiver.starEquivCostar_apply {u v : U} (e : u ⟶ v) :
    Quiver.starEquivCostar u (Quiver.Star.mk e) = Quiver.Costar.mk (reverse e) 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] {u v : U} (e : u ⟶ v)
Goal: (Quiver.starEquivCostar u) (Quiver.Star.mk e) = Quiver.Costar.mk (Quiver.reverse e)
-- Quiver.starEquivCostar_symm_apply
@[simp]
theorem Quiver.starEquivCostar_symm_apply {u v : U} (e : u ⟶ v) :
    (Quiver.starEquivCostar v).symm (Quiver.Costar.mk e) = Quiver.Star.mk (reverse e) 
Arguments: {U : Type u_1} [Quiver U] [Quiver.HasInvolutiveReverse U] {u v : U} (e : u ⟶ v)
Goal: (Quiver.starEquivCostar v).symm (Quiver.Costar.mk e) = Quiver.Star.mk (Quiver.reverse e)
-- Prefunctor.costar_conj_star
theorem Prefunctor.costar_conj_star (u : U) :
    φ.costar u = Quiver.starEquivCostar (φ.obj u) ∘ φ.star u ∘ (Quiver.starEquivCostar u).symm 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) [Quiver.HasInvolutiveReverse U] [Quiver.HasInvolutiveReverse V] [φ.MapReverse] (u : U)
Goal: φ.costar u = ⇑(Quiver.starEquivCostar (φ.obj u)) ∘ φ.star u ∘ ⇑(Quiver.starEquivCostar u).symm
-- Prefunctor.bijective_costar_iff_bijective_star
theorem Prefunctor.bijective_costar_iff_bijective_star (u : U) :
    Bijective (φ.costar u) ↔ Bijective (φ.star u) 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) [Quiver.HasInvolutiveReverse U] [Quiver.HasInvolutiveReverse V] [φ.MapReverse] (u : U)
Goal: Function.Bijective (φ.costar u) ↔ Function.Bijective (φ.star u)
-- Prefunctor.isCovering_of_bijective_star
theorem Prefunctor.isCovering_of_bijective_star (h : ∀ u, Bijective (φ.star u)) : φ.IsCovering 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) [Quiver.HasInvolutiveReverse U] [Quiver.HasInvolutiveReverse V] [φ.MapReverse] (h : ∀ (u : U), Function.Bijective (φ.star u))
Goal: φ.IsCovering
-- Prefunctor.isCovering_of_bijective_costar
theorem Prefunctor.isCovering_of_bijective_costar (h : ∀ u, Bijective (φ.costar u)) :
    φ.IsCovering 
Arguments: {U : Type u_1} [Quiver U] {V : Type u_2} [Quiver V] (φ : U ⥤q V) [Quiver.HasInvolutiveReverse U] [Quiver.HasInvolutiveReverse V] [φ.MapReverse] (h : ∀ (u : U), Function.Bijective (φ.costar u))
Goal: φ.IsCovering
-- HasStrictFDerivAt.clm_comp
@[fun_prop]
theorem HasStrictFDerivAt.clm_comp (hc : HasStrictFDerivAt c c' x) (hd : HasStrictFDerivAt d d' x) :
    HasStrictFDerivAt (fun y => (c y).comp (d y))
      ((compL 𝕜 F G H (c x)).comp d' + ((compL 𝕜 F G H).flip (d x)).comp c') x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {d : E → F →L[𝕜] G} {d' : E →L[𝕜] F →L[𝕜] G} (hc : HasStrictFDerivAt c c' x) (hd : HasStrictFDerivAt d d' x)
Goal: HasStrictFDerivAt (fun y => (c y).comp (d y))
  (((ContinuousLinearMap.compL 𝕜 F G H) (c x)).comp d' + ((ContinuousLinearMap.compL 𝕜 F G H).flip (d x)).comp c') x
-- HasFDerivWithinAt.clm_comp
@[fun_prop]
theorem HasFDerivWithinAt.clm_comp (hc : HasFDerivWithinAt c c' s x)
    (hd : HasFDerivWithinAt d d' s x) :
    HasFDerivWithinAt (fun y => (c y).comp (d y))
      ((compL 𝕜 F G H (c x)).comp d' + ((compL 𝕜 F G H).flip (d x)).comp c') s x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {s : Set E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {d : E → F →L[𝕜] G} {d' : E →L[𝕜] F →L[𝕜] G} (hc : HasFDerivWithinAt c c' s x) (hd : HasFDerivWithinAt d d' s x)
Goal: HasFDerivWithinAt (fun y => (c y).comp (d y))
  (((ContinuousLinearMap.compL 𝕜 F G H) (c x)).comp d' + ((ContinuousLinearMap.compL 𝕜 F G H).flip (d x)).comp c') s x
-- HasFDerivAt.clm_comp
@[fun_prop]
theorem HasFDerivAt.clm_comp (hc : HasFDerivAt c c' x) (hd : HasFDerivAt d d' x) :
    HasFDerivAt (fun y => (c y).comp (d y))
      ((compL 𝕜 F G H (c x)).comp d' + ((compL 𝕜 F G H).flip (d x)).comp c') x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {d : E → F →L[𝕜] G} {d' : E →L[𝕜] F →L[𝕜] G} (hc : HasFDerivAt c c' x) (hd : HasFDerivAt d d' x)
Goal: HasFDerivAt (fun y => (c y).comp (d y))
  (((ContinuousLinearMap.compL 𝕜 F G H) (c x)).comp d' + ((ContinuousLinearMap.compL 𝕜 F G H).flip (d x)).comp c') x
-- DifferentiableWithinAt.clm_comp
@[fun_prop]
theorem DifferentiableWithinAt.clm_comp (hc : DifferentiableWithinAt 𝕜 c s x)
    (hd : DifferentiableWithinAt 𝕜 d s x) :
    DifferentiableWithinAt 𝕜 (fun y => (c y).comp (d y)) s x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {s : Set E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hc : DifferentiableWithinAt 𝕜 c s x) (hd : DifferentiableWithinAt 𝕜 d s x)
Goal: DifferentiableWithinAt 𝕜 (fun y => (c y).comp (d y)) s x
-- DifferentiableAt.clm_comp
@[fun_prop]
theorem DifferentiableAt.clm_comp (hc : DifferentiableAt 𝕜 c x) (hd : DifferentiableAt 𝕜 d x) :
    DifferentiableAt 𝕜 (fun y => (c y).comp (d y)) x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hc : DifferentiableAt 𝕜 c x) (hd : DifferentiableAt 𝕜 d x)
Goal: DifferentiableAt 𝕜 (fun y => (c y).comp (d y)) x
-- DifferentiableOn.clm_comp
@[fun_prop]
theorem DifferentiableOn.clm_comp (hc : DifferentiableOn 𝕜 c s) (hd : DifferentiableOn 𝕜 d s) :
    DifferentiableOn 𝕜 (fun y => (c y).comp (d y)) s 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {s : Set E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hc : DifferentiableOn 𝕜 c s) (hd : DifferentiableOn 𝕜 d s)
Goal: DifferentiableOn 𝕜 (fun y => (c y).comp (d y)) s
-- Differentiable.clm_comp
@[fun_prop]
theorem Differentiable.clm_comp (hc : Differentiable 𝕜 c) (hd : Differentiable 𝕜 d) :
    Differentiable 𝕜 fun y => (c y).comp (d y) 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hc : Differentiable 𝕜 c) (hd : Differentiable 𝕜 d)
Goal: Differentiable 𝕜 fun y => (c y).comp (d y)
-- fderivWithin_clm_comp
theorem fderivWithin_clm_comp (hxs : UniqueDiffWithinAt 𝕜 s x) (hc : DifferentiableWithinAt 𝕜 c s x)
    (hd : DifferentiableWithinAt 𝕜 d s x) :
    fderivWithin 𝕜 (fun y => (c y).comp (d y)) s x =
      (compL 𝕜 F G H (c x)).comp (fderivWithin 𝕜 d s x) +
        ((compL 𝕜 F G H).flip (d x)).comp (fderivWithin 𝕜 c s x) 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {s : Set E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hxs : UniqueDiffWithinAt 𝕜 s x) (hc : DifferentiableWithinAt 𝕜 c s x) (hd : DifferentiableWithinAt 𝕜 d s x)
Goal: fderivWithin 𝕜 (fun y => (c y).comp (d y)) s x =
  ((ContinuousLinearMap.compL 𝕜 F G H) (c x)).comp (fderivWithin 𝕜 d s x) +
    ((ContinuousLinearMap.compL 𝕜 F G H).flip (d x)).comp (fderivWithin 𝕜 c s x)
-- fderiv_clm_comp
theorem fderiv_clm_comp (hc : DifferentiableAt 𝕜 c x) (hd : DifferentiableAt 𝕜 d x) :
    fderiv 𝕜 (fun y => (c y).comp (d y)) x =
      (compL 𝕜 F G H (c x)).comp (fderiv 𝕜 d x) +
        ((compL 𝕜 F G H).flip (d x)).comp (fderiv 𝕜 c x) 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type u_3} [NormedAddCommGroup F] [NormedSpace 𝕜 F] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {d : E → F →L[𝕜] G} (hc : DifferentiableAt 𝕜 c x) (hd : DifferentiableAt 𝕜 d x)
Goal: fderiv 𝕜 (fun y => (c y).comp (d y)) x =
  ((ContinuousLinearMap.compL 𝕜 F G H) (c x)).comp (fderiv 𝕜 d x) +
    ((ContinuousLinearMap.compL 𝕜 F G H).flip (d x)).comp (fderiv 𝕜 c x)
-- HasStrictFDerivAt.clm_apply
@[fun_prop]
theorem HasStrictFDerivAt.clm_apply (hc : HasStrictFDerivAt c c' x)
    (hu : HasStrictFDerivAt u u' x) :
    HasStrictFDerivAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {u : E → G} {u' : E →L[𝕜] G} (hc : HasStrictFDerivAt c c' x) (hu : HasStrictFDerivAt u u' x)
Goal: HasStrictFDerivAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) x
-- HasFDerivWithinAt.clm_apply
@[fun_prop]
theorem HasFDerivWithinAt.clm_apply (hc : HasFDerivWithinAt c c' s x)
    (hu : HasFDerivWithinAt u u' s x) :
    HasFDerivWithinAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) s x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {s : Set E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {u : E → G} {u' : E →L[𝕜] G} (hc : HasFDerivWithinAt c c' s x) (hu : HasFDerivWithinAt u u' s x)
Goal: HasFDerivWithinAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) s x
-- HasFDerivAt.clm_apply
@[fun_prop]
theorem HasFDerivAt.clm_apply (hc : HasFDerivAt c c' x) (hu : HasFDerivAt u u' x) :
    HasFDerivAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) x 
Arguments: {𝕜 : Type u_1} [NontriviallyNormedField 𝕜] {E : Type u_2} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {G : Type u_4} [NormedAddCommGroup G] [NormedSpace 𝕜 G] {x : E} {H : Type u_6} [NormedAddCommGroup H] [NormedSpace 𝕜 H] {c : E → G →L[𝕜] H} {c' : E →L[𝕜] G →L[𝕜] H} {u : E → G} {u' : E →L[𝕜] G} (hc : HasFDerivAt c c' x) (hu : HasFDerivAt u u' x)
Goal: HasFDerivAt (fun y => (c y) (u y)) ((c x).comp u' + c'.flip (u x)) x