File: Mathlib/Geometry/Manifold/ContMDiffMap.lean

full_name: ContMDiffMap
code: /-- Bundled `n` times continuously differentiable maps. -/
def ContMDiffMap 
goal: Type (max 0 u_6 u_7)

full_name: SmoothMap
code: /-- Bundled smooth maps. -/
abbrev SmoothMap 
goal: Type (max 0 u_6 u_7)

full_name: Manifold.«_aux_Mathlib_Geometry_Manifold_ContMDiffMap___macroRules_Manifold_termC^_⟮_,_;_,_⟯_1»
code: @[inherit_doc]
scoped[Manifold] notation "C^" n "⟮" I ", " M "; " I' ", " M' "⟯" => ContMDiffMap I I' M M' n
goal: Lean.Macro

full_name: Manifold._aux_Mathlib_Geometry_Manifold_ContMDiffMap___unexpand_ContMDiffMap_1
code: @[inherit_doc]
scoped[Manifold] notation "C^" n "⟮" I ", " M "; " I' ", " M' "⟯" => ContMDiffMap I I' M M' n
goal: Lean.PrettyPrinter.Unexpander

full_name: Manifold.«_aux_Mathlib_Geometry_Manifold_ContMDiffMap___macroRules_Manifold_termC^_⟮_,_;_⟯_1»
code: @[inherit_doc]
scoped[Manifold]
  notation "C^" n "⟮" I ", " M "; " k "⟯" => ContMDiffMap I (modelWithCornersSelf k k) M k n
goal: Lean.Macro

full_name: ContMDiffMap.instFunLike
code: instance instFunLike : FunLike C^n⟮I, M; I', M'⟯ M M' 
goal: FunLike C^n⟮I, M; I', M'⟯ M M'

full_name: ContMDiffMap.contMDiff
code: protected theorem contMDiff (f : C^n⟮I, M; I', M'⟯) : ContMDiff I I' n f 
goal: ContMDiff I I' n ⇑f

full_name: ContMDiffMap.smooth
code: protected theorem smooth (f : C^∞⟮I, M; I', M'⟯) : Smooth I I' f 
goal: Smooth I I' ⇑f

full_name: ContMDiffMap.coeFn_mk
code: @[simp]
theorem coeFn_mk (f : M → M') (hf : ContMDiff I I' n f) :
    DFunLike.coe (F := C^n⟮I, M; I', M'⟯) ⟨f, hf⟩ = f 
goal: ⇑⟨f, hf⟩ = f

full_name: ContMDiffMap.coe_injective
code: theorem coe_injective ⦃f g : C^n⟮I, M; I', M'⟯⦄ (h : (f : M → M') = g) : f = g 
goal: f = g

full_name: ContMDiffMap.ext
code: @[ext]
theorem ext (h : ∀ x, f x = g x) : f = g 
goal: f = g

full_name: ContMDiffMap.instContinuousMapClass
code: instance : ContinuousMapClass C^n⟮I, M; I', M'⟯ M M' 
goal: ContinuousMapClass C^n⟮I, M; I', M'⟯ M M'

full_name: ContMDiffMap.id
code: /-- The identity as a smooth map. -/
nonrec def id : C^n⟮I, M; I, M⟯ 
goal: C^n⟮I, M; I, M⟯

full_name: ContMDiffMap.comp
code: /-- The composition of smooth maps, as a smooth map. -/
def comp (f : C^n⟮I', M'; I'', M''⟯) (g : C^n⟮I, M; I', M'⟯) : C^n⟮I, M; I'', M''⟯ 
goal: C^n⟮I, M; I'', M''⟯

full_name: ContMDiffMap.comp_apply
code: @[simp]
theorem comp_apply (f : C^n⟮I', M'; I'', M''⟯) (g : C^n⟮I, M; I', M'⟯) (x : M) :
    f.comp g x = f (g x) 
goal: (f.comp g) x = f (g x)

full_name: ContMDiffMap.instInhabited
code: instance [Inhabited M'] : Inhabited C^n⟮I, M; I', M'⟯ 
goal: Inhabited C^n⟮I, M; I', M'⟯

full_name: ContMDiffMap.const
code: /-- Constant map as a smooth map -/
def const (y : M') : C^n⟮I, M; I', M'⟯ 
goal: C^n⟮I, M; I', M'⟯

full_name: ContMDiffMap.fst
code: /-- The first projection of a product, as a smooth map. -/
def fst : C^n⟮I.prod I', M × M'; I, M⟯ 
goal: C^n⟮I.prod I', M × M'; I, M⟯

full_name: ContMDiffMap.snd
code: /-- The second projection of a product, as a smooth map. -/
def snd : C^n⟮I.prod I', M × M'; I', M'⟯ 
goal: C^n⟮I.prod I', M × M'; I', M'⟯

full_name: ContMDiffMap.prodMk
code: /-- Given two smooth maps `f` and `g`, this is the smooth map `x ↦ (f x, g x)`. -/
def prodMk (f : C^n⟮J, N; I, M⟯) (g : C^n⟮J, N; I', M'⟯) : C^n⟮J, N; I.prod I', M × M'⟯ 
goal: C^n⟮J, N; I.prod I', M × M'⟯

full_name: ContinuousLinearMap.hasCoeToContMDiffMap
code: instance ContinuousLinearMap.hasCoeToContMDiffMap :
    Coe (E →L[𝕜] E') C^n⟮𝓘(𝕜, E), E; 𝓘(𝕜, E'), E'⟯ 
goal: Coe (E →L[𝕜] E') C^n⟮𝓘(𝕜, E), E; 𝓘(𝕜, E'), E'⟯