funProp missing function from standard library

def Mathlib.Meta.FunProp.isOrderedSubsetOf {α : Type u_1} [Inhabited α] [DecidableEq α] (a b : Array α) : Bool

Check if a can be obtained by removing elements from b.

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def Lean.Expr.swapBVars (e : Expr) (i j : Nat) : Expr

Swaps bvars indices i and j

NOTE: the indices i and j do not correspond to the n in bvar n. Rather they behave like indices in Expr.lowerLooseBVars, Expr.liftLooseBVars, etc.

TODO: This has to have a better implementation, but I'm still beyond confused with how bvar indices work

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def Mathlib.Meta.FunProp.mkProdElem (xs : Array Lean.Expr) : Lean.MetaM Lean.Expr

For #[x₁, .., xₙ] create (x₁, .., xₙ).

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def Mathlib.Meta.FunProp.mkProdProj (x : Lean.Expr) (i n : Nat) : Lean.MetaM Lean.Expr

For (x₀, .., xₙ₋₁) return xᵢ but as a product projection.

We need to know the total size of the product to be considered.

For example for xyz : X × Y × Z

• mkProdProj xyz 1 3 returns xyz.snd.fst.
• mkProdProj xyz 1 2 returns xyz.snd.

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• Mathlib.Meta.FunProp.mkProdProj x i 0 = pure x
• Mathlib.Meta.FunProp.mkProdProj x i 1 = pure x
• Mathlib.Meta.FunProp.mkProdProj x 0 n = Lean.Meta.mkAppM `Prod.fst #[x]

def Mathlib.Meta.FunProp.mkProdSplitElem (xs : Lean.Expr) (n : Nat) : Lean.MetaM (Array Lean.Expr)

For an element of a product type (of size n) xs create an array of all possible projections i.e. #[xs.1, xs.2.1, xs.2.2.1, ..., xs.2..2]

Equations

• Mathlib.Meta.FunProp.mkProdSplitElem xs n = Array.mapM (fun (i : Nat) => Mathlib.Meta.FunProp.mkProdProj xs i n) (Array.range n)

def Mathlib.Meta.FunProp.mkUncurryFun (n : Nat) (f : Lean.Expr) : Lean.MetaM Lean.Expr

Uncurry function f in n arguments.

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def Mathlib.Meta.FunProp.etaExpand1 (f : Lean.Expr) : Lean.MetaM Lean.Expr

Eta expand f in only one variable and reduce in others.

Examples:

  f                ==> fun x => f x
  fun x y => f x y ==> fun x => f x
  HAdd.hAdd y      ==> fun x => HAdd.hAdd y x
  HAdd.hAdd        ==> fun x => HAdd.hAdd x

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def Mathlib.Meta.FunProp.betaThroughLet (f : Lean.Expr) (args : Array Lean.Expr) : Lean.Expr

Apply the given arguments to f, beta-reducing if f is a lambda expression. This variant does beta-reduction through let bindings without inlining them.

Example

beta' (fun x => let y := x * x; fun z => x + y + z) #[a,b]
==>
let y := a * a; a + y + b

Equations

• Mathlib.Meta.FunProp.betaThroughLet f args = Mathlib.Meta.FunProp.betaThroughLetAux✝ f args.toList

def Mathlib.Meta.FunProp.headBetaThroughLet (e : Lean.Expr) : Lean.Expr

Beta reduces head of an expression, (fun x => e) a ==> e[x/a]. This version applies arguments through let bindings without inlining them.

Example

headBeta' ((fun x => let y := x * x; fun z => x + y + z) a b)
==>
let y := a * a; a + y + b

Equations

• Mathlib.Meta.FunProp.headBetaThroughLet e = if Lean.Expr.isHeadBetaTargetFn true e.getAppFn = true then Mathlib.Meta.FunProp.betaThroughLet e.getAppFn e.getAppArgs else e