def Lean.Meta.Grind.Arith.isNatType (e : Expr) : Bool

Returns true if e is of the form Nat

def Lean.Meta.Grind.Arith.isIntType (e : Expr) : Bool

Returns true if e is of the form Int

def Lean.Meta.Grind.Arith.isInstAddNat (e : Expr) : Bool

Returns true if e is of the form @instHAdd Nat instAddNat

def Lean.Meta.Grind.Arith.isInstLENat (e : Expr) : Bool

Returns true if e is instLENat

def Lean.Meta.Grind.Arith.isNatAdd? (e : Expr) : Option (Expr × Expr)

Returns some (a, b) if e is of the form

@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) a b

def Lean.Meta.Grind.Arith.isNatAdd (e : Expr) : Bool

Returns true if e is of the form

@HAdd.hAdd Nat Nat Nat (instHAdd Nat instAddNat) _ _

def Lean.Meta.Grind.Arith.isNatNum? (e : Expr) : Option Nat

Returns some k if e @OfNat.ofNat Nat _ (instOfNatNat k)

def Lean.Meta.Grind.Arith.isSupportedType (e : Expr) : Bool

partial def Lean.Meta.Grind.Arith.isRelevantPred (e : Expr) : Bool

def Lean.Meta.Grind.Arith.isArithTerm (e : Expr) : Bool

def Lean.Meta.Grind.Arith.quoteIfArithTerm (e : Expr) : MessageData

Quote e using 「 and 」 if e is an arithmetic term that is being treated as a variable.

partial def Lean.Meta.Grind.Arith.gcdExt (a b : Int) : Int × Int × Int

gcdExt a b returns the triple (g, α, β) such that

• g = gcd a b (with g ≥ 0), and
• g = α * a + β * b.

partial def Lean.Meta.Grind.Arith.shrink (a : PArray Std.Internal.Rat) (sz : Nat) : PArray Std.Internal.Rat

def Lean.Meta.Grind.Arith.resize (a : PArray Std.Internal.Rat) (sz : Nat) : PArray Std.Internal.Rat

partial def Lean.Meta.Grind.Arith.resize.go (sz : Nat) (a : PArray Std.Internal.Rat) : PArray Std.Internal.Rat

Helper monad for collecting decision variables in linarith and cutsat

structure Lean.Meta.Grind.Arith.CollectDecVars.State : Type

• visited : Std.HashSet UInt64
• found : FVarIdSet

@[reducible, inline]

abbrev Lean.Meta.Grind.Arith.CollectDecVars.CollectDecVarsM (α : Type) : Type

def Lean.Meta.Grind.Arith.CollectDecVars.alreadyVisited {α : Type u_1} (c : α) : CollectDecVarsM Bool

def Lean.Meta.Grind.Arith.CollectDecVars.markAsFound (fvarId : FVarId) : CollectDecVarsM Unit

@[reducible, inline]

abbrev Lean.Meta.Grind.Arith.CollectDecVars.CollectDecVarsM.run (x : CollectDecVarsM Unit) (decVars : FVarIdSet) : FVarIdSet

def Lean.Meta.Grind.Arith.getIntModuleVirtualParent : Expr

Return auxiliary expression used as "virtual" parent when internalizing auxiliary expressions created by toIntModuleExpr. The function toIntModuleExpr converts a CommRing polynomial into a IntModule expression. We don't want this auxiliary expression to be internalized by the CommRing module since it uses a nonstandard encoding with @HMul.hMul Int α α, a virtual One.one constant, etc.

def Lean.Meta.Grind.Arith.isIntModuleVirtualParent (parent? : Option Expr) : Bool

def Lean.Meta.Grind.Arith.getIsCharInst? (u : Level) (type semiringInst : Expr) : MetaM (Option (Expr × Nat))

def Lean.Meta.Grind.Arith.getNoZeroDivInst? (u : Level) (type : Expr) : MetaM (Option Expr)

@[specialize #[]]

def Lean.Meta.Grind.Arith.split {α : Type u_1} (cs : PArray α) (getCoeff : α → Int) : PArray α × Array (Int × α)