def Lean.Meta.Grind.Arith.Linear.getZero : LinearM Expr

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• Lean.Meta.Grind.Arith.Linear.getZero = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.zero

def Lean.Meta.Grind.Arith.Linear.getOne : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.isCommRing : LinearM Bool

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• Lean.Meta.Grind.Arith.Linear.isCommRing = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.ringId?.isSome

def Lean.Meta.Grind.Arith.Linear.isOrderedCommRing : LinearM Bool

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def Lean.Meta.Grind.Arith.Linear.isLinearOrder : LinearM Bool

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• Lean.Meta.Grind.Arith.Linear.isLinearOrder = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.isLinearInst?.isSome

def Lean.Meta.Grind.Arith.Linear.hasNoNatZeroDivisors : LinearM Bool

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• Lean.Meta.Grind.Arith.Linear.hasNoNatZeroDivisors = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.noNatDivInst?.isSome

def Lean.Meta.Grind.Arith.Linear.getTermStructId? (e : Expr) : GoalM (Option Nat)

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• Lean.Meta.Grind.Arith.Linear.getTermStructId? e = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.get' pure (Lean.PersistentHashMap.find? __do_lift.exprToStructId { expr := e })

def Lean.Meta.Grind.Arith.Linear.setTermStructId (e : Expr) : LinearM Unit

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def Lean.Meta.Grind.Arith.Linear.getNoNatDivInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getLEInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getLTInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getLawfulOrderLTInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getIsPreorderInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getOrderedAddInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.isOrderedAdd : LinearM Bool

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• Lean.Meta.Grind.Arith.Linear.isOrderedAdd = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.orderedAddInst?.isSome

def Lean.Meta.Grind.Arith.Linear.getLtFn {m : Type → Type} [Monad m] [MonadError m] [MonadGetStruct m] : m Expr

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def Lean.Meta.Grind.Arith.Linear.getLeFn {m : Type → Type} [Monad m] [MonadError m] [MonadGetStruct m] : m Expr

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def Lean.Meta.Grind.Arith.Linear.getIsLinearOrderInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getRingInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getCommRingInst : LinearM Expr

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def Lean.Meta.Grind.Arith.Linear.getOrderedRingInst : LinearM Expr

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def Lean.Grind.Linarith.Poly.eval? (p : Poly) : Meta.Grind.Arith.Linear.LinearM (Option Rat)

Tries to evaluate the polynomial p using the partial model/assignment built so far. The result is none if the polynomial contains variables that have not been assigned.

Equations

• p.eval? = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct have a : Lean.PArray Rat := __do_lift.assignment pure (Lean.Grind.Linarith.Poly.eval?.go✝ a 0 p)

def Lean.Meta.Grind.Arith.Linear.IneqCnstr.satisfied (c : IneqCnstr) : LinearM LBool

Returns .true if c is satisfied by the current partial model, .undef if c contains unassigned variables, and .false otherwise.

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def Lean.Meta.Grind.Arith.Linear.DiseqCnstr.satisfied (c : DiseqCnstr) : LinearM LBool

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• c.satisfied = do let __discr ← c.p.eval? match __discr with | some v => pure (decide ((v != 0) = true)).toLBool | x => pure Lean.LBool.undef

def Lean.Meta.Grind.Arith.Linear.resetAssignmentFrom (x : Var) : LinearM Unit

Resets the assignment of any variable bigger or equal to x.

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def Lean.Meta.Grind.Arith.Linear.getVar (x : Var) : LinearM Expr

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• Lean.Meta.Grind.Arith.Linear.getVar x = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.vars[x]!

def Lean.Meta.Grind.Arith.Linear.inconsistent : LinearM Bool

Returns true if the linarith state is inconsistent.

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def Lean.Meta.Grind.Arith.Linear.eliminated (x : Var) : LinearM Bool

Returns true if x has been eliminated using an equality constraint.

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• Lean.Meta.Grind.Arith.Linear.eliminated x = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.elimEqs[x]!.isSome

def Lean.Meta.Grind.Arith.Linear.getOccursOf (x : Var) : LinearM VarSet

Returns occurrences of x.

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• Lean.Meta.Grind.Arith.Linear.getOccursOf x = do let __do_lift ← Lean.Meta.Grind.Arith.Linear.getStruct pure __do_lift.occurs[x]!

def Lean.Meta.Grind.Arith.Linear.addOcc (x y : Var) : LinearM Unit

Adds y as an occurrence of x. That is, x occurs in lowers[y], uppers[y], or diseqs[y].

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def Lean.Grind.Linarith.Poly.updateOccs (p : Poly) : Meta.Grind.Arith.Linear.LinearM Unit

Given p a polynomial being inserted into lowers, uppers, or diseqs, get its leading variable y, and adds y as an occurrence for the remaining variables in p.

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• (Lean.Grind.Linarith.Poly.add k x p_2).updateOccs = Lean.Grind.Linarith.Poly.updateOccs.go✝ x p_2
• p.updateOccs = Lean.throwError (Lean.toMessageData "`grind linarith` internal error, unexpected constant polynomial")

def Lean.Grind.Linarith.Poly.findVarToSubst (p : Poly) : Meta.Grind.Arith.Linear.LinearM (Option (Int × Var × Meta.Grind.Arith.Linear.EqCnstr))

Given a polynomial p, returns some (x, k, c) if p contains the monomial k*x, and x has been eliminated using the equality c.

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• Lean.Grind.Linarith.Poly.nil.findVarToSubst = pure none

def Lean.Grind.Linarith.Poly.gcdCoeffsAux : Poly → Nat → Nat

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• Lean.Grind.Linarith.Poly.nil.gcdCoeffsAux x✝ = x✝
• (Lean.Grind.Linarith.Poly.add k' v p).gcdCoeffsAux x✝ = p.gcdCoeffsAux (k'.gcd ↑x✝)

def Lean.Grind.Linarith.Poly.gcdCoeffs (p : Poly) : Nat

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• (Lean.Grind.Linarith.Poly.add k v p_2).gcdCoeffs = p_2.gcdCoeffsAux k.natAbs
• Lean.Grind.Linarith.Poly.nil.gcdCoeffs = 1

def Lean.Grind.Linarith.Poly.div (p : Poly) (k : Int) : Poly

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• (Lean.Grind.Linarith.Poly.add k_1 v p_2).div k = Lean.Grind.Linarith.Poly.add (k_1 / k) v (p_2.div k)
• Lean.Grind.Linarith.Poly.nil.div k = Lean.Grind.Linarith.Poly.nil

def Lean.Grind.Linarith.Poly.pickVarToElim? (p : Poly) : Option (Int × Var)

Selects the variable in the given linear polynomial whose coefficient has the smallest absolute value.

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• Lean.Grind.Linarith.Poly.nil.pickVarToElim? = none
• (Lean.Grind.Linarith.Poly.add k x_1 p_1).pickVarToElim? = some (Lean.Grind.Linarith.Poly.pickVarToElim?.go✝ k x_1 p_1)