Documentation

Lean.Meta.Tactic.Grind.Arith.CommRing.Util

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      • ringId : Nat
      • checkCoeffDvd : Bool

        If checkCoeffDvd is true, then when using a polynomial k*m - p to simplify .. + k'*m*m_2 + ..., the substitution is performed IF

        • k divides k', OR
        • Ring implements NoNatZeroDivisors.

        We need this check when simplifying disequalities. In this case, if we perform the simplification anyway, we may end up with a proof that k * q = 0, but we cannot deduce q = 0 since the ring does not implement NoNatZeroDivisors See comment at PolyDerivation.

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        We don't want to keep carrying the RingId around.

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            abbrev Lean.Meta.Grind.Arith.CommRing.RingM.run {α : Type} (ringId : Nat) (x : RingM α) :
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                            Returns some c if the current ring has a nonzero characteristic c.

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                                Returns some (charInst, c) if the current ring has a nonzero characteristic c.

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                                    Returns true if the current ring satisfies the property

                                    ∀ (k : Nat) (a : α), k ≠ 0 → OfNat.ofNat (α := α) k * a = 0 → a = 0
                                    
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                                        Returns true if the current ring has a IsCharP instance.

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                                            Returns the pair (charInst, c). If the ring does not have a IsCharP instance, then throws internal error.

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                                                Converts the given ring expression into a multivariate polynomial. If the ring has a nonzero characteristic, it is used during normalization.

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