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Lhs.lisp

Lhrange-nextbit

Signature
(lhrange-nextbit x) → next
Arguments: x — Guard (lhrange-p x).
Returns: next — Type (lhatom-p next).

Definitions and Theorems

Function: lhrange-nextbit

(defun lhrange-nextbit (x)
 (declare (xargs :guard (lhrange-p x)))
 "returns an atom representing the next bit of the range's atom after the range ends."
 (let ((__function__ 'lhrange-nextbit))
   (declare (ignorable __function__))
   (b* (((lhrange x) x)
        (xkind (lhatom-kind x.atom))
        ((when (eq xkind :z)) (lhatom-z))
        ((lhatom-var x.atom) x.atom))
     (lhatom-var x.atom.name (+ x.w x.atom.rsh)))))

Theorem: lhatom-p-of-lhrange-nextbit

(defthm lhatom-p-of-lhrange-nextbit
  (b* ((next (lhrange-nextbit x)))
    (lhatom-p next))
  :rule-classes :rewrite)

Theorem: lhrange-nextbit-of-lhrange-fix-x

(defthm lhrange-nextbit-of-lhrange-fix-x
  (equal (lhrange-nextbit (lhrange-fix x))
         (lhrange-nextbit x)))

Theorem: lhrange-nextbit-lhrange-equiv-congruence-on-x

(defthm lhrange-nextbit-lhrange-equiv-congruence-on-x
  (implies (lhrange-equiv x x-equiv)
           (equal (lhrange-nextbit x)
                  (lhrange-nextbit x-equiv)))
  :rule-classes :congruence)

Theorem: lhrange-nextbit-when-z

(defthm lhrange-nextbit-when-z
  (implies (equal (lhatom-kind (lhrange->atom x))
                  :z)
           (equal (lhrange-nextbit x) (lhatom-z))))

Theorem: lhrange-nextbit-when-var

(defthm lhrange-nextbit-when-var
  (implies (equal (lhatom-kind (lhrange->atom x))
                  :var)
           (equal (lhrange-nextbit x)
                  (lhatom-var (lhatom-var->name (lhrange->atom x))
                              (+ (lhatom-var->rsh (lhrange->atom x))
                                 (lhrange->w x))))))