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Lhrange

Lhrange->atom

Get the atom field from a lhrange.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhrange->atom$inline

(defun lhrange->atom$inline (x)
  (declare (xargs :guard (lhrange-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'lhrange->atom))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (lhatom-fix (if (and (consp x) (integerp (car x)))
                           (cdr x)
                         x)))
         :exec
         (if (and (consp x) (integerp (car x)))
             (cdr x)
           x))))

Theorem: lhatom-p-of-lhrange->atom

(defthm lhatom-p-of-lhrange->atom
  (b* ((atom (lhrange->atom$inline x)))
    (lhatom-p atom))
  :rule-classes :rewrite)

Theorem: lhrange->atom$inline-of-lhrange-fix-x

(defthm lhrange->atom$inline-of-lhrange-fix-x
  (equal (lhrange->atom$inline (lhrange-fix x))
         (lhrange->atom$inline x)))

Theorem: lhrange->atom$inline-lhrange-equiv-congruence-on-x

(defthm lhrange->atom$inline-lhrange-equiv-congruence-on-x
  (implies (lhrange-equiv x x-equiv)
           (equal (lhrange->atom$inline x)
                  (lhrange->atom$inline x-equiv)))
  :rule-classes :congruence)