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Lhprobe-constraint

Lhprobe-constraint->lhprobe

Get the lhprobe field from a lhprobe-constraint.

Signature
(lhprobe-constraint->lhprobe x) → lhprobe
Arguments: x — Guard (lhprobe-constraint-p x).
Returns: lhprobe — Type (lhprobe-p lhprobe).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: lhprobe-constraint->lhprobe$inline

(defun lhprobe-constraint->lhprobe$inline (x)
  (declare (xargs :guard (lhprobe-constraint-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'lhprobe-constraint->lhprobe))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (lhprobe-fix (car x)))
         :exec (car x))))

Theorem: lhprobe-p-of-lhprobe-constraint->lhprobe

(defthm lhprobe-p-of-lhprobe-constraint->lhprobe
  (b* ((lhprobe (lhprobe-constraint->lhprobe$inline x)))
    (lhprobe-p lhprobe))
  :rule-classes :rewrite)

Theorem: lhprobe-constraint->lhprobe$inline-of-lhprobe-constraint-fix-x

(defthm
     lhprobe-constraint->lhprobe$inline-of-lhprobe-constraint-fix-x
 (equal
     (lhprobe-constraint->lhprobe$inline (lhprobe-constraint-fix x))
     (lhprobe-constraint->lhprobe$inline x)))

Theorem: lhprobe-constraint->lhprobe$inline-lhprobe-constraint-equiv-congruence-on-x

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