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Constraint

Constraint->cond

Get the cond field from a constraint.

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

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: constraint->cond$inline

(defun constraint->cond$inline (x)
  (declare (xargs :guard (constraint-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'constraint->cond))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (svex-fix (std::prod-cdr x)))
         :exec (std::prod-cdr x))))

Theorem: svex-p-of-constraint->cond

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

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

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

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

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