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Constraint-equal

Constraint-equal->right

Get the right field from a constraint-equal.

Signature
(constraint-equal->right x) → right
Arguments: x — Guard (constraintp x).
Returns: right — Type (expressionp right).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: constraint-equal->right$inline

(defun constraint-equal->right$inline (x)
  (declare (xargs :guard (constraintp x)))
  (declare (xargs :guard (equal (constraint-kind x) :equal)))
  (let ((__function__ 'constraint-equal->right))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and (equal (constraint-kind x) :equal)
                      x)))
           (expression-fix (std::da-nth 1 (cdr x))))
         :exec (std::da-nth 1 (cdr x)))))

Theorem: expressionp-of-constraint-equal->right

(defthm expressionp-of-constraint-equal->right
  (b* ((right (constraint-equal->right$inline x)))
    (expressionp right))
  :rule-classes :rewrite)

Theorem: constraint-equal->right$inline-of-constraint-fix-x

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

Theorem: constraint-equal->right$inline-constraint-equiv-congruence-on-x

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

Theorem: constraint-equal->right-when-wrong-kind

(defthm constraint-equal->right-when-wrong-kind
  (implies (not (equal (constraint-kind x) :equal))
           (equal (constraint-equal->right x)
                  (expression-fix nil))))