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Constraint-equal

Constraint-equal->left

Get the left field from a constraint-equal.

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

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

Definitions and Theorems

Function: constraint-equal->left$inline

(defun
    constraint-equal->left$inline (x)
    (declare (xargs :guard (constraintp x)))
    (declare (xargs :guard (equal (constraint-kind x) :equal)))
    (let ((__function__ 'constraint-equal->left))
         (declare (ignorable __function__))
         (mbe :logic (b* ((x (and (equal (constraint-kind x) :equal)
                                  x)))
                         (expression-fix (std::da-nth 0 (cdr x))))
              :exec (std::da-nth 0 (cdr x)))))

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

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

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

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

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

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

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

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