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Aexp-mul

Aexp-mul->left

Get the left field from a aexp-mul.

Signature
(aexp-mul->left x) → left
Arguments: x — Guard (aexpp x).
Returns: left — Type (aexpp left).

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

Definitions and Theorems

Function: aexp-mul->left$inline

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

Theorem: aexpp-of-aexp-mul->left

(defthm aexpp-of-aexp-mul->left
  (b* ((left (aexp-mul->left$inline x)))
    (aexpp left))
  :rule-classes :rewrite)

Theorem: aexp-mul->left$inline-of-aexp-fix-x

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

Theorem: aexp-mul->left$inline-aexp-equiv-congruence-on-x

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

Theorem: aexp-mul->left-when-wrong-kind

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