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Bexp-less

Bexp-less->left

Get the left field from a bexp-less.

Signature
(bexp-less->left x) → left
Arguments: x — Guard (bexpp x).
Returns: left — Type (aexpp left).

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

Definitions and Theorems

Function: bexp-less->left$inline

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

Theorem: aexpp-of-bexp-less->left

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

Theorem: bexp-less->left$inline-of-bexp-fix-x

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

Theorem: bexp-less->left$inline-bexp-equiv-congruence-on-x

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

Theorem: bexp-less->left-when-wrong-kind

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