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3col4vecline

3col4vecline->val2

Get the val2 field from a 3col4vecline.

Signature
(3col4vecline->val2 x) → val2
Arguments: x — Guard (3col4vecline-p x).
Returns: val2 — Type (maybe-4vec-p val2).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: 3col4vecline->val2$inline

(defun 3col4vecline->val2$inline (x)
  (declare (xargs :guard (3col4vecline-p x)))
  (declare (xargs :guard t))
  (let ((__function__ '3col4vecline->val2))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (maybe-4vec-fix (std::prod-cdr (std::prod-cdr x))))
         :exec (std::prod-cdr (std::prod-cdr x)))))

Theorem: maybe-4vec-p-of-3col4vecline->val2

(defthm maybe-4vec-p-of-3col4vecline->val2
  (b* ((val2 (3col4vecline->val2$inline x)))
    (maybe-4vec-p val2))
  :rule-classes :rewrite)

Theorem: 3col4vecline->val2$inline-of-3col4vecline-fix-x

(defthm 3col4vecline->val2$inline-of-3col4vecline-fix-x
  (equal (3col4vecline->val2$inline (3col4vecline-fix x))
         (3col4vecline->val2$inline x)))

Theorem: 3col4vecline->val2$inline-3col4vecline-equiv-congruence-on-x

(defthm 3col4vecline->val2$inline-3col4vecline-equiv-congruence-on-x
  (implies (3col4vecline-equiv x x-equiv)
           (equal (3col4vecline->val2$inline x)
                  (3col4vecline->val2$inline x-equiv)))
  :rule-classes :congruence)