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Param

Param->partial-first-p

Get the partial-first-p field from a param.

Signature
(param->partial-first-p x) → partial-first-p
Arguments: x — Guard (paramp x).
Returns: partial-first-p — Type (booleanp partial-first-p).

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

Definitions and Theorems

Function: param->partial-first-p$inline

(defun param->partial-first-p$inline (x)
  (declare (xargs :guard (paramp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'param->partial-first-p))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::bool-fix (cdr (std::da-nth 10 x))))
         :exec (cdr (std::da-nth 10 x)))))

Theorem: booleanp-of-param->partial-first-p

(defthm booleanp-of-param->partial-first-p
  (b* ((partial-first-p (param->partial-first-p$inline x)))
    (booleanp partial-first-p))
  :rule-classes :rewrite)

Theorem: param->partial-first-p$inline-of-param-fix-x

(defthm param->partial-first-p$inline-of-param-fix-x
  (equal (param->partial-first-p$inline (param-fix x))
         (param->partial-first-p$inline x)))

Theorem: param->partial-first-p$inline-param-equiv-congruence-on-x

(defthm param->partial-first-p$inline-param-equiv-congruence-on-x
  (implies (param-equiv x x-equiv)
           (equal (param->partial-first-p$inline x)
                  (param->partial-first-p$inline x-equiv)))
  :rule-classes :congruence)