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Param

Param->rate

Get the rate field from a param.

Signature
(param->rate x) → rate
Arguments: x — Guard (paramp x).
Returns: rate — Type (posp rate).

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

Definitions and Theorems

Function: param->rate$inline

(defun param->rate$inline (x)
  (declare (xargs :guard (paramp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'param->rate))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (acl2::pos-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: posp-of-param->rate

(defthm posp-of-param->rate
  (b* ((rate (param->rate$inline x)))
    (posp rate))
  :rule-classes :rewrite)

Theorem: param->rate$inline-of-param-fix-x

(defthm param->rate$inline-of-param-fix-x
  (equal (param->rate$inline (param-fix x))
         (param->rate$inline x)))

Theorem: param->rate$inline-param-equiv-congruence-on-x

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