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Param

Param->prime

Get the prime field from a param.

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

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

Definitions and Theorems

Function: param->prime$inline

(defun param->prime$inline (x)
  (declare (xargs :guard (paramp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'param->prime))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((x (and t x)))
           (prime-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: primep-of-param->prime

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

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

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

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

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