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Pos-option-some

Pos-option-some->val

Get the fty::val field from a pos-option-some.

Signature
(pos-option-some->val x) → fty::val
Arguments: x — Guard (pos-optionp x).
Returns: fty::val — Type (posp fty::val).

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

Definitions and Theorems

Function: pos-option-some->val$inline

(defun pos-option-some->val$inline (x)
  (declare (xargs :guard (pos-optionp x)))
  (declare (xargs :guard x))
  (let ((__function__ 'pos-option-some->val))
    (declare (ignorable __function__))
    (mbe :logic (b* ((x (and x x))) (pos-fix x))
         :exec x)))

Theorem: posp-of-pos-option-some->val

(defthm posp-of-pos-option-some->val
  (b* ((fty::val (pos-option-some->val$inline x)))
    (posp fty::val))
  :rule-classes :rewrite)

Theorem: pos-option-some->val$inline-of-pos-option-fix-x

(defthm pos-option-some->val$inline-of-pos-option-fix-x
  (equal (pos-option-some->val$inline (pos-option-fix x))
         (pos-option-some->val$inline x)))

Theorem: pos-option-some->val$inline-pos-option-equiv-congruence-on-x

(defthm pos-option-some->val$inline-pos-option-equiv-congruence-on-x
  (implies (pos-option-equiv x x-equiv)
           (equal (pos-option-some->val$inline x)
                  (pos-option-some->val$inline x-equiv)))
  :rule-classes :congruence)

Theorem: pos-option-some->val-when-wrong-kind

(defthm pos-option-some->val-when-wrong-kind
  (implies (not x)
           (equal (pos-option-some->val x)
                  (pos-fix nil))))