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Dirabsdeclor-paren

Dirabsdeclor-paren->inner

Get the inner field from a dirabsdeclor-paren.

Signature
(dirabsdeclor-paren->inner x) → inner
Arguments: x — Guard (dirabsdeclorp x).
Returns: inner — Type (absdeclorp inner).

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

Definitions and Theorems

Function: dirabsdeclor-paren->inner$inline

(defun dirabsdeclor-paren->inner$inline (x)
  (declare (xargs :guard (dirabsdeclorp x)))
  (declare (xargs :guard (equal (dirabsdeclor-kind x) :paren)))
  (mbe :logic
       (b* ((x (and (equal (dirabsdeclor-kind x) :paren)
                    x)))
         (absdeclor-fix (cdr x)))
       :exec (cdr x)))

Theorem: absdeclorp-of-dirabsdeclor-paren->inner

(defthm absdeclorp-of-dirabsdeclor-paren->inner
  (b* ((inner (dirabsdeclor-paren->inner$inline x)))
    (absdeclorp inner))
  :rule-classes :rewrite)

Theorem: dirabsdeclor-paren->inner$inline-of-dirabsdeclor-fix-x

(defthm dirabsdeclor-paren->inner$inline-of-dirabsdeclor-fix-x
  (equal (dirabsdeclor-paren->inner$inline (dirabsdeclor-fix x))
         (dirabsdeclor-paren->inner$inline x)))

Theorem: dirabsdeclor-paren->inner$inline-dirabsdeclor-equiv-congruence-on-x

(defthm
 dirabsdeclor-paren->inner$inline-dirabsdeclor-equiv-congruence-on-x
 (implies (dirabsdeclor-equiv x x-equiv)
          (equal (dirabsdeclor-paren->inner$inline x)
                 (dirabsdeclor-paren->inner$inline x-equiv)))
 :rule-classes :congruence)

Theorem: dirabsdeclor-paren->inner-when-wrong-kind

(defthm dirabsdeclor-paren->inner-when-wrong-kind
  (implies (not (equal (dirabsdeclor-kind x) :paren))
           (equal (dirabsdeclor-paren->inner x)
                  (absdeclor-fix nil))))