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Dirdeclor-paren

Dirdeclor-paren->inner

Get the inner field from a dirdeclor-paren.

Signature
(dirdeclor-paren->inner x) → inner
Arguments: x — Guard (dirdeclorp x).
Returns: inner — Type (declorp inner).

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

Definitions and Theorems

Function: dirdeclor-paren->inner$inline

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

Theorem: declorp-of-dirdeclor-paren->inner

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

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

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

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

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

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

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