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• Amb?-declor/absdeclor-declor

Amb?-declor/absdeclor-declor->declor

Get the declor field from a amb?-declor/absdeclor-declor.

Signature

(amb?-declor/absdeclor-declor->declor x) → declor

Arguments

x — Guard (amb?-declor/absdeclor-p x).

Returns

declor — Type (declorp declor).

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

Definitions and Theorems

Function: amb?-declor/absdeclor-declor->declor$inline

(defun amb?-declor/absdeclor-declor->declor$inline (x)
  (declare (xargs :guard (amb?-declor/absdeclor-p x)))
  (declare (xargs :guard (equal (amb?-declor/absdeclor-kind x)
                                :declor)))
  (mbe :logic
       (b* ((x (and (equal (amb?-declor/absdeclor-kind x)
                           :declor)
                    x)))
         (declor-fix (cdr x)))
       :exec (cdr x)))

Theorem: declorp-of-amb?-declor/absdeclor-declor->declor

(defthm declorp-of-amb?-declor/absdeclor-declor->declor
  (b* ((declor (amb?-declor/absdeclor-declor->declor$inline x)))
    (declorp declor))
  :rule-classes :rewrite)

Theorem: amb?-declor/absdeclor-declor->declor$inline-of-amb?-declor/absdeclor-fix-x

(defthm
 amb?-declor/absdeclor-declor->declor$inline-of-amb?-declor/absdeclor-fix-x
 (equal (amb?-declor/absdeclor-declor->declor$inline
             (amb?-declor/absdeclor-fix x))
        (amb?-declor/absdeclor-declor->declor$inline x)))

Theorem: amb?-declor/absdeclor-declor->declor$inline-amb?-declor/absdeclor-equiv-congruence-on-x

(defthm
 amb?-declor/absdeclor-declor->declor$inline-amb?-declor/absdeclor-equiv-congruence-on-x
 (implies
      (amb?-declor/absdeclor-equiv x x-equiv)
      (equal (amb?-declor/absdeclor-declor->declor$inline x)
             (amb?-declor/absdeclor-declor->declor$inline x-equiv)))
 :rule-classes :congruence)

Theorem: amb?-declor/absdeclor-declor->declor-when-wrong-kind

(defthm amb?-declor/absdeclor-declor->declor-when-wrong-kind
  (implies (not (equal (amb?-declor/absdeclor-kind x)
                       :declor))
           (equal (amb?-declor/absdeclor-declor->declor x)
                  (declor-fix nil))))