		Search-engine friendly clone of the ACL2 documentation.

Cr0bits

!cr0bits->pg

Update the |X86ISA|::|PG| field of a cr0bits bit structure.

Signature
(!cr0bits->pg pg x) → new-x
Arguments: pg — Guard (bitp pg).; x — Guard (cr0bits-p x).
Returns: new-x — Type (cr0bits-p new-x).

Definitions and Theorems

Function: !cr0bits->pg$inline

(defun !cr0bits->pg$inline (pg x)
 (declare (xargs :guard (and (bitp pg) (cr0bits-p x))))
 (mbe :logic
      (b* ((pg (mbe :logic (bfix pg) :exec pg))
           (x (cr0bits-fix x)))
        (part-install pg x :width 1 :low 31))
      :exec
      (the (unsigned-byte 32)
           (logior (the (unsigned-byte 32)
                        (logand (the (unsigned-byte 32) x)
                                (the (signed-byte 33) -2147483649)))
                   (the (unsigned-byte 32)
                        (ash (the (unsigned-byte 1) pg) 31))))))

Theorem: cr0bits-p-of-!cr0bits->pg

(defthm cr0bits-p-of-!cr0bits->pg
  (b* ((new-x (!cr0bits->pg$inline pg x)))
    (cr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr0bits->pg$inline-of-bfix-pg

(defthm !cr0bits->pg$inline-of-bfix-pg
  (equal (!cr0bits->pg$inline (bfix pg) x)
         (!cr0bits->pg$inline pg x)))

Theorem: !cr0bits->pg$inline-bit-equiv-congruence-on-pg

(defthm !cr0bits->pg$inline-bit-equiv-congruence-on-pg
  (implies (bit-equiv pg pg-equiv)
           (equal (!cr0bits->pg$inline pg x)
                  (!cr0bits->pg$inline pg-equiv x)))
  :rule-classes :congruence)

Theorem: !cr0bits->pg$inline-of-cr0bits-fix-x

(defthm !cr0bits->pg$inline-of-cr0bits-fix-x
  (equal (!cr0bits->pg$inline pg (cr0bits-fix x))
         (!cr0bits->pg$inline pg x)))

Theorem: !cr0bits->pg$inline-cr0bits-equiv-congruence-on-x

(defthm !cr0bits->pg$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (!cr0bits->pg$inline pg x)
                  (!cr0bits->pg$inline pg x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->pg-is-cr0bits

(defthm !cr0bits->pg-is-cr0bits
  (equal (!cr0bits->pg pg x)
         (change-cr0bits x :pg pg)))

Theorem: cr0bits->pg-of-!cr0bits->pg

(defthm cr0bits->pg-of-!cr0bits->pg
  (b* ((?new-x (!cr0bits->pg$inline pg x)))
    (equal (cr0bits->pg new-x) (bfix pg))))

Theorem: !cr0bits->pg-equiv-under-mask

(defthm !cr0bits->pg-equiv-under-mask
  (b* ((?new-x (!cr0bits->pg$inline pg x)))
    (cr0bits-equiv-under-mask new-x x 2147483647)))