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• Tlb-key

!tlb-key->cpl

Update the |X86ISA|::|CPL| field of a tlb-key bit structure.

Signature

(!tlb-key->cpl cpl x) → new-x

Arguments

cpl — Guard (2bits-p cpl).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->cpl$inline

(defun !tlb-key->cpl$inline (cpl x)
 (declare (xargs :guard (and (2bits-p cpl) (tlb-key-p x))))
 (mbe
    :logic
    (b* ((cpl (mbe :logic (2bits-fix cpl) :exec cpl))
         (x (tlb-key-fix x)))
      (part-install cpl x :width 2 :low 8))
    :exec (the (unsigned-byte 46)
               (logior (the (unsigned-byte 46)
                            (logand (the (unsigned-byte 46) x)
                                    (the (signed-byte 11) -769)))
                       (the (unsigned-byte 10)
                            (ash (the (unsigned-byte 2) cpl) 8))))))

Theorem: tlb-key-p-of-!tlb-key->cpl

(defthm tlb-key-p-of-!tlb-key->cpl
  (b* ((new-x (!tlb-key->cpl$inline cpl x)))
    (tlb-key-p new-x))
  :rule-classes :rewrite)

Theorem: !tlb-key->cpl$inline-of-2bits-fix-cpl

(defthm !tlb-key->cpl$inline-of-2bits-fix-cpl
  (equal (!tlb-key->cpl$inline (2bits-fix cpl) x)
         (!tlb-key->cpl$inline cpl x)))

Theorem: !tlb-key->cpl$inline-2bits-equiv-congruence-on-cpl

(defthm !tlb-key->cpl$inline-2bits-equiv-congruence-on-cpl
  (implies (2bits-equiv cpl cpl-equiv)
           (equal (!tlb-key->cpl$inline cpl x)
                  (!tlb-key->cpl$inline cpl-equiv x)))
  :rule-classes :congruence)

Theorem: !tlb-key->cpl$inline-of-tlb-key-fix-x

(defthm !tlb-key->cpl$inline-of-tlb-key-fix-x
  (equal (!tlb-key->cpl$inline cpl (tlb-key-fix x))
         (!tlb-key->cpl$inline cpl x)))

Theorem: !tlb-key->cpl$inline-tlb-key-equiv-congruence-on-x

(defthm !tlb-key->cpl$inline-tlb-key-equiv-congruence-on-x
  (implies (tlb-key-equiv x x-equiv)
           (equal (!tlb-key->cpl$inline cpl x)
                  (!tlb-key->cpl$inline cpl x-equiv)))
  :rule-classes :congruence)

Theorem: !tlb-key->cpl-is-tlb-key

(defthm !tlb-key->cpl-is-tlb-key
  (equal (!tlb-key->cpl cpl x)
         (change-tlb-key x :cpl cpl)))

Theorem: tlb-key->cpl-of-!tlb-key->cpl

(defthm tlb-key->cpl-of-!tlb-key->cpl
  (b* ((?new-x (!tlb-key->cpl$inline cpl x)))
    (equal (tlb-key->cpl new-x)
           (2bits-fix cpl))))

Theorem: !tlb-key->cpl-equiv-under-mask

(defthm !tlb-key->cpl-equiv-under-mask
  (b* ((?new-x (!tlb-key->cpl$inline cpl x)))
    (tlb-key-equiv-under-mask new-x x -769)))