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          • !tlb-key->cpl
          • !tlb-key->nxe
          • Tlb-key->implicit-supervisor-access
          • !tlb-key->wp
          • !tlb-key->ac
          • Tlb-key->vpn
          • Tlb-key->smep
          • Tlb-key->smap
          • Tlb-key->r-w-x
          • Tlb-key->cpl
          • Tlb-key-fix
          • Tlb-key->wp
          • Tlb-key->nxe
          • Tlb-key->ac
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• Tlb-key

!tlb-key->nxe

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

Signature

(!tlb-key->nxe nxe x) → new-x

Arguments

nxe — Guard (bitp nxe).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->nxe$inline

(defun !tlb-key->nxe$inline (nxe x)
 (declare (xargs :guard (and (bitp nxe) (tlb-key-p x))))
 (mbe
    :logic
    (b* ((nxe (mbe :logic (bfix nxe) :exec nxe))
         (x (tlb-key-fix x)))
      (part-install nxe x :width 1 :low 4))
    :exec (the (unsigned-byte 46)
               (logior (the (unsigned-byte 46)
                            (logand (the (unsigned-byte 46) x)
                                    (the (signed-byte 6) -17)))
                       (the (unsigned-byte 5)
                            (ash (the (unsigned-byte 1) nxe) 4))))))

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

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

Theorem: !tlb-key->nxe$inline-of-bfix-nxe

(defthm !tlb-key->nxe$inline-of-bfix-nxe
  (equal (!tlb-key->nxe$inline (bfix nxe) x)
         (!tlb-key->nxe$inline nxe x)))

Theorem: !tlb-key->nxe$inline-bit-equiv-congruence-on-nxe

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

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

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

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

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

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

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

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

(defthm tlb-key->nxe-of-!tlb-key->nxe
  (b* ((?new-x (!tlb-key->nxe$inline nxe x)))
    (equal (tlb-key->nxe new-x)
           (bfix nxe))))

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

(defthm !tlb-key->nxe-equiv-under-mask
  (b* ((?new-x (!tlb-key->nxe$inline nxe x)))
    (tlb-key-equiv-under-mask new-x x -17)))