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          • !tlb-key->smap
          • !tlb-key->cpl
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          • 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
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• Tlb-key

!tlb-key->smap

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

Signature

(!tlb-key->smap smap x) → new-x

Arguments

smap — Guard (bitp smap).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->smap$inline

(defun !tlb-key->smap$inline (smap x)
  (declare (xargs :guard (and (bitp smap) (tlb-key-p x))))
  (mbe :logic
       (b* ((smap (mbe :logic (bfix smap) :exec smap))
            (x (tlb-key-fix x)))
         (part-install smap x :width 1 :low 2))
       :exec (the (unsigned-byte 46)
                  (logior (the (unsigned-byte 46)
                               (logand (the (unsigned-byte 46) x)
                                       (the (signed-byte 4) -5)))
                          (the (unsigned-byte 3)
                               (ash (the (unsigned-byte 1) smap)
                                    2))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !tlb-key->smap-equiv-under-mask
  (b* ((?new-x (!tlb-key->smap$inline smap x)))
    (tlb-key-equiv-under-mask new-x x -5)))